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diff --git a/old/53172-0.txt b/old/53172-0.txt deleted file mode 100644 index 271e87d..0000000 --- a/old/53172-0.txt +++ /dev/null @@ -1,14190 +0,0 @@ -Project Gutenberg's Stargazing: Past and Present, by J. Norman Lockyer - -This eBook is for the use of anyone anywhere in the United States and most -other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms of -the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you'll have -to check the laws of the country where you are located before using this ebook. - -Title: Stargazing: Past and Present - -Author: J. Norman Lockyer - -Release Date: September 30, 2016 [EBook #53172] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK STARGAZING: PAST AND PRESENT *** - - - - -Produced by Richard Tonsing, Chris Curnow and the Online -Distributed Proofreading Team at http://www.pgdp.net (This -file was produced from images generously made available -by The Internet Archive) - - - - - - - - - - STARGAZING: - PAST AND PRESENT - - -[Illustration] - -[Illustration: - - R. S. NEWALL’S TELESCOPE. -] - - - - - STARGAZING: - PAST AND PRESENT. - - - BY - J. NORMAN LOCKYER, F.R.S., - CORRESPONDENT OF THE INSTITUTE OF FRANCE. - - EXPANDED FROM SHORTHAND NOTES OF A COURSE OF ROYAL INSTITUTION LECTURES, - WITH THE ASSISTANCE OF G. M. SEABROKE, F.R.A.S. - - London: - MACMILLAN AND CO. - 1878. - - [_The Right of Translation and Reproduction is Reserved._] - - - - - LONDON: - R. CLAY, SONS, AND TAYLOR, - BREAD STREET HILL, E.C. - - - - - PREFACE. - - -In the year 1870 I gave a course of eight Lectures on Instrumental -Astronomy at the Royal Institution. The Lectures were taken down by a -shorthand writer, my intention being to publish them immediately. In -this, however, I was prevented by other calls upon my time. - -In 1875 my friend Mr. Seabroke generously offered to take the burden of -preparing the notes for the press off my shoulders; I avail myself of -this opportunity of expressing my very great obligations to him for his -valuable services in this particular as well as for important help in -the final revision of the proofs. - -On looking over the so completed MSS., however, I saw that the eight -hours at my disposal had not permitted me to touch upon many points of -interest which could hardly be omitted from the book. Besides this, the -progress made in the various instrumental methods in the interval, and -the results obtained by them, had been very remarkable. I felt, -therefore, that the object I had in view, namely, to further the cause -of physical astronomy, by creating and fostering, so far as in me lay, a -general interest in it, and by showing how all departments of physical -inquiry were gradually being utilized by the astronomer, would only be -half attained unless the account were more complete. I have, therefore, -endeavoured to fill up the gaps, and have referred briefly to the new -instruments and methods. - -The autotype of the twenty-five inch refractor is the gift of my friend -Mr. Newall, and I take this opportunity of expressing my obligation to -him, as also to Messrs. Cooke, Grubb and Browning for several of the -woodcuts with which the chapters on the Equatorial are illustrated; and -to Mr. H. Dent-Gardner for some of those illustrating Clock and -Chronometer Escapements, and for revising my account of them. - -Nor can I omit to thank Mr. Cooper for the pains he has taken with the -woodcuts, especially those copied from Tycho Brahe’s description of his -Observatory, and Messrs. Clay for the careful manner in which they have -printed the book. - - J. NORMAN LOCKYER. - - _November 16th, 1877._ - - - - - CONTENTS. - - - BOOK I. - - THE PRE-TELESCOPIC AGE. - - CHAP. PAGE - - I.— THE DAWN OF STARGAZING 1 - - II.— THE FIRST INSTRUMENTS 16 - - III.— HIPPARCHUS AND PTOLEMY 25 - - IV.— TYCHO BRAHE 37 - - - BOOK II. - - THE TELESCOPE. - - V.— THE REFRACTION OF LIGHT 55 - - VI.— THE REFRACTOR 73 - - VII.— THE REFLECTION OF LIGHT 90 - - VIII.— THE REFLECTOR 100 - - IX.— EYEPIECES 109 - - X.— PRODUCTION OF LENSES AND SPECULA 117 - - XI.— THE “OPTICK TUBE” 139 - - XII.— THE MODERN TELESCOPE 152 - - - BOOK III. - - TIME AND SPACE MEASURERS. - - XIII.— THE CLOCK AND CHRONOMETER 175 - - XIV.— CIRCLE READING 211 - - XV.— THE MICROMETER 218 - - - BOOK IV. - - MODERN MERIDIONAL OBSERVATIONS. - - XVI.— THE TRANSIT CIRCLE 233 - - XVII.— THE TRANSIT CLOCK AND CHRONOGRAPH 253 - - XVIII.— “GREENWICH TIME,” AND THE USE MADE OF IT 271 - - XIX.— OTHER INSTRUMENTS USED IN ASTRONOMY OF PRECISION 284 - - - BOOK V. - - THE EQUATORIAL. - - XX.— VARIOUS METHODS OF MOUNTING LARGE TELESCOPES 293 - - XXI.— THE ADJUSTMENTS OF THE EQUATORIAL 328 - - XXII.— THE EQUATORIAL OBSERVATORY 337 - - XXIII.— THE SIDEROSTAT 343 - - XXIV.— THE ORDINARY WORK OF THE EQUATORIAL 349 - - - BOOK VI. - - ASTRONOMICAL PHYSICS. - - XXV.— THE GENERAL FIELD OF PHYSICAL INQUIRY 371 - - XXVI.— DETERMINATION OF THE LIGHT AND HEAT OF THE STARS 377 - - XXVII.— THE CHEMISTRY OF THE STARS: CONSTRUCTION OF THE 386 - SPECTROSCOPE - - XXVIII.— THE CHEMISTRY OF THE STARS (CONTINUED): PRINCIPLES OF 401 - SPECTRUM ANALYSIS - - XXIX.— THE CHEMISTRY OF THE STARS (CONTINUED): THE 422 - TELESPECTROSCOPE - - XXX.— THE TELEPOLARISCOPE 441 - - XXXI.— CELESTIAL PHOTOGRAPHY.—THE WAYS AND MEANS 454 - - XXXII.— CELESTIAL PHOTOGRAPHY (CONTINUED): SOME RESULTS 463 - - XXXIII.— CELESTIAL PHOTOGRAPHY (CONTINUED): RECENT RESULTS 469 - - - - - LIST OF ILLUSTRATIONS. - - - FIG. PAGE - - 1. The heavens according to Ptolemy 3 - - 2. The zodiac of Denderah 7 - - 3. Illustration of Euclid’s statements 10 - - 4. The plane of the ecliptic 13 - - 5. The plane of the ecliptic, showing the inclination of the 14 - earth’s axis - - 6. The first meridian circle 20 - - 7. The first instrument graduated into 360° (west side) 21 - - 8. Astrolabe (armillæ æquatoriæ of Tycho Brahe) similar to the 26 - one contrived by Hipparchus - - 9. Ecliptic astrolabe (the armillæ zodiacales of Tycho Brahe), 28 - similar to the one used by Hipparchus - - 10. Diagram illustrating the precession of the equinoxes 31 - - 11. Revolution of the pole of the equator round the pole of the 32 - ecliptic caused by the precession of the equinoxes - - 12. The vernal equinox among the constellations, B.C. 2170 34 - - 13. Showing how the vernal equinox has now passed from Taurus and 34 - Aries - - 14. Instrument for measuring altitudes 35 - - 15. Portrait of Tycho Brahe (from original painting in the 39 - possession of Dr. Crompton, of Manchester) - - 16. Tycho Brahe’s observatory on the island of Huen 43 - - 17. Tycho Brahe’s system 46 - - 18. The quadrans maximus reproduced from Tycho’s plate 48 - - 19. Tycho’s sextant 50 - - 20. View and section of a prism 56 - - 21. Deviation of light in passing at various incidences through 57 - prisms of various angles - - 22. Convergence of light by two prisms base to base 59 - - 23. Formation of a lens from sections of prisms 60 - - 24. Front view and section of a double convex lens 61 - - 25. Double concave, plane concave, and concavo-convex lenses 61 - - 26. Double convex, plane convex, and concavo-convex lenses 62 - - 27. Convergence of rays by convex lens to principal focus 62 - - 28. Conjugate foci of convex lens 63 - - 29. Conjugate images 64 - - 30. Diagram explaining Fig. 29 64 - - 31. Dispersion of rays by a double concave lens 65 - - 32. Horizontal section of the eyeball 66 - - 33. Action of eye in formation of images 68 - - 34. Action of a long-sighted eye 69 - - 35. Diagram showing path of rays when viewing an object at an 70 - easy distance - - 36. Action of short-sighted eye 71 - - 37. Galilean telescope 73 - - 38. Telescope 75 - - 39. Diagram explaining the magnifying power of object-glass 76 - - 40. Scheiner’s telescope 78 - - 41. Dispersion of light by prism 80 - - 42. Diagram showing the amount of colour produced by a lens 81 - - 43. Decomposition and recomposition of light by two prisms 83 - - 44. Diagram explaining the formation of an achromatic lens 84 - - 45. Combination of flint- and crown-glass lenses in an achromatic 86 - lens - - 46. Diagram illustrating the irrationality of the spectrum 87 - - 47. Diagram illustrating the action of a reflecting surface 91 - - 48. Experimental proof that the angle of incidence = angle of 92 - reflection - - 49. Convergence of light by concave mirror 94 - - 50. Conjugate foci of convex mirror 94 - - 51. Formation of image of candle by reflection 95 - - 52. Diagram explaining Fig. 51 96 - - 53. Reflection of rays by convex mirror 98 - - 54. Reflecting telescope (Gregorian) 101 - - 55. Newton’s telescope 102 - - 56. Reflecting telescope (Cassegrain) 103 - - 57. Front view telescope (Herschel) 103 - - 58. Diagram illustrating spherical aberration 105 - - 59. Diagram showing the proper form of reflector to be an ellipse 106 - - 60. Huyghens’ eyepiece 110 - - 61. Diagram explaining the achromaticity of the Huyghenian 111 - eyepiece - - 62. Ramsden’s eyepiece 112 - - 63. Erecting or day eyepiece 113 - - 64. Images of planet produced by short and long focus lenses, &c. 123 - - 65. Showing in an exaggerated form how the edge of the speculum 128 - is worn down by polishing - - 65*. Section of Lord Rosse’s polishing machine 131 - - 66. Mr. Lassell’s polishing machine 132 - - 67. Simple telescope tube, showing arrangement of object-glass 140 - and eyepiece - - 68. Appearance of diffraction rings round a star when the 141 - object-glass is properly adjusted - - 69. Appearance of same object when object-glass is out of 141 - adjustment - - 70. Optical part of a Newtonian reflector of ten inches aperture 143 - - 71. Optical part of a Melbourne reflector 143 - - 72. Mr. Browning’s method of supporting small specula 144 - - 73. Support of the mirror when vertical 146 - - 74. Division of the speculum into equal areas 147 - - 75. Primary, secondary, and tertiary systems of levers shown 148 - separately - - 76. Complete system consolidated into three screws 148 - - 77. Support of diagonal plane mirror (Front view) 150 - - 78. Support of diagonal plane mirror (Side view) 150 - - 79. A portion of the constellation Gemini seen with the naked eye 154 - - 80. The same region, as seen through a large telescope 155 - - 81. Orion and the neighbouring constellations 156 - - 82. Nebula of Orion 157 - - 83. Saturn and his moons 160 - - 84. Details of the ring of Saturn 161 - - 85. Ancient clock escapement 177 - - 86. The crown wheel 178 - - 87. The clock train 180 - - 88. Winding arrangements 181 - - 89. The cycloidal pendulum 185 - - 90. Graham’s, Harrison’s, and Greenwich pendulums 188 - - 91. Greenwich clock: arrangement for compensation for barometric 194 - pressure - - 92. The anchor escapement 197 - - 93. Graham’s dead beat 199 - - 94. Gravity escapement (Mudge) 200 - - 95. Gravity escapement (Bloxam) 202 - - 96. Greenwich clock escapement 204 - - 97. Compensating balance 207 - - 98. Detached lever escapement 208 - - 99. Chronometer escapement 209 - - 100. The fusee 209 - - 101. Diggs’ diagonal scale 213 - - 102. The vernier 214 - - 103. System of wires in a transit eyepiece 220 - - 104. Wire micrometer 221 - - 105. Images of Jupiter 224 - - 106. Object-glass cut into two parts 225 - - 107. The parts separated, and giving two images of any object 225 - - 108. Double images seen through Iceland spar 227 - - 109. Diagram showing the ordinary and extraordinary rays in a 227 - crystal of Iceland spar - - 110. Crystals of Iceland spar 228 - - 111. Double image micrometer 229 - - 112. Tycho Brahe’s mural quadrant 235 - - 113. Transit instrument (Transit of Venus Expedition) 236 - - 114. Transit instrument in a fixed observatory 237 - - 115. Diagram explaining third adjustment 239 - - 116. The mural circle 241 - - 117. Transit circle, showing the addition of circles to the 242 - transit instrument - - 118. Perspective view of Greenwich transit circle 243 - - 119. Plan of the Greenwich transit circle 245 - - 120. Cambridge (U.S.) meridian circle 248 - - 121. Diagram illustrating how the pole is found 249 - - 122. Diagram illustrating the different lengths of solar and 255 - sidereal day - - 123. System of wires in transit eyepiece 257 - - 124. The Greenwich chronograph. (General view) 261 - - 125. Details of the travelling carriage which carries the magnets 262 - and prickers. (Side view and view from above) - - 126. Showing how on the passage of a current round the soft iron 263 - the pricker is made to make a mark on the spiral line on - the cylinder - - 127. Side view of the carriage carrying the magnets and the 263 - pointer that draws the spiral - - 128. Wheel of the sidereal clock, and arrangement for making 266 - contact at each second - - 129. Arrangement for correcting mean solar time clock at Greenwich 268 - - 130. The chronopher 276 - - 131. Reflex zenith tube 286 - - 132. Theodolite 288 - - 133. Portable alt-azimuth 289 - - 134. The 40-feet at Slough 294 - - 135. Lord Rosse’s 6-feet 295 - - 136. Refractor mounted on alt-azimuth tripod for ordinary 296 - star-gazing - - 137. Simple equatorial mounting 298 - - 138. Cooke’s form for refractors 300 - - 139. Mr. Grubb’s form applied to a Cassegrain reflector 301 - - 140. Grubb’s form for Newtonians 303 - - 141. Browning’s mounting for Newtonians 304 - - 142. The Washington great equatorial 309 - - 143. General view of the Melbourne reflector 312 - - 144. The mounting of the Melbourne telescope 313 - - 145. Great silver-on-glass reflector at the Paris observatory 316 - - 146. Clock governor 319 - - 147. Bond’s spring governor 320 - - 148. Foucault’s governor 323 - - 149. Illuminating lamp for equatorial 325 - - 150. Cooke’s illuminating lamp 326 - - 151. Dome 338 - - 152. Drum 338 - - 153. New Cincinnati observatory—(Font elevation) 338 - - 154. Cambridge (U.S.) equatorial 339 - - 155. Section of main building—United States naval observatory 341 - - 156. Foucault’s siderostat 344 - - 157. The siderostat at Lord Lindsay’s observatory 348 - - 158. Position circle 353 - - 159. How the length of a shadow thrown by a lunar hill is measured 354 - - 160. The determination of the angle of position of the axis of 358 - Saturn’s ring - - 161. Measurement of the angle of position of the axis of a figure 359 - of a comet - - 162. Double star measurement 360 - - 163. Ring micrometer 368 - - 164. Thermopile and galvanometer 374 - - 165. Rumford’s photometer 378 - - 166. Bouguer’s photometer 379 - - 167. Kepler’s diagram 387 - - 168. Newton’s experiment, showing the different refrangibilities 388 - of colours - - 169. First observation of the lines in the solar spectrum 391 - - 170. Solar spectrum 392 - - 171. Student’s spectroscope 393 - - 172. Section of spectroscope 394 - - 173. Spectroscope with four prisms 396 - - 174. Automatic spectroscope (Grubb’s form) 397 - - 175. Automatic spectroscope (Browning’s form) 397 - - 176. Last prism of train for returning the rays 398 - - 177. Spectroscope with returning beam 399 - - 178. Direct-vision prism 399 - - 179. Electric lamp 404 - - 180. Electric lamp arranged for throwing a spectrum on a screen 405 - - 181. Comparison of the line spectra of iron, calcium, and 406 - aluminium, with common impurities - - 182. Coloured flame of salts in the flame of a Bunsen’s burner 408 - - 183. Spectroscope arranged for showing absorption 409 - - 184. Geissler’s tube 413 - - 185. Spectrum of sun-spot 415 - - 186. Diagram explaining long and short lines 416 - - 187. Comparison of the absorption spectrum of the sun with the 418 - radiation spectra of iron and calcium, with common - impurities - - 188. Comparison prism 423 - - 189. Comparison prism 423 - - 190. Foucault’s heliostat 424 - - 191. Object-glass prism 426 - - 192. The eyepiece end of the Newall refractor 427 - - 193. Solar telespectroscope (Browning’s form) 428 - - 194. Solar telespectroscope (Grubb’s form) 428 - - 195. Side view of spectroscope 429 - - 196. Plan of spectroscope 429 - - 197. Cambridge star spectroscope elevation 430 - - 198. Cambridge spectroscope plan 430 - - 199. Direct-vision star spectroscope (Secchi) 431 - - 200. Types of stellar spectra 433 - - 201. Part of solar spectrum near F 436 - - 202. Distortions of F line on sun 438 - - 203. Displacement of F line on edge of sun 439 - - 204. Diagram showing the path of the ordinary and extraordinary 445 - ray in crystals of Iceland spar - - 205. Appearance of the spots of light on the screen shown in the 446 - preceding figure, allowing the ordinary ray to pass and - rotating the second crystal - - 206. Appearance of spots of light on screen on rotating the second 447 - crystal, when the extraordinary ray is allowed to pass - through the first screen - - 207. Instrument for showing polarization by reflection 448 - - 208. Section of plate-holder 456 - - 209. Enlarging camera 458 - - 210. Instantaneous shutter 460 - - 211. Photoheliograph as erected in a temporary observatory for 461 - photographing the transit of Venus in 1874 - - 212. Copy of photograph taken during the eclipse of 1869 474 - - 213. Part of Beer and Mädler’s map of the moon 476 - - 214. The same region copied from a photograph by De La Rue 477 - - 215. Comparison between Kirchhoff’s map and Rutherfurd’s 480 - photograph - - 216. Arrangement for photographically determining the coincidence 481 - of solar and metallic lines - - 217. Telespectroscope with camera for obtaining photographs of the 482 - solar prominences - - - - - BOOK I. - _THE PRE-TELESCOPIC AGE._ - - - - - STARGAZING: PAST AND PRESENT - - - - - CHAPTER I. - THE DAWN OF STARGAZING. - - -Some sciences are of yesterday; others stretch far back into the youth -of time. Among these there is one of the beginnings of which we have -lost all trace, so coeval was it with the commencement of man’s history; -and that science is the one of which we have to trace the instrumental -developments. - -Although our chief task is to enlarge upon the modern, it will not be -well, indeed it is impossible, to neglect the old, because, if for no -other reason, the welding of old and new has been so perfect, the -conquest of the unknown so gradual. - -The best course therefore will be to distribute the different fields of -thought and work into something like marked divisions, and to commence -by dividing the whole time during which man has been observing the -heavens into two periods, which we will call the Pre-telescopic and the -Telescopic Ages. The work of the Pre-telescopic age of course includes -all the early observations made by the unaided eye, while that of the -Telescopic age includes those of vastly different kinds, which that -instrument had rendered possible; so that it divides itself naturally -into some three or four sub-ages of extreme importance. - -It is unnecessary to say one word here on the importance of the -invention of the telescope; it is well for the present purpose, however, -to emphasize the further distinctions we obtain when we consider the -various additions made from time to time to the telescope. - -The Telescope, in fact, was comparatively little used until astronomy -annexed that important branch of physics to its aid which gave us a -Clock—a means of dividing time in the most accurate manner. - -In quite recent times the addition of the Camera to the Telescope marks -an important advance; indeed the importance of photography is not yet -recognised in the way it should be. - -Then, again, there is the addition of the Spectroscope, which, though it -is only now beginning to yield us rich fruit, really dates from the -beginning of the present century. This is an ally to the telescope of -such power that he would be a bold man who would venture to set bounds -to the conquests their combined forces will make. - -Now not only is it essential for the proper understanding of the -instruments used nowadays in every observatory, by every stargazer, to -go back to the origin of the science of observation, but in no other way -can one fully see in what way the new instrumental methods have added -themselves to the old ones. - -Further, it is of importance to go back to the actual old field of work -in which the geometric conceptions which grew up in the minds of the men -of ancient time—conceptions which we are now utilizing and -extending—were gradually elaborated. To do this, there is no better way -than to dwell very briefly on the work actually done by the old -astronomers. - - * * * * * - -This programme, then, being agreed to, the first point is to trace the -progress of astronomical instruments down to the time of Copernicus and -Galileo. During all this period the most generally received doctrine -was, that the earth was the centre of the visible heavens; and although -there were many variations of this, still the arrangement of Ptolemy, -Fig. 1, is a good type of the ideas of the ancients. - -[Illustration: - - FIG. 1.—The Heavens according to Ptolemy. -] - -We begin with man’s first feeble efforts, the work which man was enabled -to do by his unaided eye; and we end with the tremendous addition which -he got to his observing powers by the invention of the telescope. - -The first instrument used for astronomical observations was none of -man’s making. In the old time the only instrument was the horizon; and, -truth to tell, in a land of extended plains and isolated hills, it was -not a bad one. Hence it was, doubtless, that observations in the first -instance were limited to certain occurrences such as the risings and -settings of the stars and the relative apparent distances of the -heavenly bodies from each other. - -So far as we are able to learn from ancient authors, the observations -next added were those of the conjunctions of the planets and of -eclipses. The Egyptians are stated to have recorded 373 solar, and 832 -lunar eclipses; and this statement is probably correct, as the -proportions are exact, and there should be the above number of each in -from 1,200 to 1,300 years. - -The Chinese also record an observation, made between the years 2514 and -2436 B.C., of five planets being in conjunction. - -The Chaldeans appear to have observed the motions of the moon, and an -observation in 2227 B.C. is recorded; but these old dates are probably -fictitious. - -It is impossible to regard without surprise the general attention given -to astronomical investigation in those early days compared with what we -find now. Yet if we attempt to build up for ourselves any idea as to the -problems of which the ancients attempted the solution, it is difficult -if not impossible to do it; we cannot realize the blank which the -heavens presented to them, so many great men have lived between their -time and our own, by whose labours we, even if unconsciously, have -profited. The first idea seems to have been to observe which stars were -rising or setting at seed or harvest time, to divide the heavens into -Moon Stations, and then to mark astronomically their monthly and yearly -festivals. - -If one looks into the old records we find that all the labours of man -which had to be performed in the country or elsewhere were determined, -by the rising or setting of the stars. All the exertions of the -navigator and the agriculturist were thus regulated. Of the planets in -those early times we hear little, except from the Chinese annals which -record conjunctions. - -This was before man began to use the sun as a standpoint, and hence it -is that there are so many references in the ancient writers to the -rising and setting of the most striking star cluster—the Pleiades, and -the most striking constellation—Orion. It is known that the year, in -later times at all events, began in Egypt when the brightest star in the -heavens, Sirius, the dog-star, rose with the sun, this day being called -the 1st of the month Thoth,[1] which was the commencement of the Sothiac -period of 1461 years. - -It would appear that observations of culminations, that is, of the -highest points reached by the stars, were not made till long after -horizon observations were in full vigour; and here it is a question -whether pyramids and the like were not the first astronomical -instruments constructed by man, because for great nicety in such -observations—a nicety, let us say, sufficient to determine -astronomically by means of culminations the time for holding a -festival—a fixed instrument of some kind was essential. The rich mine -recently opened up by Mr. Haliburton and Mr. Ernest de Bunsen concerning -the survival in all nations—in our own one takes the name the Feast of -All Souls’—of ancient festivals governed by the midnight culmination of -the Pleiades will doubtless ere long call general attention to this -earliest form of accurate astronomical observation, and the -determination by Professor Piazzi Smyth of the fact that in 2170 B.C., -when the Pleiades culminated at midnight at the vernal equinox, the -passages in the north and south faces of the pyramid of Gizeh were -directed, the southern one to this culmination, and the northern one to -the then pole star, α Draconis, at its transit, about 4° from the pole. - -Hence one may regard the pyramid as the next astronomical instrument to -the horizon. While then it is possible that such culmination -observations soon replaced in some measure that class of observations -which heretofore had been made on the horizon, another teaching of -horizon observations became apparent. By and by travellers observed that -as they travelled northwards the stars that were just visible on the -southern horizon, when culminating, gradually disappeared below it. -These observations were at once seized on, and Anaximander accounted for -them by supposing that the earth was a cylinder.[2] The idea of a sphere -did not come till later; when it did come then came the circle as an -astronomical instrument. For let us consider that a person on the earth -stands, say, at the equator; then he will just be able to see along his -north and south horizon the stars pointed to by the axis of the globe: -if now he is transported northwards, his horizon will change with him; -he will no longer be able to see the southern stars, but the northern -ones will gradually rise above his horizon till he gets to the north -pole, when the north pole star, instead of being on his horizon, as was -the case when he was at the equator, will be over his head. So by moving -from the equator to the pole (or a quarter of the distance round the -earth) the stars have moved from the horizon to the point overhead, or -the zenith, that is also a quarter of a circle. So it appears that if an -observer moves to such a distance that the stars appear to move over a -certain division of a circle with reference to the horizon, he must have -moved over an equal division on the earth’s surface. Then, as now, the -circle in the Western world was divided into 360°, so that the observer -in moving 1° by the stars would have moved over 1/360 of the distance -round the earth, on the assumption that the earth is a globe; and if the -distance over which the observer has moved be multiplied by 360, the -result will be the distance round the earth. - -[Illustration: - - FIG. 2.—The Zodiac of Denderah. -] - -Now let us see how Posidonius a long time afterwards (he was born about -135 years B.C.) applied this conception. He observed that at Rhodes the -star Canopus grazed the horizon at culmination, while at Alexandria it -rose above it 7½°. Now 7½° is 1/48 of the whole circle; so he found that -from the latitude of Rhodes to that of Alexandria was 1/48 of the -circumference of the earth. He then estimated the distance, getting -5,000 stadia as the result; and this multiplied by 48 gave him 240,000 -stadia, his measure of the circumference of the earth. - -When the sun’s yearly course in the heavens had been determined, it was -found that it was restricted to that band of stars called the Zodiac, -Fig. 2; the sun’s position in the zodiac at any one time of the year -being found by the midnight culmination of the stars opposite the sun; -this and the apparent and heliacal risings and settings were alone the -subjects of observation. - -It is obvious, then, that when observations of this nature had gone on -for some time, men would be anxious to map the stars, to make a chart of -the field of heaven; and such a work was produced by Autolycus three and -a half centuries before Christ. We also owe to Autolycus and Euclid, who -flourished about the same time (300 B.C.), the first geometrical -conceptions connected with the apparent motions of the stars. - -In the theorems of Autolycus there is a particular reference to the -twelve parts of the zodiac, as denoted by constellations. The following -are the most important propositions which he lays down:— - - 1. “The zodiacal sign occupied by the sun neither rises nor sets, - but is either concealed by the earth or lost in the sun’s rays. The - opposite sign neither rises nor sets, _i.e._, visibly, _i.e._, after - sundown, but it is visible during the whole night. - - 2. “Of the twelve signs of the zodiac, that which precedes the sign - occupied by the sun rises visibly in the morning; that which - succeeds the same sign sets visibly in the evening. - - 3. “Eleven signs of the zodiac are seen every night. Six signs are - visible, and the five others, not occupied by the sun, afterwards - rise. - - 4. “Every star has an interval of five months between its morning - and its evening rising, during which time it is visible. It has an - interval of at least thirty days—between its evening setting, and - its morning rising—during which time it is invisible.” (That is, the - space passed over by the sun in its annual path is such that a star - which you see on one side of the sun, when the sun rises at one - time, would be seen a month afterwards on the other side of the - sun.) - -Autolycus makes no mention of the planets. Their irregular movements -rendered them unsuited to the practical object which he had in view. He -is, however, stated by Simplicius, as quoted by Sir G. C. Lewis to have -proposed some hypothesis for explaining their anomalous motions, and to -have failed in his attempt. - -Euclid carries the results arrived at in this early pre-telescopic age -much further; in a little-known treatise, the _Phenomena_,[3] he thus -sums up the knowledge then acquired:— - - “The fixed stars rise at the same point, and set at the same point; - the same stars always rise together, and set together, and in their - course from the east to the west they always preserve the same - distance from one another. Now, as these appearances are only - consistent with a circular movement, when the eye of the observer is - equally distant from the circumference of the circle in every - direction (as has been demonstrated in the treatise on Optics), it - follows that the stars move in a circle and are attached to a single - body, and that the vision is equally distant from the circumference. - -[Illustration: - - FIG. 3.—Illustration of Euclid’s statements. _P_ the star between - the Bears. _D D´_ the region of the always visible. _C B A_ the - regions of the stars which rise and set. -] - - “A star is visible between the Bears, not changing its place, but - always revolving upon itself. Since this star appears to be equally - distant from every part of the circumference of each circle - described by the other stars, it must be assumed that all the - circles are parallel, so that all the fixed stars move along - parallel circles, having this star as their common pole. - - “Some of these neither rise nor set, on account of their moving in - elevated circles, which are called the ‘always visible.’ They are - the stars which extend from the visible pole to the Arctic circle. - Those which are nearest the pole describe the smallest circle, and - those upon the Arctic circle the largest. The latter appears to - graze the horizon. - - “The stars to the south of this circle all rise and set, on account - of their circles being partly above and partly below the earth. The - segments above the earth are large and the segments below the earth - are small in proportion as they approach the Arctic circle, because - the motion of the stars nearest the circle above the earth is made - in the longest time, and of those below the earth in the shortest. - In proportion as the stars recede from this circle, their motion - above the earth is made in less time, and that below the earth in - greater. Those that are nearest the south are the least time above - the earth, and the longest below it. The stars which are upon the - middle circle make their times above and below the earth equal; - whence this circle is called the Equinoctial. Those which are upon - circles equally distant from the equinoctial make the alternate - segments in equal times. For example, those above the earth to the - north correspond with those below the earth to the south; and those - above the earth to the south correspond with those below the earth - to the north. The joint times of all the circles above and below the - earth are equal. The circle of the milky way and the zodiacal circle - being oblique to the parallel circles, and cutting each other, - always have a semicircle above the earth. - - “Hence it follows that the heaven is spherical. For if it were - cylindrical or conical, the stars upon the oblique circles, which - cut the equator, would not in the revolution of the heaven always - appear to be divided into semicircles; but the visible segment would - sometimes be greater and sometimes less than a semicircle. For if a - cone or a cylinder were cut by a plane not parallel to the base, the - section is that of an acute-angled cone, which resembles a shield - (an ellipse). It is, therefore, evident that if a figure of this - description is cut in the middle both in length and breath, its - segments will be unequal. But the appearances of the heaven agree - with none of these results. Therefore the heaven must be supposed to - be spherical, and to revolve equally round an axis of which one pole - above the earth is visible and the other below the earth is - invisible. - - “The Horizon is the plane reaching from our station to the heaven, - and bounding the hemisphere visible above the earth. It is a circle; - for if a sphere be cut by a plane the section is a circle. - - “The Meridian is a circle passing through the poles of the sphere, - and at right angles to the horizon. - - “The Tropics are circles which touch the zodiacal circle, and have - the same poles as the sphere. The zodiacal and the equinoctial are - both great circles, for they bisect one another. For the beginning - of Aries and the beginning of the Claws (or Scorpio) are upon the - same diameter; and when they are both upon the equinoctial, they - rise and set in conjunction, having between their beginnings six of - the twelve signs and two semicircles of the equinoctial; inasmuch as - each beginning, being upon the equinoctial, performs its movement - above and below the earth in equal times. If a sphere revolves - equally round its axis, all the points on its surface pass through - similar axes of the parallel circles in equal times. Therefore these - signs pass through equal axes of the equinoctial, one above and the - other below the earth; consequently the axes are equal, and each is - a semicircle; for the circuit from east to east and from west to - west is an entire circle. Consequently the zodiacal and equinoctial - circles bisect one another; each will be a great circle. Therefore - the zodiacal and equinoctial are great circles. The horizon is - likewise a great circle; for it bisects the zodiacal and - equinoctial, both great circles. For it always has six of the twelve - signs above the earth, as well as a semicircle of the equator. The - stars above the horizon which rise and set together reappear in - equal times, some moving from east to west, and some from west to - east.” - -We have given this long extract in justice to the men of old, containing -as it does many of those geometrical principles which all our modern -instruments must and actually do fulfil. - -It is true that the present idea of the earth’s place in the system is -different. Euclid imagined the earth to be at the centre of the -universe. It is now known that the earth is one of various planets which -revolve round the sun, and further, that the journey of the earth round -the sun is so even and beautifully regulated that its motion is confined -to a single plane. Year after year the earth goes on revolving round the -sun, never departing, except to a very small extent, from this plane, -which is one of the fundamental planes of the astronomer and called the -Plane of the Ecliptic. - -[Illustration: - - FIG. 4.—The Plane of the Ecliptic. -] - -Suppose this plane to be a tangible thing, like the surface of an -infinite ocean, the sun will occupy a certain position in this infinite -ocean, and the earth will travel round it every year. - -If the axis of the earth were upright, one would represent the position -of things by holding a globe with its axis upright, so that the equator -of the earth is in every part of its revolution on a level with this -ecliptic sea. But it is known that the earth, instead of floating, as it -were, upright, as in Fig. 4, has its axis inclined to the plane of the -ecliptic, as in Fig. 5. - -It is also known that by turning a globe round, distant objects would -appear to move round an observer on the globe in an opposite direction -to his own motion, and these distant objects would describe circles -round a line joining the places pointed to by the poles of the earth, -_i.e._, round the earth’s axis. - -[Illustration: - - FIG. 5.—The Plane of the Ecliptic, showing the Inclination of the - Earth’s Axis. -] - -It is now easy to explain the observations referred to by Euclid by -supposing the surface of the water in the tub to represent the plane of -the ecliptic, that is, the plane of the path which the sun apparently -takes in going round the earth; and examining the relative positions of -the sun and earth represented by two floating balls, the latter having a -wire through it inclined to the upright position; it will be seen at -once by turning the ball on the wire as an axis to represent the diurnal -motion of our earth, how Euclid finds the Bear which never sets, being -the place in the heavens pointed to by the earth’s pole; and how all the -stars in different portions of the heavens appear to move in complete -circles round the pole-star when they do not set, and in parts of -circles when they pass below the horizon. By moving the ball -representing the earth round the sun and so examining their relative -positions, during the course of a year it will be seen how the sun -appears to travel through all the signs of the zodiac in succession in -his yearly course, remaining a longer or shorter time above the horizon -at different times of the year. - -For it will be seen that if the spectator on the globe, when in the -position that its inclined axis, as shown in Fig. 5, points towards the -sun, were looking at the sun from a place where one can imagine England -to be at midday, the sun would appear to be very high up above the -horizon; and if he looked at it from the earth in the opposite part of -its orbit it would be very low and near the horizon. When the earth, -therefore, occupied the intermediate positions, the sun would be half -way between the extreme upper position and the extreme lower position as -the earth moves round the sun, and in this way the solstices, equinoxes, -and the seasonal changes on the surface of our planet, are easily -explained. - ------ - -Footnote 1: - - Corresponding to 20th July, 139 B.C. - -Footnote 2: - - Anaximander flourished about 547 B.C. - -Footnote 3: - - Quoted by Sir G. C. Lewis in his _Astronomy of the Ancients_, p. 187. - - - - - CHAPTER II. - THE FIRST INSTRUMENTS. - - -The ancients called the places occupied by the sun when highest and -lowest the Solstices, and the intermediate positions the Equinoxes. The -first instrument made was for the determination of the sun’s altitude in -order to fix the solstices. This instrument was called the Gnomon. It -consisted of an upright rod, sharp at the end and raised perpendicularly -on a horizontal plane, and its shadow could be measured in the plane of -the meridian by a north and south line on the ground. Whenever the -shadow was longest the sun was naturally lowest down at the winter -solstice, and _vice versâ_ for the summer solstice. - -Here then we leave observations on the horizon and come to those made on -the meridian. - -The Gnomon is said to have been known to the Chinese in the time of the -Emperor Yao’s reign (2300 B.C.), but it was not used by the Greeks[4] -till the time of Thales, about 585 B.C., who fixed the dates of the -solstices and equinoxes, and the length of the tropical year—that is, -the time taken by the sun to travel from the vernal equinoctial point -round to the same point again. - -The next problem was to discover the inclination of the ecliptic, or, -what is the same thing, the amount that the earth’s equator is inclined -to the ecliptic plane (represented by the surface of the water in our -tub). - -Now in order to ascertain this, the angular distance between the -positions occupied by the sun when at the solstices must be measured; -or, since one solstice is just as much below the equinoctial line as the -other is above it, we might take half the angle between the solstices as -being the obliquity required. - -The first method of measuring the angle was to measure the length of the -sun’s shadow at each solstice, and so, by comparison of the length of -the shadow with the height of the gnomon, calculate the difference in -altitude, the half of which was the angle sought. And this was probably -the method of the Chinese, who obtained a result of 23° 38´ 11˝ in the -time of Yao; and also of Anaximander in his early days, who obtained a -result of 24°. But before trigonometrical tables, the first of which -seem to have been constructed by Hipparchus and Ptolemy, were known, in -order to find this angle it was constructed geometrically, and then what -_aliquot part_ of the circumference it was, or _how much of the -circumference_ it contained was determined; for the division of the -circle into 360° is subsequent to the first beginning of astronomy—and -hence it was that Eratosthenes said that the distance from the tropics -was 11/83 of the circumference, and not that it was 47° 46´ 26˝. - -The gnomon is, without exception, of all instruments the one with which -the ancients were able to make the best observations of the sun’s -altitude. But they did not give sufficient attention to it to enable it -to be used with accuracy. The shadow projected by a point when the sun -is shining is not well defined, so that they could not be quite certain -of its extremity, and it would seem that the ancient observations of the -height of the sun made in this manner ought to be corrected by about -half the apparent diameter of the sun; for it is probable that the -ancients took the strong shadow for the true shadow; and so they had -only the height of the upper part of the sun and not that of the centre. -There is no proof that they did not make this correction, at least in -the later observations. - -In order to obviate this inconvenience, they subsequently terminated the -gnomon by a bowl or disc, the centre of which answered to the summit; so -that, taking the centre of the shadow of this bowl, they had the height -of the centre of the sun. Such was the form of the one that Manlius the -mathematician erected at Rome under the auspices of Augustus. - -But in comparatively modern times astronomers have remedied this defect -in a still more happy manner, by using a vertical or horizontal plate -pierced with a circular hole which allows the rays of the sun to enter -into a dark place, and in fact to form a true image of the sun on a -floor or other convenient receptacle, as we find is the case in many -continental churches. - -Of course at this early period the reference of any particular -phenomenon to true time was out of the question. The ancients at the -period we are considering used twelve hours to represent a day, -irrespective of the time of the year—the day always being reckoned as -the time between sunrise and sunset. So that in summer the hours were -long and in winter they were short. The idea of equal hours did not -occur to them till later; but no observations are closer than an hour, -and the smallest division of space of which they took notice was -something like equal to a quarter or half of the moon’s diameter. - -When we come down, however, to three centuries before Christ, we find -that a different state of things is coming about. The magnificent museum -at Alexandria was beginning to be built, and astronomical observations -were among the most important things to be done in that vast -establishment. The first astronomical workers there seem to have been -Timocharis and Aristillus, who began about 295 B.C., and worked for -twenty-six years. We are told that they made a catalogue of stars, -giving their positions with reference to the sun’s path or ecliptic. - -It was soon after this that the gnomon gave way to the invention of the -Scarphie. It is really a little gnomon on the summit of which is a -spherical segment. An arc of a circle passing out of the foot of the -style was divided into parts, and we thus had the angle which the solar -ray formed with the vertical. Nevertheless the scarphie was subject to -the same inconveniences, and it required the same corrections, as the -gnomon; in short, it was less accurate than it. That did not, however, -hinder Eratosthenes from making use of it to measure the size of the -earth and the inclination of the ecliptic to the equator. The method -Eratosthenes followed in ascertaining the size of the earth was to -measure the arc between Syene and Alexandria by observing the altitude -of the sun at each place. He found it to be 1/50 of the circumference -and 5,000 stadia, so that if 1/50 of the circumference of the earth is -5,000 stadia, the whole circumference must be 50 times 5,000, or 250,000 -stadia.[5] - -[Illustration: - - FIG. 6.—The First Meridian Circle. -] - -And now still another instrument is introduced, and we begin to find the -horizon altogether disregarded in favour of observations made on the -meridian. - -The instrument in question was probably the invention of Eratosthenes. -It consisted of two circles of nearly the same size crossing each other -at right angles, (Fig. 6); one circle represented the equator and the -other the meridian, and it was employed as follows:— - -The circle A was fixed perfectly upright in the meridian, so that the -greatest altitude of the sun each day could be observed; the circle B -was then placed exactly in the plane of the earth’s equator by adjusting -the line joining C and D to the part of the heavens between the Bears, -about which the stars appear to revolve. This done, the occurrence of -the equinox was waited for, at which time the shadow of the part of the -circle E must fall upon the part marked F, so as exactly to cover it. - -[Illustration: - - FIG. 7.—The First Instrument Graduated into 360° (West Side). -] - -We now come to the time when the circle began to be divided into 360 -divisions or degrees—about the time of Hipparchus (160 B.C.). There are -two instruments described by Ptolemy for measuring the altitude of the -sun in degrees instead of in fractions of a circle. They, like the -gnomon, were used for determining the altitude of the sun. The first, -Fig. 7, consisted of two circles of copper, one, C D, larger than the -other, having the smaller one, B, so fitted inside it as to turn round -while the larger remained fixed. The larger was divided into 360°, and -the smaller one carried two pointers. This instrument was placed -perfectly upright and in the plane of the meridian, and with a fixed -point, C, always at the top by means of a plumb-line hanging from C over -a mark, D. On this small circle are two square knobs projecting on the -side, E and F. When the sun was on the meridian the small circle was -turned so as to bring the shadow of the knob E over the knob F, and then -the degree to which the pointer pointed was read off on the larger -circle. And of course, as the position of the knobs had to be changed as -the sun moved in altitude, the angle through which the sun moved was -measured, and the circle being fixed, the sun’s altitude could always be -obtained. - -The other instrument consisted of a block of wood or stone, one side of -which was placed in the plane of the meridian; and on the top corner of -this side was fixed a stud; and round it as a centre a quarter of a -circle was described, divided into 90°. Below this stud was another, and -by means of a plumb-line one stud could always be brought over the -other; so that the instrument could always be placed in a true position. -At midday then, when the sun was shining, the shadow of the upper stud -would fall across the scale of degrees, and at once give the altitude of -the sun. - -Ptolemy, who used this instrument, found that the arc included between -the tropics was 47⅔°. - -The result of all these accurate determinations of the solstices and -equinoxes was the fixing of the length of the year. - -We have so far dealt with the methods of observation which depend upon -the use of the horizon and of the meridian; we will now turn our -attention to extra-meridional observations, or those made in any part of -the sky. - -Before we discuss them, let us consider the principles on which we -depend for fixing the position of a place on a globe. On a terrestrial -globe there are lines drawn from pole to pole, called meridians of -longitude; and if a place is on any one meridian it is said to be in so -many degrees of longitude, east or west of a certain fixed meridian, as -there are degrees intercepted between this meridian and the one on which -the place is situated. There are also circles at right angles to the -above and parallel to the equator; these are circles of latitude, and a -place is said to have so many degrees N. or S. latitude as the circle -which passes through it intercepts on a meridian between itself and the -equator, so that the latitude of a place is its angular distance from -the equator, and the longitude is its angular distance E. or W. of a -fixed meridian—that of Greenwich being the one used for English -calculation; and each large country takes the meridian of its central -observatory for its starting-point. The distance round the equator is -sometimes expressed in hours instead of degrees; for as the earth turns -round in twenty-four hours, so the equator can be divided into hours, -minutes, and seconds. So that if a star be just over the meridian of -Greenwich, which is 0° 0´ 0˝, or 0^h 0^m 0^s longitude at a certain -time, in an hour after it will be over a meridian 15° or one hour west -of Greenwich, and so on, till at the end of twenty-four hours it would -be over Greenwich again. - -Now let us turn to the celestial globe. - -What we call latitude and longitude on a terrestrial globe is called -declination and right ascension on the celestial globe, because in the -heavens there is a latitude and longitude which does not correspond to -our latitude and longitude on the earth. If we imagine the lines of -latitude and longitude on the earth to be projected, say as shadows -thrown on the heavens by a light in the centre of the earth, the lines -of right ascension (generally written R.A.) and declination (written -Dec. or D.) will be perfectly depicted. - -But there is another method of co-ordinating the stars, in which we have -the words latitude and longitude used also, as we have said, for the -heavens; meaning the distance of a star from the ecliptic instead of the -equator, and its distance east or west measured by meridians at right -angles to the ecliptic. - -This premised, we are in a position to see the enormous advance rendered -possible by the methods of observation introduced by Hipparchus and -Ptolemy. - ------ - -Footnote 4: - - This instrument is also reported to have been used by the Chaldeans in - 850 B.C.; the invention of it being attributed to Anaximander. This - philosopher, says Diogenes Laertes, observed the revolution of the - sun, that is to say, the solstices, with a gnomon; and probably he - measured the obliquity of the ecliptic to the equator, which his - master had already discovered. - -Footnote 5: - - 28,279 miles. - - - - - CHAPTER III. - HIPPARCHUS AND PTOLEMY. - - -Among the astronomers of antiquity there are two figures who stand out -in full relief—Hipparchus and Ptolemy. The former, “the father of -astronomy,” is especially the father of instrumental astronomy. As he -was the first to place observation on a sure basis, and left behind him -the germs of many of our modern instruments and methods, it is desirable -to refer somewhat at length to his work and that of his successor, -Ptolemy. - -Hipparchus introduced extra-meridional observations. He followed Meton, -Anaximander, and others in observing on the meridian instead of on the -horizon, and then it struck him that it was not necessary to keep to the -meridian, and he conceived an instrument, called an Astrolabe, fixed on -an axis so that the axis would point to the pole-star, like the one -represented in Fig. 8. This engraving is of one of Tycho Brahe’s -instruments, which is similar to but more elaborate than that of -Hipparchus no drawing of which is extant. C, D, is the axis of the -instrument pointed to the pole of the heavens; E, B, C, the circle -placed North and South representing the meridian; R, Q, N, the circle -placed at right angles to the polar axis, representing the equator, but -in the instrument of Hipparchus it was fixed to the circle E, B, C, and -not movable in its own plane as this one is. M, L, K, is a circle at -right angles to the equator, and moving round the poles, being a sort of -movable meridian. Thus, then, if the altitude of a star from the equator -(or its declination) was required to be observed, the circle was turned -round on the axis, and the sights, Q, M, moved on the circle till they, -together with the sight A, pointed to the star; the number of degrees -between one of the sights and the equator, was then read off, giving the -declination required. The number of degrees, or hours and minutes, of -Right Ascension, from K to E could be then read off along the circle R, -Q, N, giving the distance of the object from the meridian. As the stars -have an apparent motion, the difference in right ascension between two -stars only could be obtained by observing them directly after each -other, and allowing for the motion during the interval between the two -observations. - -[Illustration: - - FIG. 8.—Astrolabe (Armillæ Æquatoriæ of Tycho Brahe) similar to the - one contrived by Hipparchus. -] - -In this manner, then, Hipparchus could point to any part of the heavens -and observe, on either side of the meridian, the sun, moon, planets or -any of the stars, and obtain their distance from the equatorial plane; -but another fixed plane was required; and Hipparchus, no longer content -with being limited to measuring distances from the equator, thought it -might be possible to get another starting-point for distances along the -equator. It was the determination of this plane, or starting-point from -which to reckon right ascension, that was one of the difficulties -Hipparchus had to encounter. This point he decided should be the place -in the heavens where the sun crosses the equator at the spring equinox. -But the stars could not be seen when the sun was shining; how, then, was -he to fix that point so that he could measure from it at night? - -[Illustration: - - FIG. 9.—Ecliptic Astrolabe (the Armillæ Zodiacales of Tycho Brahe), - similar to the one used by Hipparchus. -] - -He found it at first a tremendous problem, and at last hit upon this -happy way of solving it. He reasoned in this way: “As an eclipse of the -moon is caused by the earth’s shadow being thrown by the sun on the -moon, if this happen near the equinox, the sun and moon must then be -very near the equator, and very near the ecliptic—in fact, near the -intersection of the two fundamental planes which are supposed to cross -each other. If I can observe the distance, measured along the equator, -between the moon and a star, I shall have obtained the star’s actual -place, because, of course, if the moon is exactly opposite the sun, the -sun will be 180 degrees of right ascension from the moon, and the right -ascension of the sun being known it will give me the position of the -star.” This method of observation was an extremely good one for the -time, but it could only have been used during an eclipse of the moon, -and when the sun was so near the equator that its distance from the -equinoctial point along the ecliptic, as calculated by the time elapsed -since the equinox, differed little from the same distance measured along -the equator, or its right ascension, so that the right ascension of the -sun was very nearly correct. Hipparchus hit upon a very happy alteration -of the same instrument to enable him to measure latitude and longitude -instead of declination and right ascension—in fact, to measure along the -ecliptic instead of the equator. Instead of having the axis of the inner -rings parallel to the axis of the earth, as in Fig. 9, he so arranged -matters that the axis of this system was separated from the earth’s axis -to the extent of the obliquity of the ecliptic, the circle R, Q, N, -therefore instead of being in the plane of the equator, was in that of -the ecliptic. Then it was plain to Hipparchus that he would, instead of -being limited to observe during eclipses of the moon, be able to reckon -from the sun at all times; because the sun moves always along the -ecliptic and the latitude of the sun is nothing. - -We will now describe the details of the instrument. There is first a -large circle, E, B, C, Fig. 9 (which is taken from a drawing of this -kind of instrument as constructed subsequently by Tycho Brahe), fixed in -the plane of the meridian, having its poles, D, C, pointing to the poles -of the heavens; inside this there is another circle, F, I, H, turning on -the pivots D, C, and carrying fixed to it the circle, O, P, arranged in -a plane at right angles to the points I, K, which are placed at a -distance from C and D equal to the obliquity of the ecliptic; so that I -and K represent the poles of the ecliptic, and the circle, O, P, the -ecliptic itself. There is then another circle, R, M, turning on the -pivots I and K, representing a meridian of latitude, and along which it -is measured. - -Then, as the sun is on that part of the ecliptic nearest the north pole, -in summer, its position is represented by the point F on the ecliptic, -and by N at the winter solstice; so, knowing the time of the year, the -sight Q can be placed the same number of degrees from F as the sun is -from the solstice, or in a similar position on the circle O P as the sun -occupies on the ecliptic. - -The circle can then be turned round the axis C, D, till the sight Q, and -the sight opposite to it, Q´, are in line with the sun. The circle, O, -R, will then be in the plane of the ecliptic, or of the path of the -earth round the sun. The circle, R, M, is then turned on its axis, I, K, -and the sights, R, R, moved until they point to the moon. The distance -Q, L, measured along O, P, will then be the difference in longitude of -the moon and sun, and its latitude, L, R, measured along the circle R, -M. - -But why should he use the moon? His object was to determine the -longitude of the stars, but his only method was to refer to the motion -of the sun, which could be laid down in tables, so that its longitude or -distance from the vernal equinox was always known. But we do not see the -stars and the sun at the same time; therefore in the day time, while the -moon was above the horizon, he determined the difference of longitude -between the sun and the moon, the longitude of the sun or its distance -from the vernal equinox being known by the time of the year; and after -the sun had set he determined the difference of longitude between the -moon and any particular star; and so he got a fair representation of the -longitude of the stars, and succeeded in tabulating the position of -1,022 of them. - -It is to the use of this instrument that we owe the discovery of the -precession of the equinoxes. - -[Illustration: - - FIG. 10.—Diagram Illustrating the Precession of the Equinoxes. -] - -After Hipparchus had fixed the position of a number of stars, he found -that on comparing the place amongst them of the sun at the equinoxes in -his day with its place in the time of Aristillus that the positions -differed—that the sun got to the equinox, or point where it crossed the -equator, a short time before it got to the place amongst the stars where -it crossed in the time of Aristillus; in fact, he found that the -equinoctial points retrograded along the equator, and Ptolemy (B.C. 135) -appears to have established the fact that the whole heavens had a slow -motion of one degree in a century which accounted for the motion of the -equinoxes. - -[Illustration: - - FIG. 11.—Revolution of the Pole of the Equator round the Pole of the - Ecliptic caused by the Precession of the Equinoxes. -] - -Let us see what we have learned from the observation of this motion, for -motion there is, and the ancients must be looked on with reverence for -their skill in determining it with their comparatively rude instruments. -In Fig. 10, A represents the earth at the vernal equinox, and at this -time the sun appears near a certain star, S, which was fixed by -Aristillus; but in the time of Hipparchus the equinox happened when the -sun was near a star, S´, and before it got to S. Now we know that the -sun has no motion round the earth, and that the equinox simply depends -on the position of the earth’s equator in reference to the ecliptic; so -that in order to produce the equinox when the earth is at E and before -it get to A, its usual place, all we have to do is to turn the pole of -the earth through a small arc of the dotted circle, and so alter its -position to that shown at F, when its equator and poles will have the -same position as regards the sun as they have at A, so the equinox will -happen when the earth is at E, and before it reaches A. This may be -practically represented by taking an orange and putting a -knitting-needle through it, and drawing a line representing the equator -round it, and half immersing it in a tub of water, the surface of which -represents the ecliptic. We are then able to examine these motions by -moving the orange round the tub to represent the earth’s annual motion, -and at the same time making the orange slowly whobble like a -spinning-top just before it falls, by moving the top of the -knitting-needle through a small arc of a circle in the same direction as -the hands of a clock at every revolution of the orange round the centre -of the tub. - -The points where the equator is cut by the surface of the water (or -ecliptic) will then change, as the orange whobbles, and the line joining -them, will rotate, and as the equinox happens when this line passes -through the sun, it will be seen that this will take place earlier at -each revolution of the orange round the tub. - -The equinox will therefore appear to happen earlier each year, so that -the tropical year, or the time from equinox to equinox, is a little -shorter than the sidereal year, or the time that the earth takes to -travel from a certain place in its orbit to the same again; for if the -earth start from an equinoctial point, the equinox will happen before it -gets to the same place where the equinoctial point was at starting. - -This is called the precession of the equinoxes. - -[Illustration: - - FIG. 12.—The Vernal Equinox among the Constellations, B.C. 2170. -] - -[Illustration: - - FIG. 13.—Showing how the Vernal Equinox has now passed from Taurus and - Aries. -] - -This discovery must be regarded as the greatest triumph obtained by the -early stargazers, and there is much evidence to show that when the -zodiac was first marked out among the central zone of stars, the Bull -and not the Ram was the first of the train. Even the Ram, owing to -precession, is no longer the leader, for the _sign_ Aries is now in the -constellation Pisces. The two accompanying drawings by Professor Piazzi -Smyth of the position of the vernal equinox among the stars in the years -2170 B.C. and 1883 A.D. will show how precession has brought about -celestial changes which have not been unaccompanied by changes of -religious ideas and observances in origin connected with the stars. - -[Illustration: - - FIG. 14.—Instrument for Measuring Altitudes. -] - -We now come to Ptolemy. There was another instrument used by Ptolemy, -and described by him, which we may mention here; it was called the -Parallactic Rules, so named perhaps because that ancient astronomer used -it first for the observation of the parallax of the moon. It consists of -three rods, D E, D F, E F, Fig. 14, two of which formed equal sides of -an isosceles triangle; and the third, which had divisions on it, made -the one at the base, or was the chord of the angle at the summit. One of -the equal sides, D F, was furnished with pointers, over which a person -observed the star, whilst the other, D E, was placed vertically, so that -they read off the divisions on E F, and then, by means of a table of -chords, the angle was found; this angle was the distance of the star -from the zenith. Ptolemy, wishing to observe with great accuracy the -position of the moon, made himself an instrument of this kind of a -considerable size; for the equal rulers were four cubits long, so that -its divisions might be more obvious. He rectified its position by means -of a plumb-line. Purbach, Regiomontanus, and Walther, astronomers of the -fifteenth century, employed this manner of observing, which, considering -the youth of astronomy, was by no means to be despised. This instrument, -constructed with great care, would have sufficiently been useful as far -as concerns certain measurements and would have furnished results -sufficiently exact; but the part of ancient astronomy that failed was -the way of measuring time with any precision. - -There were astronomers who proposed clepsydras for this purpose; but -Ptolemy rejected them as very likely to introduce errors; and indeed -this method is subject to much inconvenience and to irregularities -difficult to prevent. However, as the measurement of time is the soul of -astronomy, Ptolemy had recourse to another expedient which was very -ingenious. It consisted in observing the height of the sun if it were -day, or of a fixed star if it were night, at the instant of a phenomenon -of which he wished to know the time of occurrence, for the place of the -sun or star being known to some minutes of declination and right -ascension as also was the latitude of the place, he was able to -calculate the hour; thus when they observed, for example, an eclipse of -the moon, it was only necessary to take care to get the height of some -remarkable star at each phase of the eclipse, say at the commencement -and at the end, in order to be able to conclude the true time at which -it took place. This was the method adopted by astronomers until the -introduction of the pendulum. - - - - - CHAPTER IV. - TYCHO BRAHE. - - -Leaving behind us the results of the researches of Ptolemy, who -succeeded Hipparchus and whose methods have been described, and passing -over the astronomy of the Arabs and Persians as being little in advance -of Hipparchus and Ptolemy, we come down to the sixteenth century of our -era. - -Here we find ourselves in presence of the improvements in instruments -effected by a man whose name is conspicuous—Tycho Brahe—a Danish -nobleman who, in the year 1576, established a magnificent observatory at -Huen, which may be looked upon as the next building of importance after -that great edifice at Alexandria which has already been referred to. - -What Hipparchus was to the astronomy of the Ancients such was Tycho to -the astronomy of the Middle Ages. As such his life merits a brief notice -before we proceed to his work. He was born at Knudsthorp, near -Helsingborg, in Sweden, in 1546, and went to the University of -Copenhagen to prepare to study law; while there he was so struck with -the prediction of an eclipse of the sun by the astrological almanacks -that he gave all his spare time to the study of astronomy. In 1565 his -uncle died and Tycho Brahe fell into possession of one of his uncle’s -estates; and as astronomy, or astrology as it was then called, was -thought degrading to a man in his position by his friends, who took -offence at his pursuits and made themselves very objectionable, he left -for a short stay at Wittenberg, then he went to Rostock and afterwards -to Augsburg, where he constructed his large quadrant. He returned to his -old country in 1571; while there, Frederick II., King of Denmark, -requested him to deliver a course of lectures on astronomy and astrology -and became his most liberal patron. The King granted to Tycho Brahe for -life the island of Huen, lying between Denmark and Sweden, and built -there a magnificent observatory and apartments for Tycho, his assistants -and servants. The main building was sixty feet square, with observing -towers on the north and south, and a library and museum. Tycho called -this Uraniberg—the city of the heavens; and he afterwards built a -smaller observatory near called by him Sternberg—city of the stars, the -former being insufficiently large to contain all his instruments. - -The following is a list of these instruments as given in Sir David -Brewster’s excellent memoir of Brahe, in _Martyrs of Science_:— - - _In the South and greater Observatory._ - - 1. A semicircle of solid iron, covered with brass, four cubits - radius. - - 2. A sextant of the same materials and size. - - 3. A quadrant of one and a half cubits radius, and an azimuth circle - of three cubits. - - 4. Ptolemy’s parallactic rules, covered with brass, four cubits in - the side. - - 5. Another sextant. - - 6. Another quadrant, like No. 3. - -[Illustration: - - FIG. 15.—Portrait of Tycho Brahe (from original painting in the - possession of Dr. Crompton, of Manchester). -] - - 7. Zodiacal armillaries of melted brass, and turned out of the - solid, of three cubits in diameter. - - Near this observatory there was a large clock with one wheel two - cubits in diameter, and two smaller ones which, like it, indicated - hours, minutes, and seconds. - - _In the South and lesser Observatory._ - - 8. An armillary sphere of brass, with a steel meridian, whose - diameter was about four cubits. - - _In the North Observatory._ - - 9. Brass parallactic rules, which revolved in azimuth above a brass - horizon, twelve feet in diameter. - - 10. A half sextant, of four cubits radius. - - 11. A steel sextant. - - 12. Another half sextant with steel limb, four cubits radius. - - 13. The parallactic rules of Copernicus. - - 14. Equatorial armillaries. - - 15. A quadrant of a solid plate of brass, five cubits in radius, - showing every ten seconds. - - 16. In the museum was the large globe made at Augsburg. - - _In the Sternberg Observatory._ - - 17. In the central part, a large semicircle, with a brass limb, and - three clocks, showing hours, minutes, and seconds. - - 18. Equatorial armillaries of seven cubits, with semi-armillaries of - nine cubits. - - 19. A sextant of four cubits radius. - - 20. A geometrical square of iron, with an intercepted quadrant of - five cubits, and divided into fifteen seconds. - - 21. A quadrant of four cubits radius, showing ten seconds, with an - azimuth circle. - - 22. Zodiacal armillaries of brass, with steel meridians, three - cubits in diameter. - - 23. A sextant of brass, kept together by screws, and capable of - being taken to pieces for travelling with. Its radius was four - cubits. - - 24. A movable armillary sphere, three cubits in diameter. - - 25. A quadrant of solid brass, one cubit radius, and divided into - minutes by Nonian circles. - - 26. An astronomical radius of solid brass, three cubits long. - - 27. An astronomical ring of brass, a cubit in diameter. - - 28. A small brass astrolabe. - -Tycho Brahe carried on his work at Uraniberg for twenty-one years, and -appears to have been visited by many of the princes of the period and by -students anxious to learn from so great a man. In Frederick’s treatment -of Tycho Brahe we have an early and munificent and, in its results, most -successful instance of the endowment of research. On the death of -Frederick II., in 1588, Christian IV. came to the throne. The successor -cared little for astronomy, and his courtiers, who were jealous of -Tycho’s position, so acted upon him that the pension, estate and canonry -with which Tycho had been endowed were taken away. Unable to put up with -these insults and loss of his money, he left for Wandesburg in 1597, -where he was entertained by Count Henry Rantzau. It was now that he -wrote and published the _Astronomiæ instauratæ Mechanica_, a copy of -which, together with his catalogue of 1000 stars, was sent to the -Emperor Rudolph II., who invited him to go to Prague. This he accepted, -and he and his family went to the castle of Benach in 1599, and a -pension of 3000 crowns was given to him. Ten years afterwards he removed -with his instruments into Prague to a house purchased and presented to -him by the Emperor; here he died in the same year. - -The wonderful assistance which Tycho Brahe was able to bring to -astronomy shows that then, as now, any considerable advance in physical -investigation was more or less a matter of money, and whether that money -be found by individuals or corporations, now or then, we cannot expect -any considerable advance without such a necessary adjunct. - -[Illustration: - - FIG. 16.—Tycho Brahe’s Observatory on the Island of Huen. -] - -The principal instruments used at first by Tycho Brahe resembled the -Greek ones, except that they were much larger. Hipparchus was enabled to -establish the position of a heavenly body within something less than one -degree of space—some say within ten minutes; but there was an immense -improvement made in this direction in the instruments used by Tycho. - -One of the instruments which he used was in every way similar to the -equatorial astrolabe designed, by Hipparchus, and was called by Tycho, -the ‘armillæ equatoriæ’ (Fig. 8). With that instrument in connection -with others Tycho was enabled to make an immense advance upon the work -done by Hipparchus. - -Tycho, like Hipparchus, having no clock, in the modern sense, was not -able to determine the difference of time between the transit of the sun -or a particular star over the meridian, so that he was compelled to -refer everything to the sun at the instant of observation, and he did -that by means of the moon. Hipparchus, as we have seen, determined the -difference of longitude, or right ascension, between the sun and the -moon and between the moon and the stars, in the manner already -described, and so used the moon as a means of determining differences -between the longitude or right ascension of the sun and the stars. - -Now Tycho, using an instrument similar to that of Hipparchus, saw that -he would make an improvement if instead of using the Moon he used Venus; -for the measure of the surface of the moon was considerable, and could -not be easily reckoned, and its apparent position in the heavens was -dependent on the position of a person on the earth,—because it is so -near the earth that it has a sensible parallax, that is, a person at the -equator of the earth might see the moon in the direction of a certain -star; but, on going to the pole, the moon would appear below the line of -the star. If one were looking at a kite in the air to the south and then -walked towards the south, the kite would gradually get over head, and on -proceeding further it would get north. To persons at different stations -the kite would appear in different positions, and the nearer the kite -was to the observer the less distance he would have to go to make it -change its place. So also with the moon; it is so near to us that a -change of place on the earth makes a considerable difference in the -direction in which it is seen. Instead, therefore, of using the Moon, -Tycho used Venus, and so mapped 1,500 stars after determining their -absolute right ascensions, in this manner without the use of clocks. - -Fig. 8 shows the instrument called the “armillæ equatoriæ,” which he -constructed, and which was based upon the principle of that which -Hipparchus had used. Here the axis of motion, C, D, of these circles is -so arranged that it is absolutely parallel to the axis of the earth; but -instead of the circle R, Q, N, representing the equator, being fixed, it -revolved in its own plane while held by the circle G, H, I, making its -use probably more easy, but leaving the principles unaltered. - -Tycho Brahe also used another similar instrument of much larger size for -the same purposes as the one we have just considered. It consisted of a -large circle, which was seven cubits in diameter, corresponding to the -circle K, L, M, Fig. 8; and carrying the sights in the same manner, it -was placed in a circular pit in the ground, with its diameter pointing -towards the pole. This was used for measuring declinations. The circle -R, Q, N, Fig. 9, was represented by a fixed circle carried on pillars -surrounding the pit, and along which the right ascension of the star was -measured. This instrument, therefore, was more simple than the smaller -one, and probably much more accurate. - -Tycho was not one of those who was aware of the true system of the -universe; he thought the earth fixed, as Ptolemy and others did; but -whether we suppose the earth to be movable in the middle of the vault of -stars or stationary, in either case that position is absolutely -immaterial in ascertaining the right ascension of stars. If one takes -the terrestrial globe, and looks upon the meridians, it is at once clear -that the distance from meridian to meridian remains unaltered, whether -the globe is still or turning round: so the stars maintain their -relative positions to each other, whether we consider the earth in -motion or the sphere in which the stars are placed to revolve round it. - -[Illustration: - - FIG. 17.—Tycho Brahe’s System. -] - -The introduction of clocks gave Tycho the invention of the next -instrument, which was the transit circle. At this time the pendulum had -not been invented; but it struck him and others that there was no -necessity for having two or more circles rotating about an axis parallel -to the earth’s axis, as in the astrolabes or armillæ, but only to have -one circle in the plane of the meridian of the place. So that, by the -diurnal movement of the earth round its own axis, all the stars in the -heavens would gradually and seriatim be brought to be visible along the -arc of the circle, so he arranged matters in the following way. - -The stars were observed through a hole in a wall and through an eyehole, -sliding on a fixed arc. The number of degrees marked at the eyehole on -the arc at once gave the altitude of the heavenly bodies as seen through -that hole. If a star was very high, it would be necessary for an -observer to place his eye low down to be able to see it. If it were near -the horizon, he would have to travel up to the top of this circle to -determine its altitude, and having done that, and knowing the latitude -of the place of observation, the observer will be able to determine the -position of the star with reference to the celestial equator. The actual -moment at which the star was seen was noted by the clock, and the time -that the sun had passed the hole being also previously noted, the length -of time between the transits was known; and as the stars appear to -transit or pass the meridian every twenty-four hours, it was at once -known what part of the heavens was intercepted between the sun and the -star in degrees, or, as is usually the case, the right ascension of the -star was left expressed in hours and minutes instead of degrees; thus he -had a means of determining the two co-ordinates of any celestial body. - -The places of the comet of 1677, which Tycho discovered, and of many -stars, were determined with absolute certainty; but astronomers began to -be ambitious. It was necessary in using this instrument to wait till a -celestial body got to the meridian. If it was missed, then they had to -wait till the next day; and further, they had no opportunity whatever of -observing bodies which set in the evening. - -[Illustration: - - FIG. 18.—The Quadrans Maximus reproduced from Tycho’s plate. -] - -Seeing, therefore, that clocks were improving, it was suggested by one -of Tycho’s compeers, the Landgrave of Hesse-Cassel, that by an -instrument arranged something like Fig. 18, it would be possible to -determine the exact position of any body in the heavens when examined -out of the meridian, and so they got again to extra-meridional -observations. - -The instrument used by Tycho Brahe for the purpose, called the _Quadrans -Maximus_, is represented in Fig. 18. In this there is the quadrant B, D, -one pointer being placed, as shown at the bottom, near H, and the other -at the top, C. These pointers or sights were directed at the star by -moving the arm C, H, on the pivot A, and turning the whole arm and -divided arc round on the axis N, R. The altitude of the star is then -read off on the quadrant B, D, and the azimuth, or number of degrees -east or west of the north and south line, is then read off on the circle -Q, R, S. The screws Y, Y, served to elevate the horizontal circle, and -level it exactly with the horizon, and the plummets W and V, hanging -from G, were to show when the circle was level or not; for the part A, -G, being at right angles to the circle should be upright when the circle -is level, so that if A, G, is upright in all positions when moved round -the circle in azimuth, the circle is horizontal. - -Here, then, is an instrument very different in principle from what we -had before. In this case the heavens are viewed from the most general -standpoint we can obtain—the horizon; but observations such as these -refer to the position of the place of observation absolutely, without -any reference to the position of the body with respect to the equator or -the ecliptic; but knowing the latitude of the place of observation _and -the time_, it was possible for a mathematical astronomer to reduce the -co-ordinates to right ascension and declination, and so actually to look -at the position of these bodies with reference to the celestial sphere. - -Tycho also had various other instruments of the same kind, differing -only in the position of the quadrant D, B, and of the circle on which -the azimuth was measured. These instruments are the same in principle as -our modern alt-azimuth, which will be described hereafter, one form -having a telescope and the other being without it. - -[Illustration: - - FIG. 19.—Tycho’s Sextant. -] - -Fig. 19 is yet another very important instrument invented by Tycho -Brahe; it is the prototype of our modern much used sextant. It was used -by Tycho Brahe for determining the distance from one body to another in -a direct line; a star or the moon, say, was observed by the pointers C, -A, while another was observed by the pointers N, A, by another observer. -The number of degrees then between N and C gave the angular distance of -the two bodies observed. This instrument was mounted at E, so that it -could be turned into any position. Not only then had this instrument its -representative in our present sextant, but it was used in the same way, -not requiring to be fixed in any one position. We also find represented -in Tycho Brahe’s book another form of the same instrument, the sight A -being next the observer, instead of away from him, so that he could -observe the two stars through the sights N and C without moving the eye. -In this form only one observer was required instead of two as in the -last. - -There was also another instrument, Fig. 6, used by this great -astronomer, very similar to Ptolemy’s parallactic rules, used for -measuring zenith distances, or the distances of stars from the part -exactly overhead. The star or moon was observed by the sights H, I, and -the angle from the upright standard D, K, given by divisions on the rod -E, F, D, E being placed exactly upright by a plummet, and being also -able to turn on hinges at B and C, any part of the sky could be reached. -There is one more of his instruments that needs notice—he had so many of -all kinds that space will not allow reference to more than a very few. -This one was for measuring the altitudes of the stars as they passed the -meridian; it is a more convenient form of the mural quadrant, and -instead of a hole in the wall, there are sights on a movable arm, -working over a divided quadrant fixed in the plane of the meridian, just -like the quadrant outside the horizontal circle, so the observer had no -reason to move up or down according as the star was high or low. - -Here then ends the pre-telescopic age. Tycho was one of the very last of -the distinguished astronomers who used instruments without the -telescope. We began with the horizon, and we have now ended with the -meridian. We also end with a power of determining the position of a -heavenly body to ten seconds of space, the instrument of the Greeks -reading to 10´ and those of Tycho to 10˝. - -We began with the immovable earth fixed in the midst of the vault of the -sky, and on this assumption Tycho Brahe made all his observations, which -ended in enabling Kepler to give us the true system of the world, which -was the requisite basis for the crowning triumph of Newton. - - - - - BOOK II. - _THE TELESCOPE._ - - - - - CHAPTER V. - THE REFRACTION OF LIGHT. - - -It is difficult to give the credit of the invention of the telescope to -any one particular person, for, as in the case of most instruments, its -history has been a history of improvements; and whether we should give -the laurel to Jansen, Baptista Porta, Galileo or to others whose names -are unknown, is an invidious task to decide; we will therefore not enter -in any way into the question, interesting though it be, as to who was -the inventor of the “optick tube,” as the telescope was called by its -first users. - -The telescope is not a thing in the ordinary sense—it is a combination -of things, the things being certain kinds of lenses, concave and convex, -known and used as spectacles long before they were combined to form the -telescope. - -The first telescopes depended on the refraction of light; others, to -which attention will be called in a future chapter, depended on -reflection. - -[Illustration: - - FIG. 20.—View and Section of a Prism. -] - -In order to understand the action of a lens, it is necessary to -understand the action of a prism. By the aid of Fig. 20 the action of -the lenses of which telescopes are constructed will be understood. A -prism is a piece of glass, or other transparent substance, the sides of -which are so inclined to each other that its section is a triangle, and -its action on light passing through it is to change the direction of the -course of the beam. If we examine Fig. 21 we shall understand the action -clearly. It is a known law, that when a beam of light falls obliquely on -the surface of a medium more dense than that through which it has been -passing, its direction is changed to a new one, nearer the line drawn at -right angles to that surface, railed the normal. For instance, the ray -S, I, falling on the prism at I, is bent into the course I, E, which is -in a direction nearer to that of N, I, produced inside the prism. On -emerging, the reverse takes place, and the ray is bent away from the -normal E, N´, and takes the course E, R. In the second diagram, Fig. 21, -the ray S, I, called the incident ray, coincides with the normal to the -surface, so it is not refracted until it reaches the second surface, -when it has its path changed to E, R, instead of taking its direct -course shown by the dotted line. This bending of the ray is very plainly -shown with an electric lamp and screen. If a trough with parallel sides -be placed so as to intercept part of the light coming from the electric -lamp, so that part shall pass through it and part above, we have the -image of the hole in the diaphragm of the lantern on the screen -unchanged. Now, if the trough be filled with water, no difference -whatever is made in the position of the light on the screen, because the -water, which is denser than the air, is contained in a trough with -parallel sides; but by opening the sides like opening a book, or by -interposing another trough with inclined sides, shaped like a =V=, that -parallelism is destroyed, and then the light passing through it will be -deflected upwards from its original course, and will fall higher on the -screen; by opening the sides more and more, one is able to alter the -direction of the light passing through the prism, which has been -constructed by destroying the parallelism of the two sides. - -[Illustration: - - FIG. 21.—Deviation of Light in Passing at Various Incidences through - Prisms of Various Angles. -] - -The refraction of light then depends upon the density of the substance -through which it passes, on the angle of incidence of the ray, on the -angle of the prism, and also on the colour of the light, about which we -shall have something to say presently. - -Let us now pass from the prism to the lens; for having once grasped the -idea of refraction there will be no difficulty in seeing what a lens -really is. - -With the prism just considered, placed so that a vertical section is -represented by a =V=, a ray is thrown upwards; if another similar prism -be placed with its base in contact with the base of the other, and its -apex upwards, so that its section will be represented by a =V= reversed, -=Ʌ=, it is clear this will turn the rays downwards, so that the rays, on -emerging from both prisms will tend to meet each other, as shown, in -Fig. 22, where one ray is turned down to the same extent that the other -is turned up; so that by the combination of two prisms the two rays are -brought to a point, which is called a _focus_. Now, if instead of -putting the prisms base to base, they are put apex to apex, a contrary -action takes place, and by this means one is able to cause two rays of -light to diverge instead of converging, so that the prisms, placed apex -to apex, cause the rays to diverge, and when placed base to base they -cause the light to converge. - -[Illustration: - - FIG. 22.—Convergence of Light by Two Prisms Base to Base. -] - -If instead of having two prisms merely, there be taken a system having -different angles at their apices, and from each prism there be cut a -section, beginning by cutting off the apex of the most powerful prism, a -slice from below the apex of the next, and a slice below the -corresponding part of the next, and so on; and then if these slices be -laid on each other so as to form a compound prism, and another similar -prism be placed with its base to this one, we get what is represented in -Fig. 23. These different slices of prisms become more and more -prismatic, that is, they form parts of prisms of greater angle, as they -approach the ends. We can imagine a section of such a system as thin as -we please. Suppose we had such a section and put it in a lathe, rotating -it on the axis A B, we should describe a solid figure, and if we suppose -all the angles rounded off, so that it is made thinner and thinner as we -recede from the centre, the prism system is turned into a lens having -the form represented in Fig. 24. In a similar manner, lenses thinner in -the middle than at the edges, called concave lenses, can he constructed, -some forms of which are represented in section in Fig. 25. It is also -obvious that convex lenses of all curves and combinations of curves can -be made, some of which appear in Fig. 26. - -[Illustration: - - FIG. 23.—Formation of a Lens from Sections of Prisms. -] - -[Illustration: - - FIG. 24.—Front View and Section of a Double Convex Lens. -] - -[Illustration: - - FIG. 25.—Double Concave, Plane Concave, and Concavo-Convex Lenses. -] - -The action of such lenses upon the light proceeding from any source may -now be considered. If there is a parallel beam proceeding from a lamp, -or from the sun, and it falls on the form of lens, called a convex lens, -which bulges out in the middle, we learn from Fig. 27, that the upper -part acts like the upper prism just considered and turns the light down, -and the lower acts in the reverse manner and turns the light up, and the -sides act in a similar manner; and as the inclination of the surfaces of -the lens increases as we approach the edge, the rays falling on the -parts near the edge are turned out of their course more than those -falling near the centre, so that we have the rays converged to a point -F, called the focus of the lens; and as the rays from an electric lamp -are generally rendered parallel by means of the lenses in the lantern, -called the condensers, the rays from such a lamp falling on a convex -lens will come to a focus at just the same distance from the lens, -called its principal focal length as they would do if they came from the -sun or stars. - -[Illustration: - - FIG. 26.—Double Convex, Plane Convex, and Concavo-Convex Lenses. -] - -[Illustration: - - FIG. 27.—Convergence of Rays by Convex Lens to Principal Focus. -] - -So far we have brought rays to a focus, and on holding a piece of paper -at the focus of the convex lens, as just mentioned, there appears on it -a spot of light; and every one knows that if this experiment be -performed with the sun, one brings all the rays falling on the lens -almost to a point, and the longer waves of light will set fire to the -paper; and on this principle burning-glasses are constructed. If, -however, the rays are not parallel when falling on the lens, but -diverging, they are not brought to a focus so near the lens, and the -nearer the luminous source or object is, the further off will the light -be brought to a focus on the other side. If matters are reversed, and -the luminous source be placed in the focus, the rays of light, when they -leave the lens, will converge to the position of the original source; so -that there are two points, one on either side of the lens, which are the -foci of each other S, S´, Fig. 28, called conjugate foci; as one -approaches the lens the other recedes, and _vice versâ_, and it is -obvious that when the one approaches the lens so as to coincide with the -principal focus, the other recedes to an infinite distance, and the -emergent rays are parallel. - -[Illustration: - - FIG. 28.—Conjugate Foci or Convex Lens. -] - -[Illustration: - - FIG. 29.—Conjugate Images. -] - -[Illustration: - - FIG. 30.—Diagram explaining Fig. 29. -] - -Now let us consider how images are formed. If we take a candle, Fig. 29, -and hold the lens a little distance away from it, then, on placing a -screen of paper just on the other side of the lens, there will be a -small flame depicted on it, an exact representation of the real flame: -and it is formed in this way: Consider the rays proceeding from the top -of the flame, which are represented separately in Fig. 30, where A -represents the top. One of these rays, A _a_, passing through the centre -of the lens _o_, will he unaffected because the surfaces through which -it passes are parallel to each other; and we know from the property of -the lens that all the other rays from A will, on passing through it, be -brought to a focus somewhere on A _a_, depending on the curvature of the -lens, and in the case of our lens it is at _a_. - -[Illustration: - - FIG. 31.—Dispersion of Rays by a Double Concave Lens. -] - -In like manner also all the rays from B are brought to a focus at _b_, -and so on with all other parts of A, B, which in this case represents -the flame, each will have its corresponding focus; there being cones of -rays from every point of the object and to every point of the image, -having for their bases the convex lens, and we get an image or exact -representation of our candle flame. It will further be noticed that the -image _a b_ is smaller than A B, in proportion as the distance _a b_ is -less than A B; so that if we increase the focal length of the lens till -_a b_ is twice the distance away from the lens, it will become double -its present size. - -If now the flame be brought nearer the lens, its image _a b_ becomes -indistinct; and we must move the screen further away in order to render -the image again clear; hence the place of the focus depends on the -distance of the object, and the candle and its image must correspond to -two conjugate foci. - -[Illustration: - - FIG. 32.—Horizontal Section of the Eyeball. _Scl_, the sclerotic coat; - _Cn_, the cornea; _R_, the attachments of the tendons of the recti - muscles; _Ch_, the choroid; _Cp_, the ciliary processes; _Cm_, the - ciliary muscle; _Ir_, the iris; _Aq_, the aqueous humour; _Cry_, the - crystalline lens; _Vi_, the vitreous humour; _Rt_, the retina; _Op_, - the optic nerve; _Ml_, the yellow spot. -] - -If now rays be passed from the lantern or sun through a concave lens, -Fig. 31, they are not brought to a focus, but are dispersed and travel -onwards, as if they came from a point, F, which is called its virtual -focus; and if rays are first converged by a convex lens, and then, -before they reach the focus are allowed to fall on a concave one, we -can, by placing the lenses a certain distance apart, render the -converging rays again parallel; or we can make them slightly divergent, -as if they came, not from an infinite distance, but from a point a foot -or two off. The application of this arrangement will appear hereafter. - -What has now been said on the action of the convex lens will enable us -to consider the optical action of the eye, without which we do little in -astronomy. As to the way that the brain receives impressions from the -eye we need say nothing, for that belongs to the domain of physiology, -except indeed this, that an image is formed on the retina by a chemical -decomposition, brought about by the dissociating action of certain rays -of light in exactly the same way as on a photographic plate. Optically -considered, the eye consists of nothing more than a convex lens, _Cry_, -Fig. 32, and a surface, _Rt_, extending over the back of the eyeball, -called the retina, on which the objects are focussed, but the rays of -light falling on the cornea _Cn_, are refracted somewhat, so that it is -not quite true to say that the crystalline lens does all the work, but -for our present purpose it is sufficiently correct, and we shall -consider their combined action as that of a single lens. - -The outer coat of the eyeball, shown in section in Fig. 32, is called -the sclerotic, with the exception of that more convex part in front of -the eye, called the cornea; behind this comes the aqueous humour and -then the iris, that membrane of which the colour varies in different -people and races. In the centre of this is a circular aperture called -the pupil, which contracts or expands according to the brightness of the -objects looked at, so that the amount of light passing into the eye is -kept as far as possible constant. Close behind the iris comes the -crystalline lens, the thickness of which can be altered slightly by the -ciliary muscle. In the space between the lens and the back of the eye is -a transparent jelly-like substance called the vitreous humour. Finally -comes the retina, a most delicate surface chiefly composed of nerve -fibres. It is on this surface, that the image is formed by the curved -surfaces of the anterior membranes, and through the back of the eyeball -is inserted the mass of filaments of the optic nerve making -communication with the brain; these filaments on reaching the inside of -the eye spread out to receive the impressions of light. - -Here then, we have a complete photographic camera; the crystalline lens -and cornea, separated by the aqueous humour, representing the -compound-glass camera lens, and the retina standing in the place of the -sensitive plate. - -[Illustration: - - FIG. 33.—Action of Eye in Formation of Images. -] - -The path of the light forming an image on the retina is shown in Fig. -33, where A B is the object, and _a b_ its image, formed in exactly the -same way as the image of the candle-flame which we have just considered; -in fact, the eye is exactly represented by a photographic camera, the -iris acting in the same manner as the stops in the lens, limiting its -available area, and by contracting, decreasing the amount of light from -bright objects, and at the same time increasing the sharpness of -definition, for in the case of the eye, the luminous rays obey the known -laws of propagation of light in media of variable form and density, and -we have only simple refraction to deal with. The next matter to be -considered is that the nearer the object A B is to the eye, the larger -is the angle A, _o_, B, and also _a_, _o_, _b_, and therefore the image -on the retina is larger; but there is a limit to the nearness to which -the object can be brought, for, as we found with the candle, the -distance between the lens and the image must be increased as the object -approaches, or the curvature of the lens itself must be altered, for if -not the ray forming the rays from each point of the object will be too -divergent for the lens to be able to bring them to a focus. Now in the -eye there is an adjustment of this sort, but it is limited so that -objects begin to get indistinct when brought nearer the eye than perhaps -six inches, because the rays become too divergent for the lens to bring -them to a focus on the retina, and they tend to come to a focus behind -the retina, as in Fig. 34; but we may assist the eye lens by using a -glass convex lens in front of it, between it and the object. It is for -this reason that spectacle glasses are used to enable long-sighted -persons to see clearly. - -[Illustration: - - FIG. 34.—Action of a Long-sighted Eye. -] - -We may also use a much stronger lens, and so get the object very near -the lens and eye, as in Fig. 35, where _a b_ is the object so near the -eye that, if it were not for the lens L, its image would not come to a -focus on the retina at all. The effect of the lens is to make the rays -proceeding in a cone from _a_ and _b_ less divergent, so that after -passing through it, they proceed to the eye-lens as if they were coming -from the points A and B, a foot or so away from the eye, and so the -object _a b_ appears to be a much larger object at a greater distance -from the eye. - -[Illustration: - - FIG. 35.—1. Diagram showing path of rays when viewing an object at an - easy distance. 2. Object brought close to eye when the lens L is - required to assist the eye-lens to observe the image when it is - magnified. -] - -A convex lens then has the power of magnifying objects when brought near -the eye, and its action is clearly seen in Fig. 35, where the upper -figure shows the arrow at as short a distance from the eye as it can be -seen distinctly with an ordinary eye, and the lower figure shows the -same arrow brought close to the eye, and rendered distinctly visible by -the lens when a magnified image is thrown on the retina, as if there was -a real larger arrow somewhere between the dotted lines at the ordinary -distance of distinct vision. It is also obvious that the nearer the -object can be brought to the eye-lens the more magnified it is, just as -an object appears larger the nearer it is brought to the unaided eye. - -We have been hitherto dealing with the effect of a _convex_ lens on the -rays passing to the eye. We will now deal with a _concave_ one. - -We found that the power of adjustment of the normal eye was sufficient -to bring parallel rays, or those proceeding from a very distant object, -and also slightly diverging rays, to a focus on the retina. Parallel or -slightly divergent rays are most easily dealt with, and slightly -convergent rays can also be focussed on the retina; but if the eye-lens -is too convex, as is the case with short-sighted people, Fig. 36, a -concave lens of slight curvature is used to correct the eye-lens and -bring the image to a focus on the retina instead of in front of it. - -[Illustration: - - FIG. 36.—Action of Short-sighted Eye. -] - -If the rays are very convergent, as those proceeding from a convex lens -and coming to a focus, the lens of a normal eye will bring them to a -focus far in front of the retina, as if the person were very -short-sighted. But by interposing a sufficiently powerful concave lens -the rays are made less convergent or parallel, and the eye-lens brings -them to a focus on the retina, as if they came from a near object, so -the use of convex and concave lenses placed close to the eye is to -render divergent or convergent rays nearly parallel, so that the -eye-lens can easily focus them, and therefore one of the conditions of -the telescope is that the rays which come into our eye shall be parallel -or nearly so. - - - - - CHAPTER VI. - THE REFRACTOR. - - -In the telescope as first constructed by Galileo there are two lenses, -so arranged that the first, a convex one, A B Fig. 37, converges the -rays, while the second, C D, a concave one, diverges them, and renders -them parallel, ready for the eye; the rays then, after passing through C -D, go to the eye as if they were proceeding along the dotted lines from -an object M M, closer to the eye instead of from a distant object, and -so, by means of the telescope, the object appears large and close. - -[Illustration: - - FIG. 37.—Galilean Telescope. A B, convex lens converging rays; C D, - concave lens sending them parallel again and fit for reception by - the eye. -] - -It is this that constitutes the telescope. But nowadays we have other -forms, as we are not content with the convex combined with the concave -lens, and modern astronomy requires the eyepiece to be of more elaborate -construction than those adopted by Galileo and the first users of -telescopes, although this form is still used for opera-glasses and in -cases where small power only is required. Having the power of converging -the light and forming an image by the first convex lens or object glass, -as we saw with the candle flame (Fig. 29), and an opportunity of -enlarging this image by means of a magnifying or convex eyepiece, we can -bring an image of the moon, or any other object, close to the eye, and -examine it by means of a convex lens, or a combination of such lenses. -So we get the most simple form of refracting telescopes represented in -Fig. 38, in which the rays from all points of the object—let us take for -instance an arrow—are brought to a focus by the object-glass A, forming -there an exact representation of the real arrow. In the figure two cones -of rays only are delineated, namely, those forming the point and feather -of the arrow, but every other point in the arrow is built up by an -infinite number of cones in the same way, each cone having the -object-glass for its base. By means of the lens C we are able to examine -the image of the arrow B, since the rays from it are thus rendered -parallel, or nearly so, and to the eye they appear to come from a much -larger arrow at a short distance away. We can draw their apparent -direction, and the apparent arrow (as is done in Fig. 37 by the dotted -lines), and so the object appears as magnified, or, what comes to the -same thing, as if it were nearer. - -The difference between this form and that contrived by Galileo is this: -in the latter the rays are received by the eyepiece while converging, -_and rendered parallel by a concave lens_, while in the former case the -rays are received by the eyepiece on the other side of the focus, where -they have crossed each other and are diverging, _and are rendered -parallel by a convex lens_. - -We may now sum up the use of the eye-lens. The image is brought to a -focus on the retina, because the object is some distance off, and the -rays from every point, (as from A and B, Fig. 35), on reaching the eye, -are nearly parallel; but it is not necessary that they should be -absolutely parallel, as the eye is capable of a small adjustment, but if -one wishes to see an object much nearer (as in the lower figure), it is -impossible to do it unless some optical aid is obtained, for the rays -are too divergent, and cannot be brought to a focus on the retina. What -does that optical aid effect? It enables us to place the object in the -focus of another lens which shall make the rays parallel, and fit for -the lens of the eye to focus on the retina, and since the object can by -this means be brought close to the lens and eye, it forms a larger image -on the retina. Dependent on this is the power of the telescope. - -[Illustration: - - FIG. 38.—Telescope. A, object-glass, giving an image at B; C, lens for - magnifying image B. -] - -We shall refer later on to the mechanical construction of the telescope. -Here it may be merely stated that the smaller ones consist of a brass -tube, the object-glass held in a brass ring screwed in at one end of the -tube and a smaller tube carrying the eyepiece sliding in and out of the -large tube and sometimes moved by a rack and pinion motion, at the -other. The larger ones as mounted for special uses will also be fully -described farther on. - -[Illustration: - - FIG. 39.—Diagram Explaining the Magnifying Power of Object-glass. -] - -The power of the telescope depends on the object-glass as well as on the -eyepiece; if we wish to magnify the moon, for instance, we must have a -large image of the moon to look at, and a powerful lens to see that -image. By studying Fig. 39 the fundamental condition of producing a -large image by a lens will be seen. Suppose we wish to look at an object -in the heavens, the diameter of which is one degree; if the lens throws -an image of that body on to the circumference of a circle of 360 inches, -then, as there are 360 degrees in a circle, that image will cover one -inch; let the circle be 360 yards, and the image of a body of one degree -will cover one yard; and to take an extreme case and suppose the -circumference of the circle to be 360 miles, then the image will be one -mile in diameter. - -This is one of the principal conditions of the action of the -object-glass in enabling us to obtain images which can be magnified by a -lens, and by such magnification made to appear nearer to us than they -are. - -Galileo used telescopes which magnified four or five times, and it was -only with great trouble and expense that he produced one which magnified -twenty-three times. - -Now, after what has been said of focal length, one will not be surprised -to hear of those long telescopes produced in the very early days, a few -of which are still extant; these show as well as anything the enormous -difficulty which the early employers of telescopes had to deal with in -the material they employed. One can scarcely tell one end of the -telescope from the other; all the work was done in some cases by an -object-glass not more than half an inch in effective diameter. - -It might be supposed that those who studied the changes of places and -the positions of the heavenly bodies would have been the first to gain -by the invention of the telescope, and that telescopes would have been -added to the instruments already described, replacing the pointers. For -such a use as this a telescope of half an inch aperture would have been -a great assistance. But things did not happen so, because the invention -of the telescope gave such an impetus to physical astronomy that the -whole heavens appeared novel to mankind. Groups of stars appeared which -had never been seen before; Jupiter and Saturn were found to be attended -by satellites; the sun, the immaculate sun, was determined after all to -have spots, and the moon was at once set upon and observed with -diligence and care; so that there was a very good reason why people -should not limit the powers of the telescope to employing it to -determine positions only. The number of telescopes was small, and they -could not be better employed than in taking a survey of all the -marvellous things which they revealed. It was at this time that the -modern equatorial was foreshadowed. Galileo, and his contemporaries -Scheiner and others, were observing sun-spots, and the telescope, Fig. -40, which Scheiner arranged, a very rough instrument, with its axis -parallel to the earth’s axis, and allowed to turn so that Scheiner might -follow the sun for many hours a day, was one of the first. This -instrument is here reproduced, because it was one of the most important -telescopes of the time, and gathered in to the harvest many of the -earliest obtained facts. - -[Illustration: - - FIG. 40.—Scheiner’s Telescope. -] - -Since by means of little instruments like these, so much of beauty and -of marvel could be discovered in the skies, it is no wonder that every -one who had anything to do with telescopes strained his nerves to make -them of greater power, by which more marvels could be revealed. - -It was not long before those little instruments of Scheiner expanded -into the long telescopes to which reference has been made. But there was -a difficulty introduced by the length of the instrument. The length of -the focus necessary for magnification spread the light over a large -area, and therefore it was necessary to get an equivalent of light by -increasing the aperture of the object-glasses in order that the object -might be sufficiently bright to bear considerable magnification by the -eyepiece,—and now arose a tremendous difficulty. - -One part of refraction, namely, deviation, enables us to obtain, but the -other half, dispersion, prevents our obtaining, except under certain -conditions, an image we can make use of. By dispersion is meant the -property of splitting up ordinary light into its component colours, of -which we shall say more in dealing with spectrum analysis. If we wish to -get more light by increasing the aperture of the telescope, the -deviation of the light passing through the edge of the object-glass is -increased, and with it the dispersion, the result of this increase of -deviation. If the light of the sun be allowed to fall through a hole -into a darkened chamber, and then through a prism, Fig. 41, it is -refracted, and instead of having an exact reproduction of the bright -circle we have a coloured band or spectrum. The white light when -refracted is not only driven out of its original course—deviated—but it -is also broken up—dispersed—into many colours. We have a considerable -amount of colour; and this the early observers found when they increased -the size of their telescopes, for it must be remembered that a lens is -only a very complex prism. - -[Illustration: - - FIG. 41.—Dispersion of Light by Prism. -] - -First, they increased the size by enlarging the object-glasses, and not -the focal length; but when they had done that they had that extremely -objectionable colour which prevented them seeing anything well. The -colour and indistinctness came from an overlapping of a number of -images, as each colour had its own focus, owing to varying -refrangibilities. They found, therefore, that the only _effective_ way -of increasing the power of the telescope was by increasing its focal -length so as to reduce the _dispersing_ action as much as possible, and -so enlarging the size of the actual image to be viewed, without at the -same time increasing the angular deviation of the rays transmitted -through the edges of the lens. The size of the image corresponding to a -given angular diameter of the object is in the direct proportion of the -focal length, while the flexure of the rays which converge to form any -point of it is in the same proportion inversely. - -[Illustration: - - FIG. 42.—Diagram Showing the Amount of Colour Produced by a Lens. -] - -To take an example. In the case of an object-glass of crown-glass, the -space over which the rays are dispersed is one-fiftieth of the distance -through which they are deviated, and it will be seen by reference to -Fig. 42, that if the red rays are at R, and the blue at B, the distance -A B is fifty times R B, and as these distances depend on the diameter of -the lens only, we can increase the focal length, and so increase the -size of the image without altering the dispersion R B, and so throw the -work of magnifying on the object-glass instead of on the eyepiece, which -would magnify R B equally with the image itself. So that in that time, -and in the time of Huyghens, telescopes of 100, 200, and 300 feet focal -length were not only suggested but made, and one enthusiastic stargazer -finished an object-glass, the focal length of which was 600 feet. -Telescopes of 100 and 150 feet focal length were more commonly used. The -eyepiece was at the end of a string, and the object-glass was placed -free to move on a tall pole, so that an observer on the ground, by -pulling the string, might get the two glasses in a line with the object -which he wished to observe. - -So it went on till the time of Sir Isaac Newton, who considered the -problem very carefully—but not in an absolutely complete way. He came to -the conclusion, as he states in his _Optics_, that the improvement of -the refracting telescope was “desperate;” and he gave his attention to -reflecting telescopes, which are next to be noticed. - -Let us examine the basis of Sir Isaac Newton’s statement, that the -improvement of the refracting telescope was desperate. He came to the -conclusion that in refraction through different substances there is -always an unchanged relation between the amount of dispersion and the -amount of deviation, so that if we attempt to correct the action of one -prism by another acting in an opposite direction in order to get white -light, we shall destroy all deviation. But Sir Isaac Newton happened to -be wrong, since there are substances which, for equivalent deviations, -disperse the light more or less. So by means of a lens of a certain -substance of low dispersive power we can form an image slightly -coloured, and we can add another lens of a substance having a high -dispersive power and less curvature and just reverse the dispersion of -the first lens without reversing all its deviating power. - -The following experiments will show clearly the application of this -principle. We first take two similar prisms arranged as in Fig. 43. The -last through which the light passes corrects the deviation and -dispersion of the first. We then take two prisms, one of crown glass and -the other of flint glass, and since the dispersion of the flint is -greater than that of the crown, we imagine with justice that the -flint-glass prism may be of a less angle than the other and still have -the same dispersive power, and at the same time, seeing that the angles -of the prisms are different, we may expect to find that we shall get a -larger amount of deviation from the crown-glass prism than from the -other. - -[Illustration: - - FIG. 43.—Decomposition and Recomposition of Light by Two Prisms. -] - -If then a ray of light be passed through the crown-glass prism, we get -the dispersion and deviation due to the prism A Fig. 44, giving a -spectrum at D. And now we take away the crown glass and place in its -stead a prism of flint glass inverted; the ray in this instance is -deviated less, but there is an equal amount of colouring at D´. If now -we use both prisms, acting in opposite directions, we shall be able to -get rid of the colours, but not entirely compensate the deviation. We -now place the original crown-glass prism in front of the lantern and -then interpose the flint-glass prism, so that the light shall pass -through both. The addition of this prism of flint, of greater dispersive -power, combines, or as it were shuts off, the colour, leaving the -deviation uncompensated, so that we get an uncoloured image of the hole -in front of the lantern at D˝. This is the foundation of the modern -achromatic telescope. - -[Illustration: - - FIG. 44.—Diagram Explaining the Formation of an Achromatic Lens. A, - crown-glass prism; B, flint-glass prism of less angle, but giving - the same amount of colour; C, the two prisms combined, giving a - colourless yet deviated band of light at D˝. -] - -Another method of showing the same thing is to bring a V-shaped -water-trough into the path of the rays from the lantern; then, while no -water is in it, the beam of light passing through it is absolutely -uncoloured and undeviated. In this case we have no water inclosed by -these surfaces, and it is not acting as a prism at all. If, however, a -prism of flint glass, a substance of high dispersive power, is -introduced into it, with its refracting edge upwards, it destroys the -condition we had before, and we have a coloured band on the screen, -because the glass that the prism is made of has the faculty of strong -dispersion in addition to its deviation. We can get rid of that -dispersion by throwing dispersion in a contrary direction by filling up -the trough with water, and so making, as it were, a water prism on -either side of the glass one, water being a substance of low dispersive -power. We have a colourless beam thrown on the screen, which is deviated -from the original level, because the water prisms are together of a -greater angle than the glass one. - -The experiments of Hall and Dolland have resulted in our being able to -combine lenses in the same way that we have here combined prisms, -bearing in mind what has been said in reference to the action of lenses -being like that of so many prisms; and we may consider two lenses, one -of crown and the other of flint glass, Fig 45. The crown glass being of -a certain curvature will give a certain dispersion; the flint glass, in -consequence of its great dispersive power, will require less curvature -to correct the crown glass. What will happen will be this: assuming the -second lens to be away, the rays will emerge from the first (convex) -lens and form a coloured image at A. But if the second flint-glass -concave lens be interposed it will, by means of its action in a contrary -direction, undo all the dispersion due to this first lens and a certain -amount of deviation, so that we shall get the combination giving an -almost colourless image at B. - -[Illustration: - - FIG. 45.—Combination of Flint- and Crown-glass Lenses in an Achromatic - Lens. -] - -It will not be absolutely colourless, for the reasons which will be now -explained. If light be passed through different substances placed in -hollow prisms, or through prisms of flint and crown glass, and the -spectra thus produced be observed, we find there are important -differences. When we expand the spectra considerably, we see that the -action of these different substances is not absolutely uniform, some -colours extending over the spectrum further than others. In the case of -one kind of glass the red end of the spectrum is crushed up, while in -the other we have the red end expanded. - -This is called the _irrationality of the spectrum_ produced by prisms of -different substances. The crown and the flint-glass lenses—and for -telescopes we must use such glass—give irrational spectra, so that the -achromatic telescope is not absolutely achromatic, in consequence of -this peculiarity; for if R, G, B, Fig. 46, are the centres of the red, -green, and violet in the spectrum given by a prism composed of the glass -of which one lens is made, and R´, G´, B´, are those of the other, if -the lenses are placed so as to counteract each other, and are of such -curves that the reds and violets are combined, the greens will remain -slightly outstanding. Suppose, as in the drawing, the second prism -disperses the violet as much as the first one does, then, when these are -reversed they will exactly compensate red and violet. But the second one -acts more strongly on the green than the first, which will be -over-compensated; and if we weaken the second prism so that the green -and red are correct, then the violet will be slightly outstanding, which -in practice is not much noticed, except with a very bright object when -there is always outstanding colour. - -[Illustration: - - FIG. 46.—Diagram Illustrating the Irrationality of the Spectrum. -] - -This is, however, not a matter of any very great importance for ordinary -work, since the visual rays all lie in the neighbourhood of the yellow, -so that opticians take care to correct their lenses for the rays in this -part of the spectrum, and at the same time, as a matter of necessity, -over-correct for the violet rays, that is, reverse the dispersion of the -exterior lens, so that the violet rays have a longer instead of a -shorter focus than the red, and, therefore, in looking at a bright -object, such as a first magnitude star, it appears surrounded by a -violet halo; with fainter objects the blue light is not of sufficient -intensity to be visible. It is, therefore, always preferable to correct -for the most visible rays and leave the outstanding violet to take care -of itself; but nevertheless various proposals have been made to get rid -of it. Object-glasses containing fluids of different kinds have been -tried, but they have never become of any practical value, and it does -not seem probable that they ever will. - -In order to get rid of the outstanding violet colour when the remainder -of the spectrum was corrected, Dr. Blair constructed object-glasses the -space between the lenses of which were filled with certain liquids, -generally a solution of a salt of mercury or antimony, with the addition -of hydrochloric acid; for in the spectrum given by the metallic solution -the green is proportionally nearer the red than is the case with the -spectrum produced by hydrochloric acid, so that by the adjustment of the -different solutions he exactly destroyed the outstanding colour of the -ordinary combination. In this way Sir John Herschel tells us he was able -to construct lenses of three inches aperture and only nine inches focal -length, free from chromatic and spherical aberration. - -It was proposed by Mr. Barlow to correct a convex crown-glass lens for -chromatic aberration by a hollow concave lens containing bisulphide of -carbon, a highly dispersive fluid, having double the power of flint -glass. This lens was placed in the cone of rays between the object-glass -and the eyepiece. Its surfaces were concavo-convex, calculated to -destroy spherical aberration, and its distance from the object-glass was -varied until exact achromatism was obtained. A telescope of this -principle of eight inches aperture was made by Mr. Barlow, which proved -highly satisfactory. In the early part of the last century it was -proposed by Wolfius to interpose between the object-glass and eyepiece a -concave lens in order to give greater magnification of the image, with a -slight increase of focal length; if an ordinary lens be used the -achromatism of the images given by the object-glass will be destroyed. -Messrs. Dolland and Barlow, however, proposed to make the concave lens -achromatic, so that the image is as much without colour when the lens is -used as without it. Mr. Dawes found such a lens to work extremely well. -These lenses, usually called “Barlow lenses,” are generally made about -one inch in diameter, and by varying their distance from the eyepiece -the image is altered in size at pleasure. - -In the reflecting telescope, with which we will now proceed to deal, -there is an absence of colour; but the reflector is not without its -drawbacks, for there are imperfections in it as great as those we have -been considering in the case of the refractor. - - - - - CHAPTER VII. - THE REFLECTION OF LIGHT. - - -We have now dealt with the refraction of light in general, including -deviation and dispersion, in order to see how it can assist us in the -formation of the telescope; and we have shown how the chromatic effect -of a single lens can be got rid of by employing a compound system -composed of different materials, and so we have got a general idea of -the refracting telescope. We have now to deal with another property of -light, called reflection; and our object is to see how reflection can -help us in telescopes. - -In the case of reflection we get the original direction of the ray -changed as in the case of refraction, but the deviation is due to a -different cause. Take a bright light, a candle will do, and a mirror -fixed so that the light falls on its surface and is thrown back to the -eye, Fig. 47, we see the image of the candle apparently behind the -mirror; the rays of light falling on the mirror are reflected from it at -exactly the same angle at which they reach it. This brings us in the -presence of the first and most important law of reflection; and it is -this, at whatever angle the light falls on a mirror, at that angle will -it be reflected. As it is usually expressed, the angle of incidence, -which is the angle made by the incident ray with an imaginary line drawn -at right angles to the mirror, called the normal, is equal to the angle -of reflection, that is, the angle contained by the reflected ray, and -the normal to the surface. In order, therefore, to find in what -direction a ray of light will travel after striking a flat polished -surface, we must draw a line at right angles to the surface at the point -where the ray impinges on it, then the reflected ray will make an angle -with the normal equal to that which the incident ray makes, or the -angles of incidence and reflection will be equal. - -[Illustration: - - FIG. 47.—Diagram Illustrating the Action of a Reflecting Surface. -] - -Very simple experiments, which every one can make will show us the laws -which govern the phenomena of reflection. Let us employ a bath of -mercury for a reflecting surface, and for a luminous object a star, the -rays of which, coming from a distance which is practically infinite, to -the surface of the earth, may be considered exactly parallel. The -direction of the beams of light coming from the star, and falling on the -mirror formed by the mercury, is easily determined by means of a -theodolite, Fig. 48. If we look directly at the star, the line I´ S´ of -the telescope indicates the direction of the incident luminous rays, and -the angle S´ I´ N´, equal to the angle S, I, N, is the angle of -incidence, that is to say, that formed by the luminous ray with the -normal to the surface at the point of incidence. - -[Illustration: - - FIG. 48.—Experimental Proof that the Angle of Incidence = Angle of - Reflection. -] - -In order to find the direction of the reflected luminous rays, we must -turn the telescope on its axis, until the rays reflected by the surface -of the mercury bath enter it and produce an image of the star. When the -image is brought to the centre of the telescope, it is found that the -angle R´ I´ N´ is equal to the angle of reflection N, I, R. Thus, in -reading the measure on the graduated circle of the theodolite the angle -of reflection can be compared with the angle of incidence. - -Now, whatever may be the star observed, and whatever its height above -the horizon, it is always found that there is perfect equality between -these angles. Moreover, the position of the circle of the theodolite -which enables the star and its image to be seen evidently proves that -the ray which arrives directly from the luminous point and that which is -reflected at the surface of the mercury are both in the same vertical -plane. - -Now this demonstrates one of the most important laws of reflection. The -laws of refraction do not deal directly with the angles themselves, but -with the _sines_ of the angles; in reflection the _angles_ are equal; in -refraction the _sines_ have a constant relation to each other. - -So far we have dealt with plane surfaces, but in the case of telescopes -we do not use plane surfaces, but curved ones, so we will proceed at -once to discuss these. - -[Illustration: - - FIG. 49.—Convergence of Light by Concave Mirror. -] - -[Illustration: - - FIG. 50.—Conjugate Foci of Convex Mirror. -] - -In Fig. 49, A represents a curved surface, such as that of a concave -mirror, the centre of curvature being C. Now we can consider that this -curved surface is made up of an infinite number of small plane surfaces, -and since all lines drawn from the centre, C, to the mirror, will be at -right angles to the surface at the points where they meet it, we find, -from our experiment with the plane mirror, that rays falling on the -mirror at these points will be reflected so that the angles on either -side of each of these lines shall be equal; so, for instance, in Fig. -49, we wish to find to what point the upper ray will be reflected, and -we draw a line from the centre, C, to the point where it falls on the -mirror, and then draw another line from that point making the angle of -reflection equal to that made by the incident ray, and we can consider -the small surface concerned in reflection flat, so that the ray will in -this case be reflected to F. If now we take any other ray, and perform -the same operation we shall find that it is also reflected _nearly_ to -F, and so on with all other parallel rays falling on the mirror; and -this point, F, is therefore said to be the focus of the mirror. If now -the rays, instead of falling parallel on the mirror, as if they came -from the sun or a very distant object, are divergent, as if they came -from a point S, Fig. 50, near the mirror, the rays approach nearer to -the lines drawn from the centre to the mirror, one of which is -represented by the dotted line; or, in other words, the angles of -incidence become reduced, and so the angles of reflection will also be -reduced, and the focus of the rays from S will approach the centre of -the mirror, and be at _s_; just so it will be seen that if an -illuminated point be at _s_, its focus will be at S, and these two -points are therefore called conjugate foci. - -[Illustration: - - FIG. 51.—Formation of Image of Candle by Reflection. -] - -[Illustration: - - FIG. 52.—Diagram explaining Fig. 51. -] - -If a candle is held at a short distance in front of a concave mirror, as -represented in Fig. 51, its image appears on the paper between the -candle and the mirror, so that the rays from every point of the flame -are brought to a focus, and produce an image just as the image is -produced by a convex lens. If we study Fig. 52 the formation of this -image will be clearly understood. First we must note that the rays A, C, -_a_, and B, C, _b_, which pass through the centre of curvature of the -mirror C, will fall perpendicularly on the surface, and be reflected -back on themselves, so that the focus of the part a of the arrow will be -somewhere on A _a_, and that of B on B _b_, and by drawing another ray -we shall find it reflected to _a_, which will be the focus of the point -A, and so also by drawing another line from B, we shall find it is -reflected to _b_, which is the focus of the part B; and we might repeat -this process for every part of the arrow, and for every ray from those -parts. We now see that since the rays A _a_ and B _b_ cross each other -at C, the distance from _a_ to _b_ bears the same proportion to the -distance from A to B as their respective distances from the point C; or, -in other words, the image is smaller than the object in the same -proportion as the distance from the image to C is smaller than the -distance from the object to C. Now, in dealing with the stars, which are -at a practically infinite distance, the rays are parallel, and will be -brought to a focus half-way between the mirror and its centre of -curvature. In this case, therefore, the distance from the image to the -mirror is equal to that from the image to the centre, so that we can -express the size of the image by saying that it is smaller than the -object, in proportion as its distance from the mirror is smaller than -the distance of the object from C; and as it makes little difference -whether we measure the distance of the stars from C or from the mirror, -and as C is not always known, we can take the relation of the distances -of the object and image from the mirror as representing the -proportionate sizes of the two. - -We will now consider the case of rays falling on a mirror curved the -other way, that is, a convex mirror. Let us consider the ray impinging -at D, Fig. 53, which would go on to C, the centre of the mirror. Now, as -C D is drawn from the centre, it is at right angles to the mirror at D, -and the ray L D, being in the same straight line on the opposite side, -will also be at right angles, and will be reflected back on itself. Now -take the ray I A, draw C E through A, then E A will be perpendicular to -the surface at A, and I A E will be the angle of incidence, and E A G -the angle of reflection, so that this ray A G will be reflected away -from L D, and so will all the other rays falling on the mirror as K B: -and if we continue the lines G A and H B backwards, they will meet at M, -and therefore the rays diverge from the mirror as if they came from a -point at M, and this point is called the virtual focus. - -[Illustration: - - FIG. 53.—Reflection of Rays by Convex Mirror. -] - -So much for parallel rays. Next let us consider another case which -happens in the telescope, namely, where converging rays fall on a convex -mirror, as in Fig. 53, where we consider the light proceeding to the -mirror from a converging lens along the lines H B and G A, these will be -made parallel, at B K and A F, after reflection, and it is manifest that -by making the mirror sufficiently convex, these rays, tending to come to -a focus at M, could be rendered divergent; and if the curvature is -decreased by making the centre of curvature at a certain distance beyond -C, it will be seen at once by the diagram that these rays will after -reflection, converge towards L and will come to a focus in front of the -mirror at a point further in front than C is behind it, so that they -have been rendered less convergent only by the mirror in this supposed -case. - -It will be seen from what has been stated here and in Chapter V., that -we get nearly the same results from reflection as we did from refraction -when we were considering the functions of glasses instead of mirrors; -that a concave mirror acts exactly as a convex lens, and _vice versâ_, -so that they can be substituted the one for the other. If we take a -mirror, and allow the light to fall on it from a lamp, no one will have -any difficulty in seeing that the mirror grasps the beam, and forms an -image which is seen distinctly in front of the mirror, just as one gets -an image from a convex lens behind it. - - - - - CHAPTER VIII. - THE REFLECTOR. - - -The point we have next to determine is how we can utilise the properties -of reflection for the purposes of astronomical observation. Many -admirable plans have been suggested. The first that was put on paper was -made by Gregory, who pointed out that if we had a concave mirror, we -should get from this mirror an image of the object viewed at the focus -in front of it, as in Fig. 51. Of course we cannot at once utilise this -focal image by using an eyepiece in the same way as we do in a -refractor, because the observer’s head would stop the light, and the -mirror would be useless, and all the suggestions which have been made, -have reference to obtaining the image in such a position that we are -able to view it conveniently. - -Gregory, the Scottish astronomer above referred to, in 1663 suggested a -method, and it has turned out to be a good one, of utilizing reflection -by placing a small mirror D C, Fig. 54, on the other side of the focus A -of the large one, at such a distance that the image at A is again -focussed at B by reflection from the small mirror; and at B we get of -course an enlarged image of A. The rays of light proceeding to B would, -however, be intercepted by the large mirror, unless an aperture were -made in the large mirror of the size of the small one through which the -rays could pass and be rendered parallel by means of an eyepiece placed -just behind the large mirror. So that towards the object is the small -mirror C, and there is an eyepiece E, which enables the image of the -object to be viewed after two reflections, first from the large mirror -and then from the small one. Mr. Short (who made the best telescopes of -this construction, and did much for the optical science of the last -century) altered the position of the small mirror with reference to the -focus of the large one, by sliding it along the tube by a screw -arrangement, F, and so was enabled to focus both near and distant -objects without altering the eyepiece. - -[Illustration: - - FIG. 54.—Reflecting Telescope (Gregorian). -] - -But before this was put into practice, Sir Isaac Newton (in 1666) made -telescopes on a totally different plan. - -The eyepiece of the Newtonian telescope is at the side of the tube, and -not at the end, as in Gregory’s. We have next to inquire how this -arrangement is carried out, and, like most things, it is perfectly -simple when one knows how it is done. There is a large mirror at the -bottom of the tube as in the Gregorian, but not perforated, and the -focus of the mirror would be somewhere just in front of the end of the -tube. Now in this case we do not allow the beam to get to the focus at -all in the tube or in front of it; but before it comes to the focus it -is received on a small diagonal plane surface m, and thus it is at once -thrown outwards at right angles through the side of the tube, and comes -to a focus in front of an eyepiece, placed at the side, ready to be -viewed the same as an image from a refractor (Fig. 55). - -[Illustration: - - FIG. 55.—Newton’s Telescope. -] - -The next arrangement is one which Mr. Grubb has recently rescued from -obscurity, and it is called the Cassegrainian form. It will be seen on -referring to that, Fig. 56, if the small mirror, C, were removed, the -rays from the mirror A B would come to a focus at F. - -In the Gregorian construction a concave reflector was used outside that -focus (at C, Fig. 54), but Cassegrain suggested that if, instead of -using a concave reflector outside the focus, a reflector with a convex -surface were placed inside it, we should arrive at very nearly the same -result, provided we retain the hole in the large mirror. The converging -rays from A B will fall on the convex surface of the mirror C, which is -of such a curvature and at such a distance from F, the focus of the -large mirror, that the rays are rendered less converging, and do not -come to a focus until they reach D, where an image is formed ready to be -viewed by the eyepiece E. It appears from this, that the convex mirror -is in this case acting somewhat in the same manner as the concave lens -does in the Galilean telescope. - -[Illustration: - - FIG. 56.—Reflecting Telescope (Cassegrain). -] - -[Illustration: - - FIG. 57.—Front View Telescope (Herschel). -] - -Then, lastly, we have the suggestion which Sir William Herschel soon -turned into more than a suggestion. The mirror M in this arrangement is -placed at the bottom of the tube as in the other forms, but, instead of -being placed flat on the bottom it is slightly tipped, so that if the -eyepiece is placed at the edge of the extremity of the tube all parallel -rays falling on the mirror are reflected to the side of the tube at the -top where the eyepiece is, instead of being reflected to a convex or -other mirror in the middle. - -This is called the front view telescope, and it enabled Sir William -Herschel to make his discoveries with the forty-feet reflector. With -small telescopes this form could not be adopted, as the observer’s head -would cover some part of the tube and obstruct the light, but with large -telescopes the amount of light stopped by the head is small in -proportion to what would be lost by using a small mirror. - -These are in the main the four methods of arranging reflecting -telescopes—the Gregorian, the Cassegrainian, the Newtonian, and the -Herschelian. - -In order to make large reflectors perfect—large telescopes of short -focus, because that is one of the requirements of the modern -astronomer—we have to battle against spherical aberration. - -We have already seen that the power of substances to refract light -differs for different colours, and we have seen the varied refraction of -different parts of the spectrum, and the necessity of making lenses -achromatic. Now there is one enormous advantage in favour of the -reflector. We do not take our light to bits and put it together again as -with an achromatic lens. But curiously enough, there is a something else -which quite lowers the position of the reflector with regard to the -refractor. Although, in the main all the light falling in parallel lines -on a concave surface is reflected to a focus, this is only true in a -general sense, because, if we consider it, we find an error which -increases very rapidly as the diameter of the mirror increases or as the -focal length diminishes. For instance, D I, Fig. 58, is the segment of a -circle, or the section of a sphere—if we deal with a solid figure. D C, -E G and H I, are three lines representing parallel rays falling on -different parts of it. According to that law which we have considered, -we can find where the ray E G will fall. We draw a line L, G, from the -centre to the point of reflection, and make the angle F G L, equal to -the angle of incidence E G L; then F will be the focus, so far as this -part of the mirror is concerned. Now let us repeat the process for the -ray H I, and we shall find that it will be reflected to K, a point -nearer the mirror than F, and it will be seen that the further the rays -are from the axis D C, the further from the point F is the light -reflected; so that if we consider rays falling from all parts of the -reflecting surface, a not very large but a distinctly visible surface is -covered with light, so that a spherical surface will not bring all the -rays exactly to a point, and with a spherical mirror we shall get a -blurred image. We can compare this imperfection of the reflector, called -spherical aberration, with the chromatic aberration of the object-glass. - -[Illustration: - - FIG. 58.—Diagram Illustrating Spherical Aberration. -] - -[Illustration: - - FIG. 59.—Diagram Showing the Proper Form of Reflector to be an - Ellipse. -] - -Newton early calculated the ratio of imperfection depending upon these -properties of light, first of dispersion and then of spherical -aberration, and he found that in the refracting telescope the chromatic -aberration was more difficult to correct and get rid of than the -spherical aberration of the reflector, so that in Newton’s time, before -achromatic lenses were constructed, the reflector with its aberration -had the advantage. It must now be explained how this difficulty is got -over. What is required to produce a mirror capable of being used for -astronomical purposes, is to throw back the edges of the mirror to the -dotted line A C I, Fig. 58, which will make the margin of the mirror a -part of a less concave mirror, and so its focus will be thrown further -from itself—to F, instead of to K. Now let us consider what curve this -is, that will throw all the rays to one point. It is an ellipse, as will -be seen by reference to Fig. 59, in which, instead of having a spherical -surface the section of which is a circle, we deal with a surface whose -section is an ellipse. - -It will be seen in a moment, that by the construction of an ellipse any -light coming in any direction from the point A, which represents one of -the foci of the curve, must necessarily be reflected back to the other -focus, B, of the curve, for it is a well-known property of this curve -that the angles made with a tangent C D, by lines from the foci are -equal; and the same holds good for the angles made at all other -tangents; and it will be seen at once that this is better than a -circular curve, because by making the distance between the foci almost -infinite we shall have the star or object viewed at one focus and its -image at the other; if we use any portion of the reflecting surface we -shall still get the rays reflected to one point only. It must also be -noticed, that unless we have an ellipse so large that one focus shall -represent the sun or a particular star we want to look at, this curve -will not help us in bringing the light to one point, but if we use the -curve called the parabola, which is practically an ellipse with one -focus at an infinite distance, we do get the means of bringing all the -rays from a distant object to a point. Hence the reflector, especially -when of large diameter, is of no use for astronomical purposes without -the parabolic curve. - -That it is extremely difficult to give this figure may be gathered from -Sir John Herschel’s statement, that in the case of a reflecting -telescope, the mirror of which is forty-eight inches in diameter and the -focal distance of which is forty feet, the distance between the -parabolic and the spherical surface, at the edges of the mirror, will be -represented by something less than a twenty-one thousandth part of an -inch, or, more accurately, 1/21333 inch. In Fig. 58 the point A -represents the extreme edge of the curve of the parabolic mirror, and D -that of the circular surface before altered into a parabola. - -At the time of Sir William Herschel the practical difficulties in -constructing large achromatic lenses led to the adoption by him of -reflectors beginning with small apertures of six inches to a foot, and -increasing till he obtained one of four feet in diameter and forty-six -feet focal length. This has been surpassed by Lord Rosse, whose -well-known telescope is six feet diameter, and fifty-three feet focal -length. Mr. Lassell, Mr. De La Rue, M. Foucault and Mr. Grubb, have also -more recently succeeded in bringing reflectors to great perfection. - -How the work has been done will be fully stated in the sequel. - - - - - CHAPTER IX. - EYEPIECES. - - -We have considered the telescope as a combination of an object-glass and -eyepiece in the one case, and of a speculum and eyepiece in the other; -that is to say, we have discussed the optical principles which are -applied in the construction of refracting and reflecting telescopes, the -telescope being taken as consisting of an object-glass or speculum and -an eyepiece of the most simple form, viz., a simple double convex lens. - -We must now go into detail somewhat on the subject of eyepieces, and -explain the different kinds. - -It will be recollected that when we spoke of the object-glass, its -aberration, both chromatic and spherical, was mentioned. Now every -ordinary lens has these errors, and eyepieces must be corrected for -them, but this is not done in exactly the same way as with -object-glasses. - -In the case of eyepieces the error is corrected by using two lenses of -such focal lengths or at such a distance apart that each counteracts the -defects of the other; not by using two kinds of glass as in the case of -the object-glass, but by so arranging the lenses that the coloured rays -produced by the first lens shall fall at different angles of incidence -on the second and become recombined. - -[Illustration: - - FIG. 60.—Huyghens’ Eyepiece. -] - -Let us take the case of a well-known eyepiece, called the Huyghenian -eyepiece, after its inventor. It consists of two plano-convex lenses, A -and B Fig. 60, with their convexities turned towards the object-glass, -and having their focal lengths in the proportion of three to one. The -strongest lens, A, being next the eye, the lens B is placed inside the -focus of the object-glass, so that it assists in bringing the image, say -of a double star, to a focus at F, half way between the lenses, and -nearer to the object-glass than it would have been without the lens. -This image is then viewed by the eye-lens, A, and a magnified image of -it seen apparently at F´, as has been before explained. Now let us see -how the fieldlens renders this combination achromatic. Let us consider -the path of a ray falling on the lens near B, shown in section in Fig. -61: it is there refracted, but, the blue rays being refracted more than -the red, there will be two rays produced, _r_ and _v_, giving of course -a coloured edge to the image; but when this image is viewed by the -eye-glass, A, it no longer appears coloured, for the ray _v_, falling -nearer the axis of A, is less bent than _r_, and they are rendered -nearly parallel and appear to proceed from the point F´ where the whole -image appears without colour. In order to get the best result with this -form of eyepiece the focal length of the fieldlens should be three times -that of the eye-lens and they should be placed at a distance of half -their joint focal lengths apart. - -[Illustration: - - FIG. 61.—Diagram Explaining the Achromaticity of the Huyghenian - Eyepiece. -] - -The next eyepiece which comes under consideration is that called -Ramsden’s, Fig. 62. It consists of two plano-convex lenses of the same -focus, A and B, placed at a distance of two-thirds of the focal length -of either apart; they are both on the eye side of the focus of the -telescope, and act together, to render the rays parallel and give a -magnified virtual image of F´F. - -This eyepiece is not strictly achromatic, but it suffers least of all -lenses from spherical aberration; it also has the advantage of being -placed behind the focus of the object-glass, which makes it superior to -others in instruments of precision, as we shall presently see. - -[Illustration: - - FIG. 62.—Ramsden’s Eyepiece. -] - -It must be remembered that these eyepieces give an inverted image—or -rather the object glass gives an inverted image, and the eyepiece does -not right it again; but there are eyepieces that will erect the image, -and Rheita’s is one of this kind. It is, as will be seen from Fig. 63, -merely a second application of the same means that first inverts the -object, namely, a second small telescope. A is the object-glass, _a b_ -the image inverted in the usual way; B is an ordinary convex lens -sending the rays from _a_ and _b_ parallel. Now, instead of placing the -eye at C, as in the ordinary manner, another small lens, acting as an -object-glass, is placed in the path of the rays, bringing them to a -focus at _a´_, _b´_, and forming there an erect image which is viewed by -the eye-lens D. This is the erecting eyepiece or “day eyepiece,” of the -common “terrestrial telescope.” Dollond substituted an Huyghenian -eyepiece for the eye-lens D, and so made what is called his four-glass -eyepiece. - -Dr. Kitchener devised and Mr. G. Dollond made an alteration in this -eyepiece in order to vary its power at pleasure. It is done in this way: -The size of the image _a´ b´_ depends upon the relation of the distances -_a_ B and E _a´_, which can be varied by altering the distance of the -combination of the lenses B and E, from the image _a b_, and so making -_a´ b´_ larger and at a focus further from E; the tube carrying _d_ -slides in and out, so that it can be focussed on _a´ b´_ at whatever -distance from E it may be. This arrangement is called Dollond’s -Pancratic eyepiece. - -[Illustration: - - FIG. 63.—Erecting or day eyepiece. -] - -On the sliding tube carrying the lens D, or rather the Huyghenian -eyepiece in place of the single lens, are marked divisions, showing the -power of the eyepiece when drawn out to certain lengths, so that if we -want the eyepiece to magnify say 100 times, the tube carrying the -eye-lens is drawn out to the point marked 100, and the whole eyepiece -moved in or out of the telescope tube by the focussing screw, until the -image of the object viewed is focussed in the field of the eyepiece D. -To increase the power, we have only to draw out the eyepiece D, and move -the whole combination nearer to the object-glass so as to throw the -image _a´ b´_ further from the lens E. This eyepiece, though so -convenient for changing powers, is little used, owing perhaps chiefly to -four lenses being required instead of two, hence a loss of light, so a -stock of eyepieces of various powers is generally found in -observatories. When very high powers are required, a single plano-convex -lens is sometimes used, but although there is less loss of light in this -case, the field of view is so contracted in comparison with that given -with other eyepieces that the single lens is seldom used. This form is, -however, adopted in Dawes’ solar eyepiece, to be hereafter mentioned, -and a number of lenses are in this case fixed in holes near the -circumference of a disc of metal which turns on its centre, so that by -rotating the disc the lenses come in succession in front of the focus of -the object-glass, and the power can be changed almost instantaneously. - -In order that objects near the zenith may be observed with ease, a -diagonal reflector is sometimes used, so that the eye looks sidewise -into the telescope tube instead of directly upwards. This reflector may -take the form of two short pieces of tube joined together at right -angles, and having a piece of silvered glass or a right-angled prism at -the angle, so that when one tube is screwed into the telescope, the rays -of light falling on the reflector are sent up the other, in which the -ordinary eyepiece is placed. - -The eyepieces just described are suitable, without further addition, for -observing all ordinary objects, but when the sun has to be examined a -difficulty presents itself. The heat rays are brought to a focus along -with those of light, and with an object-glass of more than one or two -inches aperture there is great danger of the heat cracking the lenses, -but with such telescopes the interposition—and neglect of this may cost -an eye—of smoked or strongly-coloured glass in front of the eye is -generally sufficient to protect it from the intense glare. With larger -telescopes, however, dark glasses are apt to split suddenly and allow -the full blaze of sunlight to enter the eye and do infinite mischief, -and some other method of reducing the heat and light is required. -Perhaps the most simple method of effecting this object is to allow the -light to fall on a diagonal plane glass reflector at an angle of 45°, -which lets the greater part of the light and heat pass through, -reflecting only a small portion onwards to the eyepiece and thence to -the eye; a coloured glass is, however, required as well, and the glass -reflector must form part of a prism of small angle, otherwise there will -be two images, one produced by each surface. - -Another arrangement is to reflect the rays from the surfaces of two -plates of glass inclined to them at the polarizing angle, so that by -turning the second plate, or a Nicols’ prism, in its place round the ray -as an axis, the amount of light allowed to pass to the eye can be varied -at pleasure. - -The late Mr. Dawes constructed a very convenient solar eyepiece, -depending on the principle of viewing a very small portion of the sun’s -image at one time, and thereby diminishing the total quantity of heat -passing through the eye-lens. The details of the eyepiece are as -follows: very minute holes of varying diameters are made in a brass disc -near its circumference, and as this is turned each successive hole is -brought into the centre of the field of view and the common focus of the -eye-lens and object-glass. Small areas on the sun of different sizes can -thus be examined at pleasure. A number of eye-lenses of different powers -arranged in a disc of metal can be successively brought to bear, giving -a means of quickly varying the power, while coloured glasses of -different shades can be passed in front of the eye in the same manner. -The surface of the disc of brass containing the holes is covered on one -side—that on which the sun’s image falls—with plaster of Paris, which, -being a bad conductor, prevents the heat from affecting the whole -apparatus. - - * * * * * - -The true magnifying power of the eyepiece is found by dividing the focal -length of the object-glass by that of the eyepiece; in practice it is -found approximately by comparing the diameter of the object-glass with -that of its image formed by the eyepiece when the telescope is in its -usual adjustment; the former divided by the latter giving the power -required. The diameter of the image can be measured by a small compound -microscope carrying a transparent scale in its focus, when the image of -the object-glass is brought to a focus and enlarged on the scale and -then viewed, together with the divisions, by the microscope; or the -image can be measured with tolerable accuracy by Mr. Berthon’s -dynameter, consisting of a plate of metal traversed longitudinally by a -wedge-shaped opening. This is placed close to the eye-lens in the case -of the Huyghenian eyepiece, or at the point where the image of the -object-glass is focussed with other forms of eyepieces, and the plate -moved until the sides of the wedge-shaped opening are exactly tangential -to the image; the point of the opening at which this occurs is read off -on a scale, which gives the width of opening at this point and therefore -the diameter of the image. - - - - - CHAPTER X. - PRODUCTION OF LENSES AND SPECULA. - - -Before we go on to the use and various mountings of telescopes, the -optical principles of which have been now considered, a few words may be -said about the materials used and the method of obtaining the necessary -and proper curves. Object-glasses, of course, have always been made of -glass, and till a few years ago specula were always made of metal; but -so soon as Liebig discovered a method of coating glass with a thin film -of metallic silver, Steinheil, and after him the illustrious Foucault, -so well known for his delicate experiments on the velocity of light and -his invention of the gyroscope, suggested the construction of glass -mirrors coated by Liebig’s process with an exceedingly thin film of -silver, chemically deposited. - -This arrangement much reduced the price of reflectors and rendered their -polishing extremely easy, and at the present time discs of glass up to -four feet in diameter are being thus produced and formed into mirrors, -though in the opinion of competent judges this size is likely to be the -limit for some time. But there is this important difference, that -although glass is now used both for reflectors and refractors, almost -any glass, even common glass, will do, if we wish to use it for a -speculum; but if we wish to grind it into lenses it is impossible to -overrate the difficulty of manufacture and the skill and labour required -in order to prepare it for use, first in the simple material, and then -in the finished form in which it is used by the astronomer. In a former -chapter we considered some _chefs-d’œuvre_ of the early opticians, some -specimens of a quarter or half-an-inch in diameter, with extremely long -focus; and as we went on we found object-glasses gradually increasing in -diameter, but they were limited to the same material, namely, crown -glass. - -Dollond, whose name we have already mentioned in connection with that of -Hall, gave us the foundation of the manufacture of the precious flint -glass, the connection of which with crown glass he had insisted upon as -of critical importance. The existence of a piece of flint glass two -inches in diameter was then a thing to be devoutly desired, that is to -say, flint glass of sufficient purity for the purpose; it could not be -made of a size larger than that, and not only was the material wanted, -but the material in its pure state. - -In the year 1820 we hear of a piece of flint glass six inches in -diameter, and in 1859 Mr. Simms reported that a piece of flint glass of -seven and three-quarter inches was produced, six inches of which were -good for astronomical purposes. But even at this time they did these -things better in Germany and Switzerland, where M. Guinand made large -discs at the beginning of the present century. He was engaged by -Fraunhofer and Utzschneider at their establishment in Bavaria in 1805, -and by his process achromatics of from six to nine inches in diameter -were constructed. Afterwards Merz, the successor of Fraunhofer, -succeeded in obtaining flint glass of the then unprecedented diameter of -fifteen inches. - -Now we have in part turned the tables, and Mr. Chance, of Birmingham, -owing to the introduction of foreign talent, has since constructed discs -of glass of a workable diameter of twenty-five inches for Mr. Newall’s -telescope, and for the American Government he has completed the large -discs used in constructing the refractor of 26 inches’ diameter for the -observatory at Washington (the Americans are never content till they go -an inch beyond their rivals), while M. Feil of Paris, a descendant of -the celebrated Guinand, has also made one of nearly 28 inches’ diameter -for the Austrian Government. - -Messrs. Chance and Feil, however, have the monopoly of this manufacture, -and the production of these discs is a secret process. What we know is -that the glass is prepared in pots in large quantities, it is then -allowed to cool, and is broken up in order that it may be determined -which portions of the glass are worth using for optical purposes. These -are gathered together and fused at a red heat into a disc, and it is -this disc which, after being annealed with the utmost care, forms the -basis of the optician’s work. - -For the glass used for reflectors, purity is of little moment, as we -only require a surface to take a polish, since we look on to it, and not -through it; but in the case of the glass that has to be shaped into a -lens the purity is of the utmost importance. The practical and -scientific optician, on his commencement to make an object-glass, will -grind the two surfaces of both flint and crown as nearly parallel as -possible, and polish them. In this state he can the better examine them -as to veins, striæ, and other defects, which would be fatal to anything -made out of it. He has next to see that the annealing is perfectly done -by examining the discs with polarized light, to see by the absence of -the “black cross” that there is no unequal tension. It is so difficult -to run the gauntlet through all these difficulties when the aperture is -considerable that refractors of forty inches’ aperture may be perhaps -despaired of for years to come, though the glassmaker is willing to try -his part. - -Next, as to metallic specula. As we are dealing with the instruments -that are now used, we will be content with considering the compounds -that have been made successfully, and omit the variations which have -never been brought into practice. To put it roughly, the metal used for -Lord Rosse’s reflector consisted of two parts of copper and one part of -tin; but here we have an idea of the Scylla and the Charybdis which are -always present in these inquiries. If we use too much tin, which tends -to give a surface of brilliancy to the speculum, a few drops of hot -water poured on it will be enough to shiver it to atoms. This -brittleness is objectionable, and what we have to do is to reduce the -quantity of tin. But then comes the Charybdis. If we do this, the colour -is no longer white, but it is yellow, and in addition we have introduced -a surface that quickly tarnishes instead of a surface which remains -bright. The proportions which seem to answer best are copper sixty-four -parts and tin twenty-nine. Lord Rosse, we believe, uses 31·79 per cent, -of tin; or very nearly the above proportions. Mr. Grubb in the Melbourne -mirrors used copper and tin in the proportion of 32 to 14·77. - -Having the metal, we have roughly to cast it in the shape of a speculum, -but if an ordinary casting is made in a sand mould the speculum metal is -so spongy that we can do nothing with it. If it is put in a close mould -it will probably be cast very well, but it will shiver to atoms with a -very slight change of temperature. The difficulty was got over by Lord -Rosse, using an open mould called a “bed of hoops;” the bottom of the -mould being composed of strips of iron set edgeways, held together by an -iron ring and turned to the proper convexity; sand is then placed round -the iron to form the edges, the metal is then poured in, and the bubbles -and vapours run down through the small apertures at the bottom of the -mould, so that the speculum is fairly cast. Mr. Lassell proposed a -different method, which was introduced by Mr. Grubb in his arrangements -for the Melbourne telescope. Instead of having the bottom of the bed of -hoops perfectly horizontal it is slightly inclined; the crucible, which -contains the metal of which the speculum is to be cast, is then brought -up to it—the amount of metal being something under two tons in the case -of the Melbourne telescope—and the bed of the mould is kept tipped up as -the metal is poured into it, and so arranged as to keep the melted metal -in contact with one side; and as it gets full it is brought into a -perfectly horizontal position. - -Having cast the speculum, the next thing is to put it in an annealing -oven, raised to a temperature of 1,000°, where it is allowed to cool -slowly for weeks till it has acquired nearly the ordinary temperature. -On being removed from the oven the speculum is placed on several -thicknesses of cloth and rough ground on front, back, and edge. - -Having got the material roughly into form we now pass on to see what is -done next. - -In the case of the reflector, whether of metal or glass, the optician -next attempts to get a perfectly spherical surface of the proper -curvature for the required focus. - -In the case of the refractor matters are somewhat more complicated; we -have there four spherical surfaces to deal with, and the optician has -work to do of quite a different kind before he even commences to grind. - -Presuming the refractive and dispersive properties of the glass not -known, it will be necessary to have a small bit of glass of the same -kind to experiment with. That the optician may make no mistake in this -important matter, some glass manufacturers make the discs with -projecting pieces to be cut off; these the object-glass maker works into -prisms to determine the exact refraction and dispersion, including the -position in the spectrum of the Fraunhofer lines C and G, for both the -crown and flint glass. With these numbers and the desired focal length -he has all the necessary data for the mathematical operation of -calculating the _powers_ to be given to the two lenses—flint and crown, -and the radii of curvature of the four surfaces in order that the -object-glass may be aplanatic or free from aberration both spherical and -chromatic. The problem is what mathematicians call an indeterminate one, -as an infinite number of different curvatures is possible. Assume, -however, the radius of curvature of one surface, and all the rest are -limited. In assuming the radius of curvature on one of the crown-glass -surfaces, it is well to avoid deep ones. It is better to divide the -refraction of the four surfaces as equally as the nature of the problem -will admit, as any little deviation from a true spherical figure in the -polishing will produce less effect in injuring the performance of the -object-glass from surfaces so arranged than if the curves were deep. - -But whatever curves he chooses he goes to work so that the spherical -aberration of the compound lens shall be eliminated as far as possible, -and the chromatism in one lens shall be corrected by the other, or in -other words, that what is called the _secondary spectrum_ shall be as -small as possible; and it is to be feared that this will never be -abolished.[6] - -[Illustration: - - FIG. 64.—Images of planet produced by short and long focus lenses of - the same aperture giving images of different size, but with the same - amount of colour round the edges. -] - -This matter requires a somewhat detailed treatment in order that it may -be seen how the four surfaces to which reference has been made are -determined. - -The chromatic dispersion, in the case of the object-glass, may be -roughly stated to be measured by about one fiftieth of the aperture. -Suppose for instance the discs, Fig. 64, to represent the image of any -object, say the planet Jupiter. Then round that planet we should have a -coloured fringe, and the dimensions of that coloured fringe, that is, -the joint thickness of colour at A and D, will be found by dividing the -diameter of the object-glass used by fifty. Now this is absolutely -independent of the focal length of the telescope; therefore one way of -getting rid of it is to increase the focal length of telescopes; and as -the size of the image depends on focal length, and has nothing whatever -to do with aperture, we may imagine that with the same sized -object-glass, instead of having a little Jupiter as on the left of Fig. -64, we may have a very large Jupiter, due to the increased focal length -of the telescope. Then, it may be asked, how about the chromatic -aberration? It will not be disturbed. The aperture of the object-glass -remains unaltered, and there is no more chromatic aberration here than -in the first case; so that the relation between the visible planet -Jupiter and the colour round it is changed by altering the focal length. -But as we have seen, we are able by means of a combination of flint and -crown glass to counteract this dispersion to a very great extent. How -then about spherical aberration? - -Up to the present we have assumed that all rays falling on a convex lens -are brought to a point or focus, but this is not strictly true, for the -edges of a lens turn the rays rather too much out of their course, so -that they will not come to a point; just as the rays reflected from a -spherical mirror do not form a single focus. The marginal rays will be -spread over a certain circular surface, just as the colour due to -chromatic aberration covered a surface surrounding the focus. It was -explained that for the same diameter of lens the circle of colour -remained the same, irrespective of focal length, but in the case of -spherical aberration this is not so; it diminishes as the square of the -focal length increases; that is to say, if we double the focal length we -shall not only halve, but half-halve, or quarter the aberration. Newton -calculated the size of the circle of aberration in comparison with that -due to colour, and he found that in the case of a lens of four inches -diameter and ten feet focus, the spherical aberration was eighty-one and -a half times less than that of colour. _It is found that by altering the -relative curvatures of the surfaces of the lens, this aberration can be -corrected without altering the focal length_; for any number of lenses -can be made of different curvatures on each side but of the same -thickness in the middle, so that they have all the same focal length, -but the one, having one surface about three times more convex than the -other, will have least aberration, so that it is the adaptation of the -surfaces of lenses to each other that exercises the art of the optician. - -So far we have got rid of this aberration in a single lens; it can also -be done in the case of achromatic lenses. The foci of the two lenses in -an achromatic combination must bear a certain relation to each other, -and the curvatures of the surfaces must also have a certain relation for -spherical aberration. In the achromatic lens there are four surfaces, -_two of which can be altered for one aberration and two for the other_. -For instance, in the case of the lens, Fig. 45, where the interior -surfaces of the lenses are cemented together, although shown separate -for clearness, we find that if the exterior surface of the crown double -convex lens be of a curvature struck by a radius 672 units in length, -and the exterior surface of the flint glass lens to a curvature due to a -radius of 1,420 units, the lens will be corrected for spherical -aberration, and these conditions leave the interior surfaces to be -altered so that the relation between the powers of the lenses is such as -to give achromatism. - -The flint is as useful in correcting the spherical aberration as the -chromatic aberration; for although the relative thicknesses of the flint -and crown are fixed in order to get achromatism, still we have by -altering both the curvatures of each lens equally, and keeping the same -foci, the power of altering the extent of spherical aberration; and it -is in the applications of these two conditions that much of the higher -art of our opticians is exercised. We have now therefore practically got -rid of both aberrations in the modern object-glass, and hence it is that -lenses of the large diameter of twenty-five and twenty-six inches are -possible. - -The nearest approach to achromatism is known to be made when looking at -a star of the first or second magnitude, the eyepiece being pushed out -of focus towards the object-glass, the expanded disc has its margin of a -claret colour. When the eyepiece is pushed beyond the focus outwards the -margin of the expanded disc is of a light green colour. - -If the object-glass is well corrected for spherical aberration, the -expanded discs both within and without the focus will be constituted of -a series of rings equally dense with regard to light throughout, with -the exception of the marginal ring, which will be a little stronger than -the rest. - - * * * * * - -Having determined the radius of curvature of surface, both he who grinds -the speculum, whether of speculum metal or glass, and he who grinds the -object-glass, starts fair; only one has four times the work to do that -the other has. The grinding is managed in a simple way, and the process -of grinding or polishing an object-glass or speculum, either of glass or -of metal, is the same. - -Supposing we wish to make a reflecting telescope of six feet focus, or a -surface of an object-glass of twelve feet radius, all we have to do is -to get a long rod, a little more than twelve feet long, and pin it to a -wall at its upper end so that it can swing, pendulum fashion; then at a -distance of twelve feet below the point of suspension a pin is stuck -through the rod and its point made to scratch a line on a sheet of metal -laid against the wall; then this line will be part of a circle struck -with a radius of twelve feet. If then the plate be cut along this line -we get a convex and a concave surface of the desired radius, and then we -can take a block of iron or brass and turn its surface, convex or -concave, to fit the sheet of metal or template. For a reflector we -should make a convex tool, and for a refractor a concave one. - -Generally this grinding tool is divided into squares or furrows all over -it, in order that the emery which is used in rough grinding may flow -freely about with the water. A disc of glass is then laid on the tool, -or the tool on the glass, the two being pressed together by a weight or -spring; emery powder, with water, is strewn between them, and one is -rubbed over the other by a machine similar to those used for polishing, -which we shall explain presently. This operation is continued until the -glass is ground all over, and in this process of rough grinding the -rough emery is used between the tool and the glass, so that whatever -irregularities the glass or tool may have they are got rid of, and it is -easy to obtain a spherical surface, and indeed, it is the only surface -that can be obtained. Then finer and finer emery is used, till it ceases -to be a sufficiently fine substance to use, and a surface of iron or -lead is also too hard a surface. Now the polishing begins, and the -optician and amateur avail themselves of a suggestion due to Sir Isaac -Newton, who always saw much further through things than other people. - -[Illustration: - - FIG. 65.—Showing in an exaggerated form how the edge of the speculum - is worn down by polishing. -] - -Even when he first began to make the first reflector, he used pitch, a -substance not too hard, nor yet too soft, and one that can be regulated -by temperature; therefore for polishing, instead of having a tool made -of metal, pitch laid on glass or wood and supplied with rouge and water -is used. This polisher of pitch is divided into squares by channels to -allow free flow of rouge and water, and is laid on the mirror or -object-glass, or vice versâ, and moved about over it. - -When the maximum of polish is attained the work is done, and the -object-glass finished, as here we have to do with a spherical surface. -In the grinding of the two discs for Mr. Newall’s telescope 1,560 hours -were consumed, the thickness of the crown disc having been reduced one -inch in the process. - -In the case of specula, however, there is more to be done; and it is in -this polishing of specula that the curve is altered from a circle to a -parabola by using a certain length of stroke, size of polisher, -consistency of pitch, and numbers of other smaller matters, the proper -proportionment of which constitutes the practical skill of the optician, -and it is in accomplishing this that the finest niceties of manipulation -come into play, and the utmost patience is required. 1,170 hours were -occupied in the grinding and polishing of the four-feet Melbourne -speculum. This was equivalent to 2,050,000 strokes of the machine at 33 -per minute for rough and 24 for fine grinding. Dr. Robinson, in his -description of the grinding operations, states that at the edge of one -of the four-feet specula the distance of its parabola from the circle -was only 0·000106˝. - -In the early times of specula the polishing was invariably done by hand, -a handle being cemented by pitch to the back of the speculum to work it -with. Mudge tells us that at first, when the mirror was rough from the -emery grinding, it was worked round and round on the pitch, which was -supplied with rouge and water and cut by channels into small squares, -carrying the edge but little over the polisher, an occasional cross -stroke being made. The effect of this was to press the pitch towards the -centre where the polish always commenced, and gradually spread to the -circumference. As soon as the polishing was complete the speculum was -worked by short straight strokes across the centre, tending to bring it -back to a sphere; then the circular strokes were recommenced to restore -the paraboloid form: these were continued for a short time only, -otherwise it would pass the proper curve and require reworking with -straight strokes again. By this method some small mirrors of first-class -definition were constructed. - -When Sir W. Herschel began his labours he constructed a machine for -working the speculum over the polisher; the polisher was a little larger -than the mirror, the proportion given by him from a number of trials -being 1·06 to 1. - -The speculum was held in a circular frame, which was free to turn round -in another ring or frame; this frame was moved backwards and forwards by -a vibrating lever to which it was attached by rods, carrying the -speculum over the polisher. This motion he designates the stroke. -Besides this there was the _side motion_ produced by a rod attached to -the side of the frame opposite to that to which the rods giving it the -stroke were attached and at right angles to the direction of stroke: -this rod was in connection, by means of intermediate levers, with a pin -on a rachet wheel, which was turned a tooth at a time by a rod in -connection with the lever giving the _stroke_ motion, so that the rod -giving the _side motion_ was pushed and pulled back by the pin on the -rachet wheel every time it turned round, which it did every twenty or -thirty strokes. There were also teeth on the ring fastened round the -edge at the back of the speculum, into which claws worked which were -attached by rods to a point on the lever a little distance from the -attachment of the rod giving the stroke, so that the claws had a less -motion than the speculum and its ring, and consequently pulled the ring, -and with it the speculum, round a tooth or more at each stroke. The -polisher was also turned round in the same manner in a contrary -direction to the motion of the speculum. The speculum had therefore -three motions, a revolving one on its centre, a stroke, and a side -motion, making its centre describe a number of parallel lines over the -polisher on each side of its centre. Sir W. Herschel gives as a good -working length of stroke, 0·29, and 0·19 side motion measured from side -to side, the diameter of the speculum being 1. To produce a seven-inch -mirror with this instrument he would work continuously for sixteen -hours, his sister “putting the victuals by bits into his mouth.” - -[Illustration: - - FIG. 65*.—Section of Lord Rosse’s polishing machine. -] - -Lord Rosse adopted a similar arrangement; the polisher, K L, Fig. 65, -was worked over the speculum in straight strokes with side motion, the -requisite straight motion being given by a crank-pin and rod and the -side motion by the continuation of this latter rod on the other side of -the polisher working in a guide on another crank-pin, which threw it -from side to side as the wheel carrying the pin revolved. The trough E F -carrying the speculum also revolved slowly, and the requisite motions -were given by pulleys and straps of various sizes under the table on -which the machine rested; the weight of the polisher was in a great -measure counterpoised by strings from its upper surface to a weighted -lever M above. The polisher was free to turn in its ring, which it did -once in about twenty strokes, and for the six feet speculum the velocity -of working was about eight strokes a minute, the length of stroke being -one-third of the diameter of the speculum, and that of the side motion -one-fifth. - -The speculum was polished on the same system of levers that were -afterwards to support it, in order that no change of form might be -produced in moving it to a different mounting. The consistency of the -pitch is a matter of importance, Mr. Lassell’s test of the requisite -hardness being the number of impressions left by a sovereign standing on -edge on it; this should leave three complete impressions of the milled -edge in one minute at the ordinary temperature of the atmosphere. - -[Illustration: - - FIG. 66.—Mr. Lassell’s polishing machine. -] - -Fig. 66 represents the machine contrived by Mr. Lassell for his method -of polishing, and shows what a complicated arrangement is essential in -order to arrive at any good result in these matters. - -The speculum is placed on a bed, and above it is a train of wheels -terminating in a crank-pin that gives motion to the polisher, which is -made to take a very devious path by the motion of the wheels above. The -pin giving motion to the polisher G at its centre can be set at a -variable distance from the axis of the lowest pinion F to which it is -attached, by moving it in its slide, so that when the pinion is turned, -the pin and centre of the polisher describe a circle. The pinion in -question is carried on a slide C above it, attached to the main vertical -driving shaft A, so that as the shaft revolves the centre of the pinion -describes a circle of a diameter variable at pleasure by moving it in -the slide C, the result of the two motions being that the centre of the -polisher describes circles about a moving centre, and consequently in -constantly varying positions on the speculum. Motion is given to the -vertical shaft by the cog-wheel and endless screw above, worked by some -prime mover, and as the cogwheels on the shaft E parallel to the main -shaft are carried round the latter by the arm D holding them, they are -caused to revolve by gearing into the fixed wheel B, through the centre -of which the main shaft passes, and they in their turn impart motion to -the pinion carrying the pin giving motion to the polisher. The speculum -is also maintained in slow rotation by the wheel and endless screw below -it. The speculum and its supports are surrounded by water contained in a -circular trough not shown in the engraving, so that the consistency of -the pitch shall be constant. - -This arrangement, pure and simple, was found to bring on the polish in -rings over the speculum, and as an improvement, the speculum, or rather -the system of levers supporting it, was carried on a plate which had the -power of sliding backwards and forwards on the wheel turning it round; -the edges of this plate pressed against a fixed roller, and it was made -of such a shape that as it revolved it was forced to take a side motion -as its edges passed by the fixed roller, so that the speculum had a side -motion in addition to the rotatory one. - -Mr. De La Rue improved on this by giving the speculum a rotatory motion -irrespective of that of the sliding plate, so that the side motion -should not always be along the same diameter of the speculum. This was -done by allowing the speculum to turn freely on a pivot on the sliding -plate, and giving it a rotatory motion by means of a cord going round -the plate carrying the speculum supports. As a further improvement Mr. -De La Rue controls the motion of the polisher on the central pin, giving -it motion by a crank carrying a system of wheels in place of the lowest -crank, so that the pin gets a rotatory motion in addition to these. - -Mr. Grubb’s arrangement for polishing is different. The speculum is made -to rotate, the polisher is made to execute curves variable at pleasure -by altering the throw of the cranks which move rods attached to the -centre of the polisher, giving it a motion similar to that of Mr. -Lassell’s machine. The polisher moves a little off the edge, so that the -edge is worn down more than the centre, thus giving the parabolic form. - -M. Foucault, of whom we have already spoken, proceeds in a different -manner in parabolising his glass mirrors. He first obtains a spherical -surface, fairly reflective, by grinding. He then alters the surface to a -paraboloid form by handwork, only testing the surface from time to time -to ascertain the parts requiring reduction by the polishing pad. The -method of testing is as beautiful as it is simple. The approximate -estimate of the curvature of the speculum is made by placing a small and -well-defined object, such as the point of a pin, close to the centre of -curvature and examining its image formed close by its side with a lens. -As a nicer test, he places an object having parallel sides, say a flat -ruler, near the centre of curvature, and views its image with the naked -eye at the distance of distinct vision, then each point of the edge is -seen by rays converging only from a small portion of the surface of the -mirror, the remainder of the diverging cone from each point of the edge -passes on beside the eye, and by moving the eye about, any point of the -edge can be seen formed by rays proceeding from any particular part of -the mirror, viz., that part in line with the eye and point of the edge -examined; if the curvature be not uniform the edge will appear -distorted, and points on it will appear in different positions, as rays -from different parts of the mirror are received by the eye as it is -moved, making the edge appear to move in waves. Finally, he allows light -from a very small hole in a metal plate near the centre of curvature to -fall on the mirror, and places the eye just on the side opposite to the -point where the image is formed, so as to receive the rays as they -diverge after having come to a focus. The whole of the light thus passes -into the eye, and the mirror is seen illuminated in every part. A sharp -edge of metal is then gradually brought into the focus, when the -illumination of the mirror decreases, and just before the light -disappears the irregularities will plainly appear, showing themselves by -patches of light, which prove that those parts still bright are so -inclined as to reflect the rays by the side of the true focus. By moving -the metallic edge so as to advance upon the focus from all sides, a very -good idea of the irregularities may be obtained. If, however, the -surface be truly spherical, the light will disappear regularly over the -whole surface. - -M. Foucault commences by making the surface truly spherical, and then by -polishing off in concentric circles, increasing the polishing from the -centre, an elliptic and at last a parabolic curve is attained. The -ellipse is tested from time to time by removing the perforated plate -further and further away from the mirror until the ellipse becomes -practically a parabola. The great advantage of this method is, that the -effect of the polishing can be examined as it proceeds, and the work can -always be applied wherever necessary, and the test is entirely -independent of hot-air currents which are seen to fluctuate over the -mirror as waves of light, leaving the irregularities of form permanently -marked. It further appears that the method may be varied to form a -first-rate test of a finished mirror already mounted; for one has -nothing to do but bring a star into the field of view, and remove the -eyepiece, and bring the eye into such a position as to receive the -diverging rays from the focus of the star. A knife is then gradually -moved across in front of the eye, say from the right; then if the mirror -commences to get darkened on the right side distinctly before the left -the knife is on the mirror side of the focus; if, however, the left side -of the mirror becomes darkened first it is on the eye side of the focus. -After a few trials it can be got to cut across the focus and darken the -mirror at all points at once, and show up all irregularities. - -We have now, then, by one system or another, got our mirror, either of -speculum metal or of glass, and if of the latter substance we have to -silver it; processes have been published by Mr. Browning, and M. -Martin,[7] by which, on the plan proposed in the first instance by -Liebig, an extremely thin coating of silver is deposited on the glass. -This film is susceptible of taking a high polish, which, in the case of -small mirrors, can be renewed as often as is wished without repolishing -the mirror; the resilvering of one of large aperture however is a most -formidable affair. To those who wish to silver their own mirrors, let us -say that it should be done in summer, or in a room kept by a stove at an -equable summer heat, and the silvering solution should be kept for a day -or more to settle, and for probably some chemical change to take place -before the reducing solution is added. It will be found easy enough to -silver the small planes for Newtonian reflectors, but large mirrors -require much greater care and trouble. - ------ - -Footnote 6: - - Professor Stokes and Mr. Vernon Harcourt some time ago made - experiments with phosphatic glass, and some of this material was - worked into a lens by Mr. Grubb, who states that “the result was - successful so far as the obtaining of specimens of phosphatic glass - with rational spectra; but phosphatic glass is almost unworkable, and - when the experiment was tried on a siliceous glass it failed. Some - alleviation of this secondary spectrum can be got by using a triple - objective, but with, of course, a corresponding loss of light.” - -Footnote 7: - - Mr. Browning’s method of silvering glass specula is as follows:— - - Prepare three standard solutions: - - Solution A { Crystals of nitrate of silver 90 grains } Dissolve. - { Distilled water 4 ounces } - - Solution B { Potassa, pure by alcohol 1 ounce } Dissolve. - { Distilled water 25 ounces } - - Solution C { Milk-sugar (in powder) ½ ounce } Dissolve. - { Distilled water 5 ounces } - - Solutions A and B will keep, in stoppered bottles, for any length of - time; Solution C must be fresh. To prepare sufficient for silvering an - 8 in. speculum, pour two ounces of Solution A into a glass vessel - capable of holding thirty-five fluid ounces. Add, drop by drop, - stirring all the time (with a glass rod), as much liquid ammonia as is - just necessary to obtain a clear solution of the grey precipitate - first thrown down. Add four ounces of Solution B. The brown-black - precipitate formed must be _just_ re-dissolved by the addition of more - ammonia, as before. Add distilled water until the bulk reaches fifteen - ounces, and add, drop by drop, some of Solution A, until a grey - precipitate, which does not re-dissolve after stirring for three - minutes, is obtained; then add fifteen ounces more of distilled water. - Set this solution aside to settle; do not filter. When all is ready - for immersing the mirror, add to the silvering solution two ounces of - Solution C, and stir gently and thoroughly. Solution C may be - filtered. - - The mirror should be suspended face downwards about ½-inch deep in the - liquid, by strings attached to pieces of wood fastened to the back of - the mirror with pitch, and before being immersed should be cleaned - with nitric acid and washed with distilled water. The silvering is - completed in about an hour, and when finished the surface should be - washed in distilled water and dried, and then polished with soft - leather, finishing with a little rouge. - - The following method is used by M. Martin:— - - Make solutions: - - 1. Nitrate of silver 4 per cent. - 2. Nitrate of ammonia 6 per cent. } perfectly free - 3. Caustic potash 10 per cent. } from carbonates. - - 4. Dissolve twenty-five grammes of sugar in 250 grammes of water; add - three grammes of tartaric acid; heat it to ebullition during ten - minutes to complete the conversion of sugar; cool down, and add fifty - cubic centimetres of alcohol in summer to prevent fermentation, add - water to make the volume to ½ litre in winter and more in summer. - - _Clean well_ the surface of the glass. - - Take equal quantities of the four solutions: mix 1 and 2 together, and - 3 and 4 also together: mix the two, pouring it at once into the vessel - where the silvering is to be done. The mirror is suspended face - downwards in the liquid, and the deposit begins after about three - minutes, and is finished after twenty minutes. Take out the mirror, - clean well with water, dry it in the air, and rub it then gently with - a very fine leather. - - - - - CHAPTER XI. - THE “OPTICK TUBE.” - - -Having now obtained the lenses and specula we come, in order to complete -our consideration of the purely optical portion of the subject, to the -question of mounting these lenses and specula in tubes and thus -connecting them with the eyepieces so as to become of practical utility. -We will first consider the adjustment of lenses in a tube, the -combination forming a simple telescope that can be supported, in any -manner desirable, by mountings we shall presently consider, according to -the purpose for which it is required. The adjustment of specula will be -considered as we advance further. - -The smaller telescopes consist of a brass tube, the object-glass, held -in a brass ring, being screwed in at one end of the tube: a smaller tube -sliding in and out of the other end of the large tube, generally moved -by a rack and pinion motion, carries the eyepiece. In larger telescopes -the mounting is similar, only somewhat more elaborate, the object-glass -being carried in a brass cell, or a steel one if the dimensions are very -large. This screws into the ring at the end of the tube, and this ring -can be slightly tipped on either side by set screws, so that the -object-glass can be brought exactly at right angles to the axis of the -tube. - -[Illustration: - - FIG. 67.—Simple telescope tube, showing arrangement of object-glass - and eyepiece. -] - -It is important, in order that an object-glass shall perform its best, -that the lenses forming it shall be properly centred: this is generally -done by the maker once and for ever. Wollaston pointed out an ingenious -method of centring them; it is as follows:—The eyepiece is removed, and -a lighted candle put in its place: the object-glass is then examined -from the opposite side, when, if all the lenses are correctly placed, -the images of the candle produced by the successive reflections of the -candle from the surfaces of the lenses will be concentric, and in a -straight line from the candle through the centre of the system of -lenses, a fact easily judged of, by moving the eye slightly from side to -side, and if they are not, they are easily corrected by tipping the lens -in fault slightly in the cell. In case the lenses are cemented together, -this method of course is applicable in setting the object-glass at right -angles to the axis of the tube. The adjustment of an object-glass can -also be judged of by examining a star as it is thrown in and out of -focus by the focusing screw; the disc of the star should be perfectly -round in and out of focus, and the rings produced by interference should -also be circular when in focus, and the disc of light, when out of -focus, must be circular. Any elongation of the disc or rings, or a -“flare” appearing, shows a want of a slight alteration of the setting -screw, on the same side of the object-glass as the “flare” or elongation -appears. - -In some object-glasses the curves of the two interior surfaces are such -that three pieces of tin foil are placed at equal distances round the -edge to prevent the central portions from coming in contact. - -[Illustration: - - FIG. 68.—Appearance of diffraction rings round a star when the - object-glass is properly adjusted. -] - -[Illustration: - - FIG. 69.—Appearance of same object when object-glass is out of - adjustment. -] - -The flexure of small object-glasses by their own weight is of little -importance, because every surface is affected alike; but when the -aperture is large special precautions have to be taken. The late Mr. -Cooke when he had completed the 25-inch object-glass for Mr. Newall’s -telescope, introduced a system of counterpoise levers just within the -edge which helped to support the object-glass in all positions. Mr. -Grubb states that with an aperture of 15 inches, supported on three -points, there is decided evidence of flexure, and he proposes, in the -27-inch Vienna refractor, not only to introduce six intermediate -supports, thereby following in the footsteps of Mr. Cooke, but with -larger apertures to introduce boldly a central support, or to -hermetically seal the tube and fill it with compressed air. He has -calculated that in the case of an object-glass 40 inches aperture, -weighing 600 lbs., two-thirds of its weight could be supported by an air -pressure of one-third of a pound to the square inch. - -The tube of the telescope when of large size is usually made of iron or -wood, and a tube of the latter substance may be made very light and yet -sufficiently strong, by wrapping layers of veneer round a central core -and fastening the layers firmly with glue. There are generally two or -more tubes sliding inside each other at the eye end of the telescope, to -carry the eyepiece so as to give plenty of power of adjustment of the -length of the tube to suit the different eyepieces, or other instruments -used in their place. The tube then is ready to be adapted to any of the -mountings to be hereafter considered. - - * * * * * - -We now come to the mounting of specula, and when we recollect the -enormous weights of some of the specimens to which we have referred, it -will be obvious that some additional precautions, which are not at all -necessary in the case of a refractor, must be taken to insure success. - -In reflecting telescopes, the speculum is carried at the bottom of a -tube in a sort of tray or cell, which can be adjusted by screws at the -back, so as to set the mirror at right angles to the tube, and the -conditions of support should be such that the mirror should be as free -from strain as if it were floating in mercury. A system of lateral -supports in all positions is also necessary. - -The action of the telescope depends greatly on the backing of the -speculum, and numerous methods of carrying specula on soft backing and -systems of levers have been suggested, all aiming at carrying them so -that they are free from all possible strain and flexure occasioned by -their own weight. For smaller mirrors a soft back of flannel or cloth -can be used, and a leather strap placed round the mirror and its back, -so as to form the side of a sort of circular tray, will give it -sufficient support when inclined to the horizontal. Mr. Browning adopts -the plan of making the back of the mirror and its support perfectly -flat, so as not to require levers or soft backing; this arrangement -would probably fail for mirrors larger than one foot in diameter, -although answering admirably for those of less size. - -[Illustration: - - FIG. 70.—Optical part of a Newtonian reflector of ten inches aperture, - showing eyepiece, adjusting screws for large speculum, finder, door - for uncovering speculum, and counterpoise. -] - -[Illustration: - - FIG. 71.—Optical part of Melbourne reflector, showing the lattice - arrangement for supporting the convex mirror _Y_, _T_ more solid - part of tube fixed to declination axis, _W_ finder. -] - -[Illustration: - - FIG. 72. Mr. Browning’s method of supporting small specula. The bottom - of the speculum A is a carefully prepared plane surface, and the - outer rim of the inner iron cell B, on which it rests, is also a - plane. The speculum is kept in this cell by the ring G G, and it may - be removed from, and replaced in, the telescope, without altering - its adjustment. -] - -We will now consider the methods of mounting specula of larger size, and -will take as an instance the mounting of some of the largest specula in -existence which must act so as to prevent flexure in any position of the -speculum. The speculum is, in the case of the Melbourne telescope, of -the weight of something like two tons. When it is inclined at any -considerable angle to the horizon, it is apt to bend over at the top, -and thus destroy its proper curvature; and when horizontal, if not -equally supported, it will also bend, and unless some measures are taken -to prevent this flexure it will so entirely alter its figure by its own -weight as to render minute observations of any delicate stars absolutely -impossible. - -Mr. Lassell was the first to suggest an arrangement for preventing this -flexure. Through the back of the speculum case—the case which holds and -supports the speculum, which we shall have to speak about presently—he -inserts a large number of very small levers, the centres of which are -fixed to the exterior part of this case, the forward part of each -resting against a small aperture made in the back of the speculum. The -ends of the levers furthest from the speculum are crowned with small -weights, the weights varying on different parts of the speculum. Now so -long as the speculum is perfectly horizontal, _i.e._ so long as the -zenith is being observed, these levers will have no action whatever; but -the moment the reflector is brought into any other position, as, for -instance, when we wish to observe a star near the horizon, the more the -mirror is inclined to the horizon the greater will be the power of these -small levers, and at length their total effect comes into action when a -star close to the horizon is being observed. Then the whole weight of -the mirror is carried by these levers acting at points all over its -back. - -In the Melbourne reflector, which has recently been finished, Mr. Grubb -manages this somewhat differently, as will be seen by Figs. 73-76. - -In Fig. 73 the speculum is in a vertical position. It is supported in a -frame, B B, all round it, which consists of a slightly flexible hoop of -metal a little larger than the speculum. This in its turn is supported -by a large fixed hoop, A A, having a hook-shaped section. This hoop is -attached to the tube of the telescope C C. The hoop, B B, is rather -larger than the part of A on which it hangs, so that it can adjust -itself to the form of the mirror; and not only is the mirror supported -in the hoop B B, like as in a strap in the position shown, but in every -other position of the tube the speculum still hangs evenly supported. - -[Illustration: - - FIG. 73.—Support of the mirror when vertical. -] - -As we have already seen, there is another point to consider. Not only -must we be able to support the mirror when inclined to the horizon, but -we must support it bodily at the end of the tube when it is horizontal. -We will next examine an arrangement adopted by Mr. Grubb, similar to -that adopted by others, for supporting the Melbourne speculum, and we -cannot do better than quote Mr. Grubb’s own explanation of it. He says:— - - “To understand it, suppose the speculum to be divided into - forty-eight portions, as in Fig. 74, each of them being exactly - equal in area, and consequently in weight. Now, if the centre of - gravity of each of these pieces rested on points which would bear up - with a force = the weight of each segmental piece, it is evident - that there would be no strain in the mass from segment to segment. - -[Illustration: - - FIG. 74.—Division of the speculum into equal areas. -] - - “This is exactly what is accomplished by this system; in fact, if - when the speculum is resting on these supports it could be divided - up into segments corresponding to those lines, they would have no - inclination to leave their places, showing a perfect absence of - strain across those lines. Suppose now the points representing the - centres of gravity of these segments were supported on levers and - triangles, so as to couple them together, as at A, Fig. 75, and each - of these couplings to be supported from a point _a_, representing - the centre of gravity of the sum of the segments supported by that - particular couple, and it is evident that there can be no strain - between the components of these couples. Again, let these points, - _a_, be coupled together by the system shown at B, Fig. 75, and - their centres of gravity, _b_, coupled as at C, and it is evident - that the whole weight of the speculum ultimately condensed by this - system into these points is supported on forty-eight points of equal - support being the centres of gravity of the forty-eight segments at - Fig. 75. In Fig. 76 is seen the whole system complete. It consists - of three screws passing through the back of the speculum box (which - serve for levelling the mirror), the points of which carry levers - (_primary system_) supporting triangles on their extremities - (_secondary system_), from the vertices of which are hung two - triangles and one lever (_tertiary system_). All the joints of this - apparatus are capable of a small rocking motion, to enable them to - take their positions when the speculum is laid upon them. - -[Illustration: - - FIG. 75.—Primary, secondary, and tertiary systems of levers shown - separately. -] - -[Illustration: - - FIG. 76.—Complete system consolidated into three screws. -] - - “In the system of levers made by Lord Rosse for his six-feet - speculum, the primary, secondary, and tertiary systems were piled up - one over the other, so that the distance from the support of the - primary to the back of the speculum was about fifteen inches. This, - as will be readily seen on consideration, introduced a new strain - when the telescope was turned off the zenith, and had to be - counterpoised by another very complicated system of levers. But in - the Melbourne telescope, by the substitution of cast-steel for - cast-iron, and by hanging the tertiary system from the secondary, - and allowing it (_the tertiary_) to act in some places through the - secondary, the whole system is reduced to three and a half inches in - height, and the distance from the support of the primary lever to - the back of the speculum is only one and three-quarter inch, by - which means this cumbersome apparatus is entirely done away with. - - “The ultimate points of the tertiary system are gunmetal cups, which - hold truly ground cast-iron balls with a little play, and when the - speculum is laid on these it can be moved about a little by a - person’s finger with such ease as to seem to be floating in some - liquid.” - -It may perhaps be thought that it would be better to support these great -specula on a flat surface, and it might be, if we could do so without -extreme difficulty; but Lord Rosse has stated that if we attempt to -support a large speculum on a surface extremely flat, a thread placed -across that surface, or even a piece of dust, is quite enough to bend -the mirror and render it absolutely useless. That will show the extreme -importance of the support of the speculum. - -Let us then assume that we have the speculum and the tube perfectly -adjusted. The next thing, in all constructions except the Herschelian, -is to apply the second small reflector, concave in the case of the -Gregorian, convex in the case of the Cassegrainian, and plane in the -case of the Newtonian. - -This small mirror is generally supported by a thin strip of metal firmly -fastened to the side of the tube, with power of movement parallel to the -axis of the telescope, in the case of the Gregorian and Cassegrainian, -for the purpose of focussing. In the Newtonian, the reflecting diagonal -prism or plane mirror, inclined at an angle of 45° to the axis, is -preferably supported in the manner suggested by Mr. Browning. See Figs. -77 and 78. - -In these B B B represent strips of strong chronometer spring steel, -placed edgewise towards the speculum; by these the prism or small mirror -D is suspended. - -The mirror thus mounted, does not produce such coarse rays on bright -stars as when it is fixed to a single stout arm; it is also less liable -to vibration, which is very injurious to distinct vision, or to flexure, -which interferes with the accuracy of the adjustments. - -[Illustration: - - FIG. 77.—Support of diagonal plane mirror (Front view). -] - -[Illustration: - - FIG. 78.—Support of diagonal plane mirror (Side view). -] - -The most usual form of reflector is the Newtonian, large numbers of -which kind are now made; and just as the object-glasses of refractors -require adjusting, so do not only the large mirror, but also the “flat” -or diagonal mirror of this form. In the Newtonian the flat must be -adjusted first; to do this, first place the large mirror in its cell in -the tube, and secure it by turning it in the bayonet joint, _with the -cover on the mirror_. Then remove the glasses from one of the eyepieces, -insert it into the eyetube, and fix the diagonal mirror loosely in its -position. - -Then, looking through the eyetube, move the diagonal mirror, by means of -the motions which are provided, until the reflected image of the cover -of the speculum is seen in the _centre_ of it. - -This is accomplished by first loosening the milled-headed screw behind -the mirror, and turning the mirror until the image of the speculum cover -appears central in one direction. The screw at the back of the mirror -enables the reflected image to be brought central in the other -direction. - -Next comes the turn of the large mirror. Take off the cover by screwing -off the side opening and place the eye at the eyetube after having -removed the eyepiece; the reflection of the diagonal mirror will be seen -in the reflected image of the speculum. The adjusting screws, at the -back of the speculum, must then be moved until the diagonal mirror is -seen in the centre of the speculum. The adjustment should then be -complete. - -This may be judged of by bringing a star to the centre of the field, and -sliding the focussing-tube in or out, when the circle of light should -expand equally, and its centre should remain central in the field. As -another test a bright star should be viewed with a high power, and the -image examined; if it is round and the circles of light round it are -concentric without rays in any one direction, then all is correct; but -if a flare is seen, it is evidence that the part of the diagonal mirror -towards which the flare extends must be moved from the eye by the -setting-screws at the back. - - - - - CHAPTER XII. - THE MODERN TELESCOPE. - - -The gain to astronomy from the discovery of the telescope has been -twofold. We have first, the gain to physical astronomy from the -magnification of objects, and secondly, the gain to astronomy of -position from the magnification, so to speak, of _space_, which enables -minute portions of it to be most accurately quantified. - -Looking back, nothing is more curious in the history of astronomy than -the rooted objection which Hevel and others showed to apply the -telescope to the pointers and pinnules of the instruments used in their -day; but doubtless we must look for the explanation of this not only in -the accuracy to which observers had attained by the old method, but in -the rude nature of the telescope itself in the early times, before the -introduction of the micrometer. We shall show in a future chapter how -the modern accuracy has step by step been arrived at; in the present one -we have to see what the telescope does for us in the domain of that -grand physical astronomy which deals with the number and appearances of -the various bodies which people space. - -Let us, to begin with, try to see how the telescope helps us in the -matter of observations of the sun. The sun is about ninety millions of -miles away; suppose, therefore, by means of a telescope reflecting or -refracting, whichever we like, we use an eyepiece which will magnify say -900 times, we obviously bring the sun within 100,000 miles of us; that -is to say, by means of this telescope we can observe the sun with the -naked eye as if it were within 100,000 miles of us. One may say, this is -something, but not much; it is only about half as far as the moon is -from us. But when we recollect the enormous size of the sun, and that if -the centre of the sun occupied the centre of our earth the circumference -of the sun would extend considerably beyond the orbit of the moon, then -one must acknowledge we have done something to bring the sun within half -the distance of the moon. Suppose for looking at the moon we use on a -telescope a power of 1,000, that is a power which magnifies a thousand -times, we shall bring the moon within 240 miles of us, and we shall be -able to see the moon with a telescope of that magnifying power pretty -much as if the moon were situated somewhere in Lancashire—Lancaster -being about 240 miles from London. - -It might appear at first sight possible in the case of all bodies to -magnify the image formed by the object-glass to an unlimited extent by -using a sufficiently powerful eyepiece. This, however, is not the case, -for as an object is magnified it is spread over a larger portion of the -retina than before; the brightness, therefore, becomes diminished as the -area increases, and this takes place at a rate equal to the square of -the increase in diameter. If, therefore, we require an object to be -largely magnified we must produce an image sufficiently bright to bear -such magnification; this means that we must use an object-glass or -speculum of large diameter. Again, in observing a very faint object, -such as a nebula or comet, we cannot, by decreasing the power of the -eyepiece, increase the brightness to an unlimited extent, for as the -power decreases, the focal length of the eyepiece also increases, and -the eyepiece has to be larger, the emergent pencil is then larger than -the pupil of the eye, and consequently a portion of the rays of the cone -from each point of the object is wasted. - -[Illustration: - - FIG. 79.—A portion of the constellation Gemini seen with the naked - eye. -] - -We get an immense gain to physical astronomy by the revelations of the -fainter objects which, without the telescope, would have remained -invisible to us; but, as we know, as each large telescope has exceeded -preceding ones in illuminating power, the former bounds of the visible -creation have been gradually extended, though even now we cannot be said -to have got beyond certain small limits, for there are others beyond the -region which the most powerful telescope reveals to us; though we have -got only into the surface we have increased the 3,000 or 6,000 stars -visible to the naked eye to something like twenty millions. This -space-penetrating power of the telescope, as it is called, depends on -the principle that whenever the image formed on the retina is less than -sufficient to appear of an appreciable size the light is apparently -spread out by a purely physiological action until the image, say of a -star, appears of an appreciable diameter, and the effect on the retina -of such small points of light is simply proportionate to the amount of -light received, whether the eye be assisted by the telescope or not; the -stars always, except when sufficiently bright to form diffraction rings, -appearing of the same size. It, therefore, happens that as the apertures -of telescopes increase, and with them the amount of light, (the -eyepieces being sufficiently powerful to cause all the light to enter -the eye,) smaller and smaller stars become visible, while the larger -stars appear to get brighter and brighter without increasing in size, -the image of the brightest star with the highest power, if we neglect -rays and diffraction rings, being really much smaller than the apparent -size due to physiological effects, and of this latter size every star -must appear. - -[Illustration: - - FIG. 80.—The same region, as seen through a large telescope. -] - -The accompanying woodcuts of a region in the constellation of Gemini as -seen with the naked eye and with a powerful telescope will give a better -idea than mere language can do of the effect of this so-called -space-penetrating power. - -[Illustration: - - FIG. 81.—Orion and the neighbouring constellations. -] - -With nebulæ and comets matters are different, for these, even with small -telescopes and low powers, often occupy an appreciable space on the -retina. On increasing the aperture we must also increase the power of -the eyepiece, in order that the more divergent cones of light from each -point of the image shall enter the pupil, and therefore increase the -area on the retina, over which the increased amount of light, due to -greater aperture, is spread; the brightness therefore is not increased, -unless indeed we were at the first using an unnecessary high power. On -the other hand, if we lengthen the focus of the object-glass, and -increase its aperture, the divergence of the cones of light is not -increased and the eyepiece need not be altered, but the image at the -focus of the object-glass is increased in size by the increase of focal -length, and the image on the retina also increases as in the last case. -We may, therefore conclude that no comet or nebula of appreciable -diameter, as seen through a telescope having an eyepiece of just such a -focal length as to admit all the rays to the eye, can be made brighter -by any increase of power, although it may easily be made to appear -larger. - -[Illustration: - - FIG. 82.—Nebula of Orion. -] - -Very beautiful drawings of the nebula of Orion and of other nebulæ, as -seen by Lord Rosse in his six-foot reflector, and by the American -astronomers with their twenty-six inch refractor, have been given to the -world. - -The magnificent nebula of Orion is scarcely visible to the naked eye; -one can just see it glimmering on a fine night; but when a powerful -telescope is used, it is by far the most glorious object of its class in -the Northern hemisphere, and surpassed only by that surrounding the -variable star η Argûs in the Southern. And although, of course, the -beauty and vastness of this stupendous and remote object increase with -the increased power of the instrument brought to bear upon it, a large -aperture is not needed to render it a most impressive and awe-inspiring -object to the beholder. In an ordinary 5-foot achromatic, many of its -details are to be seen under favourable atmospheric conditions. - -Those who are desirous of studying its appearance, as seen in the most -powerful telescopes, are referred to the plate in Sir John Herschel’s -“Results of Astronomical Observations at the Cape of Good Hope,” in -which all its features are admirably delineated, and the positions of -150 stars which surround θ in the area occupied by the Nebula, laid -down. In Fig. 82 it is represented in great detail, as seen with the -included small stars, all of which have been mapped with reference to -their positions and brightness. This then comes from that power of the -telescope which simply makes it a sort of large eye. We may measure the -illuminating power of the telescope by a reference to the size of our -own eye. If one takes the pupil of an ordinary eye to be something like -the fifth of an inch in diameter, which in some cases is an extreme -estimate, we shall find that its area would be roughly about -one-thirtieth part of an inch. If we take Lord Rosse’s speculum of six -feet in diameter the area will be something like 4,000 inches: and if we -multiply the two together we shall find, if we lose no light, we should -get 120,000 times more light from Lord Rosse’s telescope than we do from -our unaided eye, everything supposed perfect. - -Let us consider for a moment what this means; let us take a case in -point. Suppose that owing to imperfections in reflection and other -matters two-thirds of the light is lost so that the eye receives 40,000 -times the amount given by the unaided vision, then a sixth magnitude -star—a star just visible to the naked eye—would have 40,000 times more -light, and it might be removed to a distance 200 times as great as it at -present is and still be visible in the field of the telescope, just as -it at present is to the unaided eye. Can we judge how far off the stars -are that are only just visible with Lord Rosse’s instrument? Light -travels at the rate of 185,000 miles a second, and from the nearest star -it takes some 3½ years for light to reach us, and we shall be within -bounds when we say that it will take light 300 years to reach us from -many a sixth magnitude star. - -But we may remove this star 200 times further away and yet see it with -the telescope, so that we can probably see stars so far off that light -takes 60,000 years to reach us, and when we gaze at the heavens at night -we are viewing the stars not as they are at that moment, but as they -were years or even hundreds of years ago, and when we call to our -assistance the telescope the years become thousands and tens of -thousands—expressed in miles these distances become too great for the -imagination to grasp; yet we actually look into this vast abyss of space -and see the laws of gravitation holding good there, and calculate the -orbit of one star about another. - -Whether the telescope be of the first or last order of excellence, its -light-grasping powers will be practically the same; there is therefore a -great distinction to be drawn between the illuminating and defining -power. The former, as we have seen, depends upon size (and subsidiarily -upon polish), the latter depends upon the accuracy of the curvature of -the surface. - -[Illustration: - - FIG. 83.—Saturn and his moons (general view with a 3¾-inch - object-glass.) -] - -If the defining power be not good, even if the air be perfect, each -increase of the magnifying power so brings out the defects of the image, -that at last no details at all are visible, all outlines are blurred, or -stellar character is lost. - -The testing of a glass therefore refers to two different qualities which -it should possess. Its quality as to material and the fineness of its -polish should be such that the maximum of light shall be transmitted. -Its quality, as to the curves, should be such that the rays passing -through every part of its area shall converge absolutely to the same -point, with a chromatic aberration not absolutely _nil_, but sufficient -to surround objects with a faint violet light. - -[Illustration: - - FIG. 84.—Details of the ring of Saturn observed by Trouvelot with the - 26-inch Washington Refractor. -] - -In close double stars therefore, or in the more minute markings of the -sun, moon, or planets, we have tests of its defining power; and if this -is equally good in the instruments examined, the revelations of -telescopes as they increase in power are of the most amazing kind. - -A 3¾-inch suffices to show Saturn with all the detail shown in Fig. 83, -while Fig. 84 shows us the further minute structure of the rings which -comes out when the planet is observed with an aperture of 26 inches. - -In the matter of double stars, a telescope of 2 inches aperture, with -powers varying from 60 to 100, should show the following stars double:— - - Polaris. - α Piscium. - μ Draconis. - γ Arietis. - ρ Herculis. - ζ Ursæ Majoris. - α Geminorum. - γ Leonis. - ξ Cassiopeæ. - -A 4-inch aperture, powers 80-120, reveals the duplicity of— - - β Orionis. - ε Hydræ. - ε Boötis. - ι Leonis. - α Lyræ. - ξ Ursæ Majoris. - γ Ceti. - δ Geminorum. - σ Cassiopeæ. - ε Draconis. - -A 6-inch, powers 240-300— - - ε Arietis. - 32 Orionis. - λ Ophiuchi. - 20 Draconis. - κ Geminorum. - ι Equulei. - ξ Herculis. - ξ Boötis. - -An 8-inch— - - δ Cygni. - γ^2 Andromedæ. - Sirius. - 19 Draconis. - μ^2 Herculis. - μ^2 Boötis. - -The “spurious disk,” which a fixed star presents, as seen in the -telescope, is an effect which results from the passage of the light -through the object-glass; and it is this appearance which necessitates -the use of the largest apertures in the observation of close double -stars, as the size of the star’s disk varies, roughly speaking, in the -inverse ratio of the aperture of the object-glass. - -In our climate, which is not so bad as some would make it, a 6- to an -8-inch glass is doubtless the size which will be found the most -constantly useful; a larger aperture being frequently not only useless, -but hurtful. Still, 4 or 3¾ inches are apertures by all means to be -encouraged; and by object-glasses of these sizes, made of course by the -_best_ makers, views of the sun, moon, planets, and double stars may be -obtained, sufficiently striking to set many seriously to work as amateur -observers, and with a prospect of securing good, useful results. - -Observations should always be commenced with the lowest power, gradually -increasing it until the limit of the aperture, or of the atmospheric -condition at the time, is reached. The former may be taken as equal to -the number of hundredths of inches which the diameter of the -object-glass contains. Thus, a 3¾-inch object-glass, if really good, -should bear a power of 375 on double stars where light is no object; the -planets, the Moon, &c., will be best observed with a much lower power. -(See chapter on eyepieces.) - -Care should be taken that the object-glass is properly adjusted. And we -may here repeat that this may be done by observing the image of a large -star out of focus. If the light be not equally distributed over the -image, or the diffraction rings are not circular, the screws of the cell -should be carefully loosened, and that part of the cell towards which -the rings are thrown very gently tapped with wood, to force it towards -the eyepiece, or the same purpose may be effected by means of the -setscrews always present on large telescopes, until perfectly equal -illumination is arrived at. This, however, should only be done in -extreme cases; it is here especially desirable that we should let well -alone. - -The convenient altitude at which Orion culminates in these latitudes -renders it particularly eligible for observation; and during the first -months of the year our readers who would test their telescopes will do -well not to lose the opportunity of trying the progressively difficult -tests, both of illuminating and separating power, afforded by its -various double and multiple systems, which are collected together in -such a circumscribed region of the heavens that no extensive movement of -their instruments—an important point in extreme cases—will be necessary. - -Beginning with δ, the upper of the three stars which form the belt, -the two components will be visible in almost any instrument which may -be used for seeing them, being of the second and seventh magnitudes, -and well separated. The companion to β, though of the same magnitude -as that to δ, is much more difficult to observe, in consequence of its -proximity to its bright primary, a first-magnitude star. Quaint old -Kitchener, in his work on telescopes, mentions that the companion to -Rigel has been seen with an object-glass of 2¾-inch aperture; it -should be seen, at all events, with a 3-inch. ζ, the bottom star in -the belt, is a capital test both of the dividing and space-penetrating -power, as the two bright stars of the second and sixth magnitudes, of -which the close double is composed, are exactly 2½˝ apart, while there -is a companion to one of these components of the twelfth magnitude -about ¾˝ distant. The small star below, which the late Admiral Smyth, -in his charming book, “The Celestial Cycle,” mentions as a test for -his object-glass of 5·9 inches in diameter, is now plainly to be seen -in a 3¾. The colours of this pair have been variously stated; Struve -dubbing the sixth magnitude—which, by the way, was missed altogether -by Sir John Herschel—“olivaceasubrubicunda.” - -That either our modern opticians contrive to admit more light by means -of a superior polish imparted to the surfaces of the object-glass, or -that the stars themselves are becoming brighter, is again evidenced by -the point of light preceding one of the brightest stars in the system -composing σ. This little twinkler is now always to be seen in a 3¾-inch, -while the same authority we have before quoted—Admiral Smyth—speaks of -it as being of very difficult vision in his instrument of much larger -dimensions. In this very beautiful compound system there are no less -than seven principal stars; and there are several other faint ones in -the field. The upper very faint companion of λ is a delicate test for a -3¾-inch, which aperture, however, will readily divide the closer double -of the principal stars which are about 5˝ apart. - -These objects, with the exception of ζ, have been given more to test the -space-penetrating than the dividing power; the telescope’s action on 52 -Orionis will at once decide this latter quality. This star, just visible -to the naked eye on a fine night, to the right of a line joining α and -δ, is a very close double. The components, of the sixth magnitude, are -separated by less than two seconds of arc, and the glass which shows a -_good wide black division_ between them, free from all stray light, the -spurious disk being perfectly round, _and not too large_, is by no means -to be despised. - -Then, again, we have a capital test object in the great nebula to which -reference has already been made. - -The star, to which we wish to call especial attention, is situate (see -Fig. 82) opposite the bottom of the “fauces,” the name given to the -indentation which gives rise to the appearance of the “fish’s mouth.” -This object, which has been designated the “trapezium,” from the figure -formed by its principal components, consists, in fact, of six stars, the -fifth and sixth (γ´ and α´) being excessively faint. Our previous -remark, relative to the increased brightness of the stars, applies here -with great force; for the fifth escaped the gaze of the elder Herschel, -armed with his powerful instruments, and was not discovered till 1826, -by Struve, who, in his turn, missed the sixth star, which, as well as -the fifth, has been seen in modern achromatics of such small size as to -make all comparison with the giant telescopes used by these astronomers -ridiculous. - -Sir John Herschel has rated γ´ and α´ of the twelfth and fourteenth -magnitudes—the latter requires a high power to observe it, by reason of -its proximity to α. Both these stars have been seen in an ordinary -5-foot achromatic, by Cooke, of 3¾-inches aperture, a fact speaking -volumes for the perfection of surface and polish attained by our modern -opticians. - -Let us now try to form some idea of the perfection of the modern -object-glass. We will take a telescope of eight inches aperture, and ten -feet focal length. Suppose we observe a close double star, such as ξ -Ursæ, then the images of these two stars will be brought to a focus side -by side, as we have previously explained, and the distance by which they -will be separated will be dependent on the focal length of the -object-glass. If we refer once again to Fig. 39 we shall see that this -distance depends on the focal length and on the angle subtended by the -images of the stars at the object-glass, which is of course the same as -the angle made by the real stars at the object-glass, which is called -their angular distance, or simply their distance, and is expressed in -seconds of arc. - -If we take a telescope ten feet long and look at two stars 1° apart, the -angle will be 1°; and at ten feet off the distance between the two -images will be something like 2⅒ inches, and therefore, if the angle be -a second, the lines will be the 1/3600th part of that, or about 1/1700th -part of an inch apart, so that in order to be able to see the double -star ξ Ursæ, which is a 1˝ star, by means of an eight-inch object-glass, -all the surfaces, the 50 square inches of surface, of both sides of the -crown, and both sides of the flint glass, must be so absolutely true and -accurate, that after the light is seized by the object-glass, we must -have those two stars absolutely perfectly distinct at the distance of -the seventeen hundredth part of an inch, and in order to see stars ½˝ -apart, their images must be distinct at one-half of this distance or at -1/3400th part of an inch from each other. - -We know that both with object-glasses and reflectors a certain amount of -light is lost by imperfect reflection in the one case, and by reflection -from the surfaces and absorption in the other; and in reflectors we have -generally two reflections instead of one. This loss is to the distinct -disadvantage of the reflector, and it has been stated by authorities on -the subject, that, light for light, if we use a reflector, we must make -the aperture twice as large as that of a refractor in order to make up -for the loss of light due to reflection. But Dr. Robinson thinks that -this is an extreme estimate; and with reference to the four-foot -reflector which has recently been constructed, and of which mention has -already been made, he considers that a refractor of 33·73 inches -aperture would be probably something like its equivalent if the glass -were perfectly transparent, which is not the case, and when the -thickness of such a lens came to be considered, it was calculated that -instead of its being equal to the four-foot reflector, it would only be -equal to one of 37¼ of similar construction, and that even a refractor -of 48 inches aperture, if such could be made, would not come up to the -same sized reflector just referred to in illuminating power. - -On the assumption, therefore, that no light is lost in transmission -through the object-glass, Dr. Robinson estimates that the apertures of a -refractor and a reflector of the Newtonian construction must bear the -relation to each other of 1 to 1·42. In small refractors the light -absorbed by the glass is small, and therefore this ratio holds -approximately good, but we see from the example just quoted how more -nearly equal the ratio becomes on an increase of aperture, until at a -certain limit the refractor, aperture for aperture, is surpassed by its -rival, supposing Dr. Robertson’s estimate to be correct. But with -specula of silvered glass the reflective power is much higher than that -of speculum metal; the silvered glass, being estimated to reflect about -90 per cent.[8] of the incident light, while speculum metal is estimated -to reflect about 63 per cent.; but be these figures correct or not, the -silvered surface has undoubtedly the greater reflective power; and, -according to Sir J. Herschel, a reflector of the Newtonian construction -utilizes about seven-eighths of the light that a refractor would do. - -Speaking generally, refractors of sizes usually obtainable are -preferable to reflectors of equal and even greater aperture for ordinary -work; as in addition to the want of illuminating power of reflectors, -the absence of rigidity of the mounting of the speculum militates -against its comfort of manipulation. - -In treating of the question of the future of the telescope, we are -liable to encroach on the domain of opinion and go beyond the facts -vouched for by evidence, but there are certain guiding principles which -are well worthy of discussion. There are the two classes of telescopes, -the refractors and reflectors, each possessing advantages over the -other. We may set out with observing that the light-grasping power of -the reflector varies as the square of the aperture multiplied by a -certain fraction representing the proportion of the amount of reflected -light to that of the total incident rays. On the other hand, the power -of the refractor varies as the square of the aperture multiplied by a -certain fraction representing the proportion of transmitted light to -that of the total incident rays. Now in the case of the reflector the -reflecting power of each unit of surface is constant whatever be the -size of the mirror, but in that of the refractor the transmitting power -decreases with the thickness of the glass, rendered requisite by -increased size, although for small apertures the transmitting power of -the refractor is greater than the reflecting power of the reflector; -still it is obvious that on increasing the size a stage must be at last -reached when the two rivals become equal to each other. This limit has -been estimated by Dr. Robinson to be 35·435 inches, a size not yet -reached by our opticians by some 10 inches, but object-glasses are -increasing inch by inch, and it would be rash to say that this size -cannot be reached within perhaps the lifetime of our present workers, -but up to the present limit of size produced, refractors have the -advantage in light-grasping power. - -The next point worthy of attention is the question of permanence of -optical qualities. Here the refractor undoubtedly has the advantage. It -is true that the flint glass of some objectives gets attacked by a sort -of tarnish, still, that is not the case generally, while, on the other -hand, metallic mirrors often become considerably tarnished after a few -years of use, and although repolishing is not a matter of any great -difficulty in the hands of the maker, still it is a serious drawback to -be obliged to return mirrors every few years to be repolished. There -are, however, some exceptions to this, for there are many small mirrors -in existence whose polish is good after many years of continuous use, -just as on the other hand there are many object-glasses whose polish has -suffered in a few years, but these are exceptions to the rule. The same -remarks apply to the silvered glass reflectors, for although the -silvering of small mirrors is not a difficult process, the matter -becomes exceedingly difficult with large surfaces, and indeed at present -large discs of glass, say of four or six feet diameter, cannot be -produced. If, however, a process should be discovered of manufacturing -these discs satisfactorily and of silvering them, there are objections -to them on the grounds of the bad conductivity of glass, whereby changes -of temperature alter the curvature to a fatal extent, and there is also -a great tendency for dew to be deposited on the surface. - -The next point to be considered is the general suitability for -observatory work, and this depends upon the quality of the work -required, whether for measuring positions, as in the case of the transit -instrument, where permanency of mounting is of great importance, or for -physical astronomy, when a steady image for a time is only required. For -the first purpose the refractor has decidedly the advantage, as the -object-glass can be fixed very nearly immovably in its cell, whereas its -rival must of necessity, at least with present appliances, have a small, -yet in comparison considerable, motion. - -Again, the refractor has the advantage over the other in not being of so -large aperture when of equal power, so that the disturbing effects of -air currents is considerably less, but the method of making the tubes of -open lattice-work materially reduces this objection. - -We have mentioned the difficulty of mounting mirrors, especially of -large size, but this has now been got over very perfectly. This -difficulty does not occur in the mounting of object-glasses of sizes at -present in use, but when we come to deal with lenses of some 30 inches -diameter, the present simple method will in all probability be found -insufficient. - -On the other hand the cost of mirrors is of course much less than that -of object-glasses, a matter of considerable importance. The late M. -Merz, on being asked as to price of a 30-inch object-glass, estimated -that, if it were possible to make it, its cost would be between £8,500 -and £9,000. - -There is one great point of advantage in the use of the reflector in -physical work,—the absence of secondary spectrum; but it is by no means -certain that stellar photography will not be more easy with refractors. - ------ - -Footnote 8: - - Sir John Herschel, in his work on the telescope, gives the following - table of reflective powers:— - - After transmission through one surface of glass not in contact 0·957 - with any other surface - - After transmission through one common surface of two glasses 1·000 - cemented together - - After reflection on polished speculum metal at a perpendicular 0·632 - incidence - - After reflection on polished speculum metal at 45° obliquity 0·690 - - After reflection on pure polished silver at a perpendicular 0·905 - incidence - - After reflection on pure polished silver at 45° obliquity 0·910 - - After reflection on glass (external) at a perpendicular 0·043 - incidence - - The effective light in reflectors (irrespective of the eyepieces) is - as follows:— - - Herschelian (Lord Rosse’s speculum metal) A. 0·632 - Newtonian (both mirrors ditto) B. 0·436 - Newtonian (small mirror or glass prism) C. 0·632 - Gregorian or Cassegrainian D. 0·399 - - { A. 0·905 - The same telescopes, all the metallic { B. 0·824 - reflections being from pure silver { C. 0·905 - { D. 0·819 - - - - - BOOK III. - _TIME AND SPACE MEASURERS._ - - - - - CHAPTER XIII. - THE CLOCK AND CHRONOMETER. - - - I. THE RISE AND PROGRESS OF TIME-KEEPING. - -When we dealt with the astronomical instruments of Hipparchus, we saw -that although the astrolabe which that great observer used was the germ -of our modern instruments, the time recorded by Hipparchus and those who -lived after him down to the later times of the Roman Empire was, as they -measured it, a time which would be entirely useless for us. - -The ancients contented themselves with dividing the interval between -sunrise and sunset, regardless whether this was in summer or winter, -into twelve equal hours. Now, as in summer the sun is longer above the -horizon than in winter in these northern latitudes, we have more time -during which the sun is above the horizon in summer than in winter, and -if that period of time is to be divided into twelve hours, the hours -would be much longer in summer than in other seasons. - -As we are informed by Herodotus, tables were made by which these varying -lengths of hours might be indicated by the shadows of a pole, which they -called a gnomon or style. This was placed in a given locality, and the -hour of the day was determined by the position of the shadow of the -gnomon; and we need scarcely say that as Hipparchus observed he was -compelled to find the position of the sun in order to determine the -absolute longitude of a star at night. The ancients were limited to such -ideas of time as could be got from slaves, who watched the risings and -settings of the constellations, and who tried to bring to their own -minds and those of their masters some idea of the lapse of time; and -this even a few centuries ago was ordinarily depended upon in several -countries. - -Then, a little later, we come to the time being measured by monks -repeating psalms—a certain number perhaps in the hour; and there were -the water and sand clocks dating from Aristophanes, which were the -predecessors of our sand-glasses. Candles were also at one time used -with divisions on them to show how long they had been burning. But when -we come to clocks proper, the history of which is very imperfectly -known, we find an enormous improvement upon this state of things; -because the clock, being dependent upon a constant mechanical action -produced by the fall of a weight, could not be got to imitate these -varying hours. - -Still the clock had to fight its own battle for all that; and the first -clocks were altered from week to week, or from month to month, so that -the time-keeper, which did its best to be constant, was made inconstant -to represent the ever-varying hours. - -Doubtless the history of the first clocks—by which we do not mean the -sand clocks or water clocks of the ancients, but such as those used by -Archimedes when he attached wheels together—is lost in obscurity; and -whether clocks, as we have them, were suggested in the sixth (Boethius, -A.D. 525) or ninth century matters little for our inquiry; but beyond -all doubt the first clock of considerable importance that was put up in -England was the one erected in Old Palace Yard in the year 1288, as the -result of a fine imposed upon the Lord Chief Justice of that time. - -[Illustration: - - FIG. 85.—Ancient Clock Escapement. -] - -If we have a falling weight as a time-measurer we must also have some -opposing force—a regulator in fact, so that the weight becomes the -source of power, and the regulator the time-measurer; therefore, in -addition to the fall of the weight, we find in the earliest clocks a -regulating power to prevent the weight falling too fast. So we have the -two contending powers, first the weight causing the motion and then the -regulator. - -The first thing which was introduced as a regulator was a fly-wheel. -There was a fly-wheel of a certain weight, and the force which was -applied to the clock had to turn the wheel against the resistance of the -air; but that did not answer well, and the first tolerable arrangement -was suggested by Henry de Wyck, who constructed a bell and a clock in -1364, in which the fall of the weight was prevented by an oscillating -balance, similar to that shown in Fig. 85. - -[Illustration: - - FIG. 86.—The Crown Wheel. -] - -Here we see what is called the crown wheel (S S, shown in plan, Fig. -86), on which the escapement depends, and into the teeth of which work -two pallets, P_{1} P_{2}, which are placed on a vertical axis pivoted -above and below. Now if we suppose a weight attached to the cord passing -over a drum, so as to propel the intermediate wheels and pull them -round, the crown wheel tends to rotate, but is prevented from moving -until the pallets give way. Let us see how the clock goes. When the -bottom tooth, presses against the pallet P_{1}, in order to make it get -out of the way and enable the wheel to go on, it twists the rod and -moves the horizontal bar M M, on which are several saw-like teeth, on -the intervals of which, as in the modern steelyard, weights are placed, -so that the wheel pushes away the pallet and makes the horizontal beam -describe a part of a circle. And what happens is this:—the upper pallet -is turned out of its position and driven into the upper teeth of the -wheel, and driven out by the further revolution of the wheel, so that -the fall of the weight depends on the oscillations of the horizontal -beam which carries the weights. The clock was regulated by the distance -of the weights from the pivots on which the balance swung. Such was the -form of clock used by Tycho Brahe, but with little success, for it was -extremely irregular in its action, and Tycho still had to compare the -position of one star with another instead of trusting to his clock. - -There is no necessity to say much regarding the train of wheels between -the weight or spring and the escapement. Their office is simply to -create a great difference in velocity of rotation between the wheel -turned by the weight or spring and the escape wheel, so that a slow -motion with great force may be transformed into a quick motion with -small force. The train of wheels is so arranged, by the consideration of -the number of teeth in the wheels, that one wheel shall go round once an -hour, and another once a minute, so that the first may carry the -minute-hand and the other the second-hand. The hour-hand wheel is also -geared to the minute-wheel, so that it shall turn once in twelve hours -or twenty-four hours, according to the purposes for which the clock is -required. Weights are usually used when space is no object, being more -regular in their action than springs; but the latter are used for -chronometers and watches, and other portable time-keepers. - -The general arrangement of the clock train is shown in Fig. 87, where W -is the weight, hung by a cord passing over the barrel B, on the axis of -wheel G. The teeth of the wheel G gear into the pinion P_{1}, which -again is carried on the axis of the wheel C, and so on up the last -wheel—the escape-wheel, which generally is cut to thirty teeth, so that -it goes round once a minute and carries a second-hand. The pinion P_{1} -is so arranged by the number of teeth between it and the escape-wheel -that it goes round once an hour or to sixty turns of the escape-wheel. - -[Illustration: - - FIG. 87.—The Clock Train. -] - -[Illustration: - - FIG. 88.—Winding Arrangements. -] - -To wind up the clock the barrel B, Fig. 88, is turned round by the key -on the square; the pawl L fastened to the wheel G allows the barrel to -be turned in one direction without turning the wheel. It is obvious, -however that directly we begin to wind up, the pressure on the pawl -tending to turn the wheel G is removed, and the clock stops—a very -objectionable thing in astronomical and other clocks supposed to keep -good time. The following is one of the devices for keeping the clock -going during winding,—in this case everything is the same as before, -with the exception of an additional rachet-wheel R_{2}, Fig. 88, -carrying the pawl L; this wheel is loose on the axis but attached to the -wheel G through the spring S. The weight therefore acts on the pawl L, -and tends to drive the wheel R_{2}, which again presses round the wheel -G by means of the spring S, and, as the whole moves round, the teeth of -the wheel R_{2} pass the pawl K K fixed to some part of the clock-frame. -When now we commence to wind, the pressure on the pawl L and wheel R_{2} -is removed, and the spring S S, which is always kept bent by the action -of the weight, endeavours to open; and since the wheel R_{2} is -prevented from going backwards by the pawl K, the wheel G is continually -urged onwards by the spring, and the clock kept going for the short -period of winding. - - - II. THE PENDULUM. - -The clock, as left by Henry de Wyck, was only an exceedingly irregular -time-keeper, and some mechanical contrivance that should beat or mark -correct intervals of time was urgently required. The contrivance for -beating correct intervals of time—the pendulum—was thought of by -Galileo, who showed that its oscillations were isochronous, although -their lengths might vary within small limits. The pendulum then was just -the very thing required, and Huyghens, in 1658, applied it to clocks. - -In the next form of clock, therefore, we find the pendulum introduced as -a regulator. There was a crown wheel like the one in the balance clock, -only instead of being vertical it was horizontal. This wheel was allowed -to go round and the weight was allowed to fall by means of alternating -pallets; it was in fact like that shown in Fig. 86, with the balance -weights and the rod carrying them removed, and instead thereof there was -a rod, attached at right angles to the end of that carrying the pallets, -and hanging downwards, which, by means of a fork at its lower end, swung -a pendulum to an extent equal to the go of the balance first used. Thus -the pendulum was adapted by Huyghens. We have here something extremely -different from the rough arrangement in which the weight was controlled -by the horizontal oscillating bar carrying the weights, for the balance -would go faster or slower as the crown wheel pressed harder or softer -against the pallets, and so, if the weight acted at all irregularly the -clock would go badly. But with the pendulum the control of the weight -over it is small, for the bob can be made of considerable weight, -because it swings from its suspending spring without friction, and such -a heavy weight at the end of a long rod is scarcely altered in its rate -by variations of pressure on the pallets. - -Galileo and Huyghens who followed him found that the oscillations of a -simple pendulum are isochronous at all places where the force of gravity -is equal, and that the time of oscillation depends on the length of the -pendulum—the shorter the pendulum the shorter time of oscillation, and -_vice versâ_. The time of oscillation varying as the square root of the -length. - -In 1658, then, the pendulum was applied to clocks, as the balance had -been before that time. But Huyghens was not slow to perceive that the -circular arc of a rigid pendulum would not be sufficiently accurate for -an astronomical time-keeper, when used with a clock like that employed -by Tycho Brahe and the Landgrave of Hesse for their astronomical -observations. Huyghens next showed that with a clock of that kind, -requiring a large swing of pendulum, the oscillations were not quite -isochronous, but varied in time according as the arc increased or -diminished. It was clear therefore that this simple form of pendulum -would not do well for the large and varying arc required to be -described, but that the theoretical requirements would be satisfied if -the pendulum, instead of being suspended from a rigid rod, were -suspended by a cord or spring or some elastic substance which would -mould itself against two curved pieces of metal, C C, Fig. 89, attached -one on either side of the suspending spring. In swinging, the spring -would wrap, as it were, gradually round either curved surface, and so -virtually alter the point of suspension, and with it, of course, the -virtual length of the pendulum; so that the extreme point of the -pendulum U, instead of describing a circular arc K B as before, would, -by means of the portions of metal at the top, have a cycloidal motion D -L, the pendulum becoming virtually shorter as the spring wrapped round -the pieces of metal, so that it becomes isochronous for any length of -swing. But it was very soon found that the theoretically perfect clock -did not after all go as well as the clock it was to replace. And it -would now be difficult to say what would have happened if a few years -afterwards clocks had not been made much more simple and perfect by the -introduction of an entirely new escapement which permitted a very small -swing. - -[Illustration: - - FIG. 89.—The Cycloidal Pendulum. -] - -If we wish a clock to go perfectly well, we have only to consider a very -few things—First, the weight should be as small as possible; secondly, -within reason, the pendulum should be as solidly suspended and as heavy -as possible; and, thirdly, the less connection there is between the -pendulum which controls the clock, and the weight which drives the -clock, the better. - -The latter point is provided for in the dead beat arrangement of Graham, -and in the “gravity” and other forms of escapement, about which more -presently. At present we have been dealing with pendulums as if they -were simple pendulums, which are almost mathematical abstractions. - -Everything that we have said assumes that there is a mass depending from -such a fine line that the mass of the line shall not be considered; but -if we examine the pendulum of some clocks we see that the rod is of -steel, and that its weight or bob is elongated, and consists of a long -cylinder of glass filled with mercury, and carried in a sort of stirrup -of steel; this is very different from our simple pendulum—it is a -compound pendulum. In a compound pendulum we have first of all the axis -of suspension, which is the axis where the pendulum is supported on the -top, and below that, near the centre of gravity of the pendulum, we have -what is called the centre of oscillation. It will at once be perceived -that as the rate of the pendulum depends upon its length, the particles -in the upper part of the pendulum will be trying to go more rapidly than -they can go, seeing that they are connected in one series of particles, -and that the particles at the lowest portion are carried with greater -velocity than they would be if they were left to themselves, because -they are connected rigidly with the upper ones. Therefore we have to -find a point, which oscillates at the same rate as it would if all the -other particles were absent. - -This is called the centre of oscillation, and it is on the distance of -this from the point of suspension that the rate depends. - -What is the use of the mercury? It is to compensate for the expansion of -the rod by temperature. We shall at once see the reason of this from the -fact that the pendulum gets longer by being heated, and the rate of the -pendulum depends on the square root of its length; that is, if we -multiply the length by four, the square root of which is two, we shall -only multiply the rate by two, or double the time of oscillation. -Therefore, since temperature causes all metals to vary in length, and -metals are the most useful things we can employ for the support of the -weights, we find that we have to consider further the alteration of the -length of the pendulum due to the variation of the length of the metal -we employ. Hence, in addition to the necessity of an arrangement which -gives the shortest possible swing, we require also a method for -compensating for changes of temperature. - -[Illustration: - - FIG. 90.—Graham’s, Harrison’s, and Greenwich Pendulums. -] - -We have not space to go through the history of compensating pendulums, -but we may direct attention to some of the best results which have been -obtained in this matter. We will first examine the mercurial pendulum, -Fig. 90, which we have referred to. In this case the compensation is -accomplished as follows: Mercury is inclosed in a glass cylinder M M; -shown in the left hand side of the figure; and as the mercury expands -more than the glass, it will rise to a higher level on being heated; and -the lengthening of the steel rod R R will be counteracted by a similar -lengthening due to the expansion of mercury, so that the centre of -oscillation is carried down by the steel rod, and up by the mercury, and -it is therefore not displaced if the proper ratio is maintained between -the length of the steel rod and the column of mercury in the glass -vessel. The mercury in the glass will lengthen fifteen times as much as -the steel rod, if we have equal lengths of each, so that in order that -they may expand equally the rod must be fifteen times as long as the -mercury column. This would keep the top of the mercury at the same -distance from the point of suspension, but we want to keep the centre of -oscillation, which is about half way down the column, at the same -distance, so we double the height of the mercury, making it -two-fifteenths of the length of the steel rod, so that the surface is -over-compensated, but the centre of oscillation is exactly corrected. An -astronomer can alter the amount of mercury as he pleases, making it now -more, now less, till the stars tell him he has done the right thing, and -the pendulum is compensated, and the clock keeps correct time at all -temperatures. - -The little sliding cup C is to carry small weights for final delicate -adjustment, the addition of a weight thus obviously tending to increase -the rate of the pendulum. - -This is Graham’s mercurial pendulum, invented by him in 1715. There is -another compensating pendulum, called Harrison’s gridiron pendulum, from -the bars of metal sustaining the pendulum being arranged gridiron -fashion, Fig. 90. At the top is a knife edge or spring for the centre of -suspension, and the pendulum bob is suspended by a system of rods, the -five black ones being made of a less expansible metal than the other -four; consequently, as the five black ones expand and tend to lower the -bob, the intermediate ones expand also and tend to raise it; the length -of the black rods exceeding that of the others, these latter must be -made of a more expansible metal to make up for their smaller length. -Thus the acting length of the shaded rods is two-thirds of the acting -length of the black ones (each pair is considered as one rod because -they act as such), so that a metal is used for the former which expands -more than that used for the latter in the proportion of about three to -two, and brass is found to answer for the most expansible metal, and -steel for the less. These rods are packed side by side, and look very -ornamental. If _l_ be the length of the brass rods, and _l´_ that of the -steel rods, and _e_ the coefficient of expansion of the brass, and _e´_ -that of the steel, then _l_: _l´_:: _e´_: _e_. The pendulum is then -compensated, and the bob remains at the same distance from the centre of -suspension at all temperatures. - -For the pendulum of the clock at the Royal Observatory a modification of -the gridiron form has been adopted; for it was found on trial with a -mercurial pendulum that the steel rod gained in temperature more rapidly -than the mercury, and lost heat quicker, so that the pendulum did not -compensate immediately on a change of temperature. The form adopted is -as follows (Fig. 90):—A steel rod is suspended as usual, and is -encircled by a zinc tube resting on the nut for rating the pendulum; the -zinc tube is again encircled by a steel tube resting on the top of the -zinc tube and carrying at its lower end a cylindrical leaden bob -attached at its centre to the steel tube; slots and holes are cut in the -tubes to expose the inner parts to the air, so that each will experience -the change of temperature at the same time. It is of course possible -that the tubes forming the pendulum rod are not of exactly the right -length to perfectly compensate; a final delicate adjustment is therefore -added. On the crutch axis, and held by a collar to it, are two compound -bars of brass and steel, _h_ and _i_, Fig. 96. The collar fits loosely -on the axis, so that the rods, which carry small weights at their -extremities, can be easily shifted to make any angle with the -horizontal; then, since brass expands more than steel for the same -degree of heat, the bars will bend on being heated or cooled, and if the -brass be uppermost the weights at the ends of the rods will be lowered -with an increase of temperature, and will tend to increase the rate of -the pendulum, and _vice versâ_. So long as the rods are horizontal and -in the same straight line their centre of gravity is in the crutch axis, -and they are therefore balanced in every position; they therefore only -retard the pendulum by their inertia; but when the ends are bent down -the centre of gravity is lowered, and they have a tendency to come to a -horizontal position and to balance each other like a scale beam, and so -swing with the pendulum and overcome its retardation. - -It is obvious that they would, if alone, swing in a shorter time than -the pendulum and so, being connected, they increase its rate. - -When the rods are vertical they have no compensating action, for the -centre of gravity is simply thrown sidewise, and acts as a continuous -force tending to make the pendulum oscillate further on one side than on -the other; and in the intermediate positions of the rods their action -varies, and a consideration of the position of their centre of gravity -will give the intensity of the compensating action. In order to make a -small change in the rate of the clock without stopping it to turn the -screw at the bottom of the pendulum, the following contrivance is -adopted. - -A weight _k_ slides freely on the crutch rod, but is tapped to receive -the screw cut on the lower portion of the spindle _l_, the upper end of -which terminates in a nut _m_ at the crutch axis. By turning this nut -the position of the small weight on the crutch rod is altered, and the -clock rate correspondingly changed. To make the clock lose, the weight -must be raised. - -There is also another method of compensation, depending on differential -expansion. Attached to an ordinary pendulum just above the bob, and at -right angles to it, is a composite rod, made of copper and iron, the -lower half being copper; then, as the pendulum rod lengthens and lets -down the bob, the copper expands more than the iron, and causes the rod -to bend, like a piece of wood wetted on one side, and by this bending or -warping the weights at either end are raised as the bob is lowered, so -the centre of oscillation keeps at the same height at all temperatures. - -We have dealt with clocks and pendulums somewhat in the order of their -invention. We may add that the great majority of clocks of modern -manufacture of any pretention to time-keepers are constructed with the -dead beat escapement of Graham or a modification of it, combined with a -mercurial or gridiron pendulum. For the best Observatory clocks of the -more expensive kind other more elaborate forms of escapement are -sometimes used, as, for example, that in the clock at the Royal -Observatory, Greenwich, which we shall refer to in detail further on, on -account of other new points in its construction. - -Now, having a clock good enough to use with the transit instrument, it -is necessary to take the utmost precautions with reference to it. The -Russian astronomers have inclosed their clock in a stone case, and -placed it many yards below the ground, endeavouring thus to get rid of -the action of temperature, which changes the length of the steel -pendulum rod. But that is not all; after we have corrected our clock as -well as we can from the point of view of temperature, it is still found -that there may be a variation, amounting to something considerable, due -to another cause. If the barometer changes an inch or an inch and a half -by change of pressure of the air, the rate of the pendulum will alter, -and the cause of the variation it is impossible to prevent without -putting the clock in a vacuum, so that changes of the barometer must be -allowed for. - -There are, however, methods of compensating the pendulum for changes of -pressure if desirable: one way of doing this is to pass the suspending -spring of the pendulum through a slit in a metal plate, which then -becomes virtually the point of suspension; this plate is then raised or -lowered by an aneroid barometer, or by a float in an ordinary cistern -barometer so that the length of the pendulum is virtually altered with -the pressure of the atmosphere. At Greenwich the Astronomer-Royal has -adopted the following expedient: A magnet at the lower end of the -pendulum passes at each swing near a magnet which is raised or lowered -by means of a float in the cistern of a barometer. The magnet then has a -greater or less influence on the pendulum magnet according as the -pressure of the air varies, and so adds a variable amount to the effect -of gravity and therefore to the rate of oscillation. - -[Illustration: - - FIG. 91.—Greenwich Clock: arrangement for Compensation for Barometric - Pressure. -] - -This principle is carried out as follows:—Two bar magnets, each about -six inches long, are fixed vertically to the bob of the clock pendulum; -one in front, _a_, Fig. 91, the other at the back. The lower pole of the -front magnet is a north pole; the lower pole of the back magnet is a -south pole. Below these a horse-shoe magnet, _b_, having its poles -precisely under those of the pendulum magnets, is carried transversely -at the end of the lever _c_, the extremity of the opposite arm of the -lever being attached by the rod _d_, to the float _e_ in the lower leg -of a syphon barometer. The lever turns on knife edges. A plan of the -lever (on a smaller scale) is given, as well as a section through the -point A. Weights can be added at _f_ to counterpoise the horse-shoe -magnet. The rise or fall of the mercurial barometer correspondingly -raises or depresses the horse shoe magnet, and, increasing or decreasing -the magnetic action between its poles and those of the pendulum magnets, -compensates, by the change of rate produced, for that arising from -variation in the pressure of the atmosphere. The shorter leg of the -barometer in which the float rests has an area of four times that of the -barometer tube at the upper surface of the mercury, so that for a large -change of barometric height the magnet is only moved a small distance, a -change of one inch of the barometer lowering the surface in the short -leg 2/10 inch; the distance between the pendulum magnets and the -horse-shoe magnets is 3¾ inches. - - - III. ESCAPEMENTS. - -The invention of the pendulum, its application, and the improvements -thereon having been described, it remains to treat of the equally -important improvements on the escapement. The first change for the -better appears to have been due to Hooke, who in 1666 brought before the -Royal Society the crutch, or anchor escapement, whereby the arc through -which the pendulum vibrated was so much reduced that Huyghens’s -cycloidal curves became unnecessary, and the power required to drive the -clock was materially reduced. - -This escapement, common in ordinary eight-day clocks, is different from -that previously described in the way in which the crown wheel or escape -wheel is regulated. - -We have come back to a vertical escape wheel as it was in the clock used -by Tycho; but instead of using two pallets on a rod which regulated the -wheel, we have here an anchor escapement (Fig. 92) in connection with -the pendulum; and what happens is this—when the pendulum is made to -oscillate, these pallets P P gradually move in and out of the teeth of -the wheel, and let a tooth pass at every swing; and it is obvious that -when the wheel and anchor are nicely adjusted, an extremely small motion -of the anchor, and consequently a small oscillation of the pendulum, -allows the escape wheel to turn round, and the clock to go. - -The greater regularity of this form of escapement is due to a smaller -oscillation of the pendulum being required than with the form first -described; for it is found that the motion of a pendulum when vibrating -through not more than six degrees is practically cycloidal, and it is -only with larger arcs that the circle materially differs from the -theoretical curve required. - -The pendulum is kept in vibration by the escape wheel, or rather by its -teeth pressing against the inclined surfaces of the pallets, and forcing -them outwards, and so giving the pendulum an impulse prior to each tick. - -[Illustration: - - FIG. 92.—The Anchor Escapement. -] - -This anchor escapement, which was invented by “Clement, of London, -clockmaker,” forms, as it were, the basis of our modern clocks, and, -with the exception of the dead beat, which was due to Graham some years -afterwards, is in almost exclusive use at the present date. - -We see that as soon as a tooth has escaped on one side, a tooth on the -other begins immediately to retard the action of the pendulum by -pressing against the inclined surface of the other pallet, and as the -pendulum swings on, the tooth gives way, and the motion of the wheel is -reversed; then when the pendulum begins to return, it is assisted again -by the tooth, so that the pendulum is always under the influence of the -escape wheel, some times accelerated, and sometimes retarded. The -principle of Graham’s dead beat is to get rid of the retarding action of -the escape wheel, so that there should be no necessity for so much -accelerating power, and the pendulum should be out of the influence of -the escape wheel during a large portion of its vibration. This he -accomplished by doing away with a large portion of the inclined surface -of the pallet (Fig. 93), so that the teeth have no accelerating action -on the pendulum until just as they leave the ends of the pallets where -they are inclined; the greater portion of both the pallets on which the -escape wheel works being at right angles to its direction of motion, the -teeth have no tendency to force the pallet outwards. In Fig. 93 the -tooth V has fallen on the pallet D, the tooth T having just been -released, and as the pendulum still swings on in the direction of the -arrow, the pallet D will be pushed further under the tooth C but without -pressing the wheel backwards, and without retardation other than that of -friction. When the pendulum returns and the pallet just gets past the -position shown, it gets an impulse, and this is given as nearly as -possible as much before the pendulum reaches its vertical position as -after it passes it, its action is therefore neither to increase nor -diminish the rate. In this escapement not only is the arc of oscillation -considerably lessened and the motion of the pendulum brought near to the -cycloidal form, but in addition to this there is this important point, -that the weight is acting upon the pendulum for the least possible time. - -[Illustration: - - FIG. 93.—Graham’s Dead Beat. -] - -[Illustration: - - FIG. 94.—Gravity Escapement (Mudge). -] - -We will now describe the more elaborate forms of escapement, and we will -take first the gravity escapement, as it is called. The principle of its -action consists in there being a small impulse given to the pendulum at -each oscillation, by means of two small rods hanging, one on each side -of it, and tending by their own weight to force the pendulum into a -vertical position; these rods are alternately pushed outwards by the -escapement before the pendulum in its swing arrives at them, and then -they are allowed to press against it on its return towards the vertical, -so that the pendulum has a constant force acting on it at each -oscillation, unconnected with the clock movement. This is carried out in -the escapement invented by Mudge, as shown in Fig. 94. The pendulum rod -is supposed to be hanging just in front of the rods hanging from the -pivots Y_{1} Y_{2}, and on swinging it presses against the pins at the -lower ends of the rods and so lifts the pallets S_{1} S_{2} out of the -teeth of the escape wheel. In the position shown the pendulum is moving -to the right, having been gently urged from the left by the weight of -the pallet rod Y_{2} S_{2}, and the pallet S_{1} has been lifted -outwards by the tooth acting on its inclined surface. On the pendulum -rod reaching the pin the rod is moved outwards and the end of the pallet -S_{1} pushed out of the tooth when the wheel moves on, at the same time -pushing outwards the pallet S_{2}. As the pendulum returns towards the -left again the rod Y_{1} follows it, giving it a gentle impulse by its -own weight until it returns nearly to the vertical or to the -corresponding position in which Y_{2} S_{2} is shown. On the pendulum -swinging on and releasing T_{2} the pallet S_{1} is again pushed -outwards by the inclined plane to the position shown in the diagram. In -this escapement there was danger of the pallets being thrown too -violently outwards so that the teeth were not caught by the flat -surfaces at the ends, and Mr. Bloxam improved on it by letting the -pallets be thrown outwards by a small wheel on the axis of the escape -wheel so that the action was less rapid; he accomplished this in the -following manner. On the end of the axis of the last wheel are a number -of arms A A, Fig. 95, say nine, about 1½ inches long, which are -prevented from revolving by studs L_{1} L_{2} on the inside of each -hanging rod P_{1} P_{2}; then, as each rod is pushed outwards by the -pendulum, an arm escapes from a stud and the clock goes on one second. -Each rod is pushed outwards by the clock almost sufficiently far for the -arm to escape, but not quite, so that the pendulum just releases the arm -at the end of its swing in the same manner as in Mudge’s escapement, -Fig. 94; but instead of the teeth of the escape wheel pushing the rods -outwards there is the small wheel T_{1} T_{2}, having the same number of -teeth as there are arms on the axis and close to them, and the -projecting pieces H_{1} H_{2} at right angles to each swinging rod rest -against the teeth of this wheel, one resting against the teeth at the -top and the other at the bottom, so that they catch against the teeth -after the manner of a ratchet, and the rods are pushed outwards by this -wheel as it revolves. The arms and ratchet wheel are so set that, during -the motion of an arm A, to a stud, a tooth of the ratchet wheel is -pushing outwards the rod carrying that stud. The action is as -follows:—The pendulum having just swung up to a rod and released the arm -pressing against its stud, the arms and ratchet wheel revolve, and the -tooth of the ratchet wheel, which had been pressing outwards the -swinging rod, passes on free of the projecting piece, which can now move -backwards to the next tooth; so the rod, being no longer supported, -presses against the pendulum rod on its return oscillation. The arms and -ratchet wheel revolve until an arm on the opposite side comes in contact -with the stud on the other rod, and in revolving the ratchet wheel -throws outwards this rod just so far that the arm is not released. The -pendulum is assisted by the weight of the first rod to the vertical -position, when the projecting piece of the rod comes in contact with the -next tooth of the ratchet wheel where it rests until the oscillation is -completed, and the second arm is released. It is then forced outwards, -and the next arm on that side presses against the stud, when a -repetition of the foregoing takes place. In this way the clock is kept -going without any direct action of the clock train on the pendulum. - -[Illustration: - - FIG. 95.—Gravity Escapement (Bloxam). -] - -Another very beautiful escapement is that devised by the -Astronomer-Royal and carried out in the clock erected in 1871 at -Greenwich.[9] In this case the pendulum is free except during a portion -of every alternate second, when it releases the escapement and receives -an impulse, so that there is a tick only at every other second. - -[Illustration: - - FIG. 96.—Greenwich Clock Escapement. -] - -The details of the escapement may be seen in Fig. 96, which gives a -general view of a portion of the back plate of the clock movement, -supposing the pendulum removed; _a_ and _b_ are the front and back -plates respectively of the clock train; _c_ is a cock supporting one end -of the crutch axis; _d_ is the crutch rod carrying the pallets, and _e_ -an arm carried by the crutch axis and fixed at _f_ to the left-hand -pallet arm; _g_ is a cock supporting a detent projecting towards the -left and curved at its extreme end; at a point near the top of the -escape wheel this detent carries a pin (jewel) for locking the wheel, -and at its extreme end there is a very light “passing spring.” The -action of the escapement is as follows:—Suppose the pendulum to be -swinging from the right hand. It swings quite freely until a pin at the -end of the arm _e_ lifts the detent; the wheel escapes from the jewel -before mentioned, and the tooth next above the left-hand pallet drops on -the face of the pallet (the state shown in the figure), and gives -impulse to the pendulum; the wheel is immediately locked again by the -jewel, and the pendulum, now detached, passes on to the left; in -returning to the right, the light passing spring, before spoken of, -allows the pendulum to pass without disturbing the detent; on going -again to the left, the pendulum again receives impulse as already -described. The right-hand pallet forms no essential part of the -escapement, but is simply a safety pallet, designed to catch the wheel -in case of accident to the locking-stone during the time that the -left-hand pallet is beyond the range of the wheel. The escape wheel -carrying the seconds hand thus moves once only in each complete or -double vibration of the pendulum, or every two seconds. - - - IV. THE CHRONOMETER. - -We have now given a description of the astronomical clock—the modern -astronomical instrument which it was our duty to consider. There is -another time-keeper—the chronometer—which we have to dwell upon. In the -chronometer, instead of using the pendulum, we have a balance, the -vibration of which is governed by a spiral spring, instead of by -gravity, as the pendulum is. By such means we keep almost as accurate -time as we do by employing a pendulum, the balance being corrected for -temperature on principles, one of which we shall describe. - -We must premise by saying that fully four-fifths of the compensation -required by a chronometer or watch-balance is owing to the change in -elasticity of the governing spiral spring, the remainder, comparatively -insignificant, being due to the balance’s own expansion or contraction. -The segments R_{1}, R_{2} of the balance (see Fig. 97) are composed of -two metals, say copper and steel, the copper being exterior; then as the -governing spiral spring loses its elasticity by heat, the segments -R_{1}, R_{2} curve round and take up positions nearer the axis of -motion, the curvature being produced by the greater expansion of copper -over steel; and thus the loss of time due to the loss of elasticity of -the spiral spring is compensated for. - -This balance may be adjustable by placing on the arms small weights, W -W, which may be moved along the arms, and so increase or diminish the -effect of temperature at pleasure. - -[Illustration: - - FIG. 97.—Compensating Balance. -] - -Of the number of watch and chronometer escapements we may mention the -detached lever—the one most generally used for the best watches, the -form is shown in Fig. 98. P P are the pallets working on a pin at S as -in the dead-beat clock escapement; the pallets carry a lever L which can -vibrate between two pins B B. R is a disc carried on the same axis with -the balance, and it carries a pin I, which as the disc goes round in the -direction of the arrow, falls into the fork of the lever, and moves it -on and withdraws the pallet from the tooth D, which at once moves -onwards and gives the lever an impulse as it passes the face of the -pallet. This impulse is communicated to the balance through the pin I, -the balance is kept vibrating in contrary directions under the influence -of the hair-spring, gaining an impulse at each swing. On the same axis -as R is a second disc O with a notch cut in it into which a tongue on -the lever enters; this acts as a safety lock, as the lever can only move -while the pin I is in the fork of the lever. - -[Illustration: - - FIG. 98.—Detached Lever Escapement. -] - -The escapement we next describe is that most generally used in -chronometers. S S, Fig. 99, is the escape wheel which is kept from -revolving by the detent D. On the axis of the balance are two discs, -R_{1}, R_{2}, placed one under the other. As the balance revolves in the -direction of the arrow, the pin P_{2} will come round and catch against -the point of the detent, lifting it and releasing the escape-wheel, -which will revolve, and the tooth T will hit against the stud P_{1}, -giving the balance an impulse. The balance then swings on to the end of -its course and returns, and the stud P_{2} passes the detent as follows: -a light spring Y Y is fastened to the detent, projecting a little beyond -it, and it is this spring, and not the detent itself, that the pin P_{2} -touches: on the return of P_{2} it simply lifts the spring away from the -detent and passes it, whereas in advancing the spring was supported by -the point of the detent, and both were lifted together. - -[Illustration: - - FIG. 99.—Chronometer Escapement. -] - -[Illustration: - - FIG. 100.—The Fusee. -] - -In watches and chronometers and in small clocks a coiled spring is used -instead of a weight, but its action is irregular, since when it is fully -wound up it exercises greater force than when nearly down. In order to -compensate for this the cord or chain which is wound round the barrel -containing the spring passes round a conical barrel called a _fusee_ -(Fig. 100): B is the barrel containing the spring and A A the fusee. One -end of the spring is fixed to the axis of the barrel, which is prevented -from turning round, and the other end to the barrel, so that on winding -up the clock by turning the fusee the cord becomes coiled on the latter, -and the more the spring is wound the nearer the cord approaches the -small end of the fusee, and has therefore less power over it; while as -the clock goes and the spring becomes unwound, its power over the axis -becomes greater. The power, therefore, acting to turn the fusee remains -pretty constant. - ------ - -Footnote 9: - - By Messrs. E. Dent and Co. of the Strand. - - - - - CHAPTER XIV. - CIRCLE READING. - - -One of the great advantages which astronomy has received from the -invention of the telescope is the improved method of measuring space and -determining positions by the use of the telescope in the place of -pointers on the old instruments. The addition of modern appliances to -the telescope to enable it to be used as an accurate pointer, has played -a conspicuous part in the accurate measurement of space, and the results -are of such importance, and they have increased so absolutely _pari -passu_ with the telescope, that we must now say something of the means -by which they have been brought about. - -For astronomy of position, in other words for the measurement of space, -we want to point the telescope accurately at an object. That is to say, -in the first instance we want circles, and then we want the power of not -only making perfect circles, but of reading them with perfect accuracy; -and where the arc is so small that the circle, however finely divided, -would help us but little, we want some means of measuring small arcs in -the eyepiece of the telescope itself, where the object appears to us, as -it is called, in the field of view; we want to measure and inspect that -object in the field of view of the telescope, independently of circles -or anything extraneous to the field. We shall then have circles and -micrometers to deal with divisions of space, and clocks and chronographs -to deal with divisions of time. - -We require to have in the telescope something, say two wires crossed, -placed in the field of view—in the round disc of light we see in a -telescope owing to the construction of the diaphragm—so as to be seen -together with any object. In the chapter on eyepieces it was shown that -we get at the focus the image of the object; and as that is also the -focus of the eyepiece, it is obvious that not only the image in the air, -as it were, but anything material we like to put in that focus, is -equally visible. By the simple contrivance of inserting in this common -focus two or more wires crossed and carried on a small circular frame, -we can mark any part of the field, and are enabled to direct the -telescope to any object. - -In the Huyghenian eyepiece, Fig. 60, the cross should be between the two -convex lenses, for if we have an eyepiece of this kind the focus will be -at F, and so here we must have our cross wires; but, if instead of this -eyepiece we have one of the kind called Ramsden’s eyepiece, Fig. 62, -with the two convex surfaces placed inwards, then the focus will be -outside, at F, and nearer to the object-glass: therefore we shall be -able to change these eyepieces without interfering with the system of -wires in the focus of the telescope. We hence see at once that the -introduction of this contrivance, which is due to Mr. Gascoigne, at once -enormously increases the possibility of making accurate observations by -means of the telescope. - -[Illustration: - - FIG. 101.—Diggs’ Diagonal Scale. -] - -Hipparchus was content to ascertain the position of the celestial bodies -to within a third of a degree, and we are informed that Tycho Brahe, by -a diagonal scale, was able to bring it down to something like ten -seconds. Fig. 101 will show what is meant by this. Suppose this to be -part of the arc of Tycho’s circle, having on it the different divisions -and degrees. Now it is clear that when the bar which carried the pointer -swept over this arc, divided simply into degrees, it would require a -considerable amount of skill in estimating to get very close to the -truth, unless some other method were introduced; and the method -suggested by Diggs, and adopted by Tycho, was to have a series of -diagonal lines for the divisions of degrees; and it is clear that the -height of the diagonal line measured from the edge of the circle could -give, as it were, a longer base than the direct distance between each -division for determining the subdivisions of the degree, and a slight -motion of the pointer would make a great difference in the point where -it cuts the diagonal line. For instance, it would not be easy to say -exactly the fraction of division on the inner circle at which the -pointer in Fig. 101 rests, but it is evident that the leading edge of -the pointer cuts the diagonal line at three-fourths of its length, as -shown by the third circle; so the reading in this case is seven and -three-quarters; but that is, after all, a very rough method, although it -was all the astronomer had to depend upon in some important -observations. - -[Illustration: - - FIG. 102.—The Vernier. -] - -The next arrangement we get is one which has held its own to the present -day, and which is beautifully simple. It is due to a Frenchman named -Vernier, and was invented about 1631. We may illustrate the principle in -this way. Suppose for instance we want to subdivide the divisions marked -on the arc of a circle, Fig. 102 _a b_, and say we wish to divide them -into tenths, what we have to do is this—First, take a length equal to -nine of these divisions on a piece of metal, _c_, called the vernier, -carried on an arm from the centre of the circle, and then, on a separate -scale altogether, divide that distance not into nine, as it is divided -on the circle, but into ten portions. Now mark what happens as the -vernier sweeps along the circle, instead of having Tycho’s pointer -sweeping across the diagonal scale. - -Let us suppose that the vernier moves with the telescope and the circle -is fixed; then when division 0 of the vernier is opposite division 6 on -the circle we know that the telescope is pointing at 6° from zero -measured by the degrees on this scale; but suppose, for instance, it -moves along a little more, we find that line 1 of the vernier is in -contact with and opposite to another on the circle, then the reading is -6° and ⅒°; it moves a little further, and we find that the next line 2, -is opposite to another, reading 6° and 2/10°, a little further still, -and we find the next opposite. It is clear that in this way we have a -readier means of dividing all those spaces into tenths, because if the -length of the vernier is nine circle divisions the length of each -division on the vernier must be as nine is to ten, so that each division -is one-tenth less than that on the circle. - -We must therefore move the vernier one-tenth of a circle division, in -order to make the next line correspond. That is to say, when the -division of the vernier marked 0 is opposite to any line, as in the -diagram, the reading is an exact number of degrees; and when the -division 1 is opposite, we have then the number of degrees given by the -division 0 plus one-tenth; when 2 is in contact, plus two-tenths; when 3 -is in contact, plus three-tenths; when 4 is in contact, plus -four-tenths, and so on, till we get a perfect contact all through by the -0 of the vernier coming to the next division on the circle, and then we -get the next degree. It is obvious that we may take any other fraction -than to for the vernier to read to, say 1/60, then we take a length of -59 circle divisions on the vernier and divide it into 60, so that each -vernier division is less than a circle division by 1/60. This is a -method which holds its own on most instruments, and is a most useful -arrangement. - -But most of us know that the division of the vernier has been objected -to as coarse and imperfect; and Sharp, Graham, Bird, Ramsden, Troughton, -and others found that it is easy to graduate a circle of four or five -feet in diameter, or more, so accurately and minutely that five minutes -of arc shall be absolutely represented on every part of the circle. We -can take a small microscope and place in its field of view two cross -wires, something like those we have already mentioned, so as to be seen -together with the divisions on the circle, and then, by means of a screw -with a divided head, we can move the cross wires from division to -division, and so, by noting the number of turns of the screw required to -bring the cross wires from a certain fixed position, corresponding to -the pointer in the older instruments, to the nearest division, we can -measure the distance of that division from the fixed point or pointer, -as it were, just as well as if the circle itself were much more closely -divided. We can have matters so arranged that we may have to make, if we -like, ten turns of the screw in order to move the cross wires from one -graduation to the next, and we may have the milled head of the screw -itself divided into 100 divisions, so that we shall be able to divide -each of the ten turns into 100, or the whole division into 1,000 parts. -It is then simply a question of dividing a portion of arc equal to five -minutes into a thousand, or, if one likes, ten thousand parts by a -delicate screw motion. - -We are now speaking of instruments of precision, in which large -telescopes are not so necessary as large circles. With reference to -instruments for physical and other observations, large circles are not -so necessary as large telescopes, as absolute positions can be -determined by instruments of precision, and small arcs can, as we shall -see in the next chapter, be determined by a micrometer in the eyepiece -of the telescope. - - - - - CHAPTER XV. - THE MICROMETER. - - -It will have been gathered from the previous chapter that the perfect -circles nowadays turned out by our best opticians, and armed in -different parts by powerful reading microscopes, in conjunction with a -cross wire in the field of view of the telescope to determine the exact -axis of collimation, enable large arcs to be measured with an accuracy -comparable to that with which an astronomical clock enables us to -measure an interval of time. - -We have next to see by what method small arcs are measured in the field -of view of the telescope itself. This is accomplished by what are termed -micrometers, which are of various forms. Thus we have the wire -micrometer, the heliometer, the double-image micrometer, and so on. -These we shall now consider in succession, entering into further details -of their use, and the arrangements they necessitate when we come to -consider the instrument in conjunction with which they are generally -employed. - -The history of the micrometer is a very curious one. We have already -spoken of a pair of cross wires replacing the pinnules of the old -astronomers in the field of view of the telescope, so that it might be -pointed to any celestial object very much more accurately than it could -be without such cross wires. This kind of micrometer was first applied -to a telescope by Gascoigne in 1639. In a letter to Crabtree he -writes:[10] “If here (in the focus of the telescope) you place the scale -that measures ... _or if here a hair be set_ that it appear perfectly -through the glass ... you may use it in a quadrant for the finding of -the altitude of the least star visible by the perspective wherein it is. -If the night be so dark that the hair or the pointers of the scale be -not to be seen, I place a candle in a lanthorn, so as to cast light -sufficient into the glass, which I find very helpful when the moon -appeareth not, or it is not otherwise light enough.” - -This then was the first “telescopic sight,” as these arrangements at the -common focus of the object-glass and eyepiece were at first called. It -is certain that we may date the micrometer from the middle of the -seventeenth century; but it is rather difficult to say who it was who -invented it. It is frequently attributed to a Frenchman named Auzout, -who is stated to have invented it in 1666; but we have reason to know -that Gascoigne had invented an instrument for measuring small distances -several years before. Though first employed by Gascoigne, however, they -were certainly independently introduced on the Continent, and took -various forms, one of them being a reticule, or network of small silver -threads, suggested by the Marquis Malvasia, the arc interval of which -was determined by the aid of a clock. Huyghens had before this proposed, -as specially applicable to the measures of the diameters of planets and -the like, the introduction of a tapering slip of metal. The part of the -slip which exactly eclipsed the planet was noted; it was next measured -by a pair of compasses, and having the focal length of the telescope, -the apparent diameter was ascertained. - -[Illustration: - - FIG. 103.—System of Wires in a Transit Eyepiece. -] - -Malvasia’s suggestion was soon seized upon for determinations of -position. Römer introduced into the first transit instrument a -horizontal and a number of vertical wires. The interval between the -three he generally used was thirty-four seconds in the equator, and the -time was noted to half seconds. The field was illuminated by means of a -polished ring placed outside of the object-glass. The simple system of -cross wires, then, though it has done its work, is not to be found in -the telescope now, either to mark the axis of collimation, or roughly to -measure small distances. For the first purpose a much more elaborate -system than that introduced by Römer is used. We have a large number of -vertical wires, the principal object of which is, in such telescopes as -the transit, to determine the absolute time of the passage of either a -star or planet, or the sun or moon, over the meridian; and one or more -horizontal ones. These constitute the modern transit eyepiece, a very -simple form of which is shown in the above woodcut. - - - THE WIRE MICROMETER. - -The wire micrometer is due to suggestions made independently by Hooke -and Auzout, who pointed out how valuable the reticule of Malvasia would -be if one of the wires were movable. - -[Illustration: - - FIG. 104.—Wire Micrometer. _x_ and _y_ are thicker wires for measuring - positions on a separate plate to be laid over the fine wires. -] - -The first micrometer in which motion was provided consisted of two -plates of tin placed in the eyepiece, being so arranged and connected by -screws that the distances between the two edges of the tin plates could -be determined with considerable accuracy. A planet could then be, as it -were, grasped between the two plates, and its diameter measured; it is -very obvious that what would do as well as these plates of tin would be -two wires or hairs representing the edges of these tin plates; and this -soon after was carried out by Hooke, who left his mark in a very decided -way on very many astronomical arrangements of that time. He suggested -that all that was necessary to determine the diameter of Saturn’s rings -was to have a fixed wire in the eyepiece, and a second wire travelling -in the field of view, so that the planet or the ring could be grasped -between those two wires. - -The wire-micrometer. Fig. 104, differs little from the one Hooke and -Auzout suggested, A A is the frame, which carries two slides, C and D, -across the ends of each of which fine wires, E and B, are stretched; -then, by means of screws, F and G, threaded through these movable slides -and passing through the frame A A, the wires can be moved near to, or -away from, each other. Care must be taken that the threads of the screw -are accurate from one end to the other, so that one turn of the screw -when in one position would move the wire the same distance as a turn -when in another position. In this micrometer both wires are movable, so -as to get a wide separation if needful, but in practice only one is so, -the other remaining a fixture in the middle of the field of view. There -is a large head to the screw, which is called the micrometer screw, -marked into divisions, so that the motion of the wire due to each turn -of the screw may be divided, say into 100 parts, by actual division -against a fixed pointer, and further into 1,000 parts by estimation of -the parts of each division. Hooke suggested that, if we had a screw with -100 turns to an inch, and could divide these into 1,000 parts, we should -obviously get the means of dividing an inch into 100,000 parts; and so, -if we had a screw which would give 100 turns from one side of the field -of view of the telescope to the other, we should have an opportunity of -dividing the field of view of any telescope into something like 100,000 -parts in any direction we chose. - -The thick wires, _x_, _y_, are fixed to the plate in front of, but -almost touching, the fine wires, and in measuring, for instance, the -distance of two stars the whole instrument is turned round until these -wires are parallel to the direction of the imaginary line joining them. - -This was the way in which Huyghens made many important measures of the -diameters of different objects and the distances of different stars. -Thus far we are enabled to find the number of divisions on the -micrometer screw that corresponds to the distance from one star to -another, or across a planet, but we want to know the number of seconds -of arc in the distance measured. - -In order to do this accurately we must determine how many divisions of -the screw correspond to the distance of the wires when on two stars, -say, one second apart. Here we must take advantage of the rate at which -a star travels across the field when the telescope is fixed, and we -separate the wires by a number of turns of the screw, say twenty, and -find what angle this corresponds to, by letting a star on or near the -equator[11] traverse the field, and noticing the time it requires to -pass from one wire to the next. Suppose it takes 26⅔ seconds, then, as -fifteen seconds of arc pass over in one second of time, we must multiply -26 by 15, which gives 400, so that the distance from wire to wire is 400 -seconds of arc; but this is due to twenty revolutions of the screw, so -that each revolution corresponds to 400/20˝, or twenty seconds, and as -each revolution is divided into 100 parts, and 20/100˝ = ⅕˝ therefore -each division corresponds to ⅕˝ of arc. - -We shall return to the use of this most important instrument when we -have described the equatorial, of which it is the constant companion. - - - THE HELIOMETER. - -[Illustration: - - FIG. 105.—A B C. Images of Jupiter supposed to be touching; B being - produced by duplication, C duplicate image on the other side of A. - - A B, Double Star; A, A´ & B, B´, the appearance when duplicate image - is moved to the right; A´, A & B´, B, the same when moved to the - left. -] - -[Illustration: - - FIG. 106.—Object-glass cut into two parts. -] - -[Illustration: - - FIG. 107.—The parts separated, and giving two images of any object. -] - -There are other kinds of micrometers which we must also briefly -consider. In the heliometer[12] we get the power of measuring distances -by doubling the images of the objects we see, by means of dividing the -object-glass. The two circles, A and B, Fig. 105, represent the two -images of Jupiter formed, as we shall show presently, and touching each -other; now, if by any means we can make B travel over A till it has the -position C, also just touching A, it will manifestly have travelled over -a distance equal to the diameters of A and B, so that if we can measure -the distance traversed and divide it by 2, we shall get the diameter of -the circle A, or the planet. The same principle applies to double stars, -for if we double the stars A and B, Fig. 105, so that the secondary -images become A´ and B´, we can move A´ over B, and then only three -stars will be visible; we can then move the secondary images back over A -and B till B´ comes over A, and the second image of A comes to A´. It is -thus manifest that the images A´ and B´ on being moved to A´ and B´ in -the second position have passed over double their distance apart. Now -all double-image micrometers depend on this principle, and first we will -explain how this duplication of images is made in the heliometer. It is -clear that we shall not alter the power of an object-glass to bring -objects to focus if we cut the object-glass in two, for if we put any -dark line across the object-glass, which optically cuts it in two, we -shall get an image, say of Jupiter, unaltered. But suppose instead of -having the parts of the object-glass in their original position after we -have cut the object-glass in two, we make one half of the object-glass -travel over the other in the manner represented in Fig. 107. Each of -these halves of the object-glass will be competent to give us a -different image, and the light forming each image will be half the light -we got from the two halves of the object-glass combined; but when one -half is moved we shall get two images in two different places in the -field of view. We can so alter the position of the images of objects by -sliding one half of the object-glass over the other, that we shall, as -in the case of the planet Jupiter, get the two images exactly to touch -each other, as is represented in Fig. 105; and further still, we can -cause one image to travel over to the other side. If we are viewing a -double star, then the two halves will give four stars, and we can slide -one half, until the central image formed by the object-glasses will -consist of two images of two different stars, and on either side there -will be an image of each star, so that there would appear to be three -stars in the field of view instead of two. We have thus the means of -determining absolutely the distance of any two celestial objects from -each other, in terms of the separation of the centres of the two halves -of the object-glass. - -But as in the case of the wire micrometer we must know the value of the -screw, so in the case of the heliometer we must know how much arc is -moved over by a certain motion of one half of the object-glass. - -[Illustration: - - FIG. 108.—Double images seen through Iceland spar. -] - -[Illustration: - - FIG. 109.—Diagram showing the path of the ordinary and extraordinary - rays in a crystal of Iceland spar, producing two images apparently - at E and O. -] - - - THE DOUBLE-IMAGE MICROMETER. - -Now there is another kind of double-image micrometer which merits -attention. In this case the double image is derived from a different -physical fact altogether, namely, double refraction. Those who have -looked through a crystal of Iceland spar, Fig. 108, have seen two images -of everything looked at when the crystal is held in certain positions, -but the surfaces of the crystal can be cut in a certain plane such that -when looked through, the images are single. For the micrometer therefore -we have doubly refracting prisms, cut in such a way as to vary the -distance of the images. Generally speaking, whenever a ray of light -falls on a crystal of Iceland spar or other double refracting substance, -it is divided up into two portions, one of which is refracted more than -the other. If we trace the rays proceeding from a point S, Fig. 109, we -find one portion of the light reaching the eye is more refracted at the -surfaces than the other, and consequently one appears to come from E and -the other from O, so that if we insert such a crystal in the path of -rays from any object, that object appears doubled. There is, however, a -certain direction in the crystal, along which, if the light travel, it -is not divided into two rays, and this direction is that of the optic -axis of the crystal, A A, Fig. 110; if therefore two prisms of this spar -are made so that in one the light shall travel parallel to the axis, and -in the other at right angles to it, and if these be fastened together so -that their outer sides are parallel, as shown in Fig. 111, light will -pass through the first one without being split up, since it passes -parallel to the axis, but on reaching the second one it is divided into -two rays, one of which proceeds on in the original course, since the two -prisms counteract each other for this ray, while the other ray diverges -from the first one, and gives a second image of the object in front of -the telescope, as shown in Fig. _b_. The separation of the image depends -on the distance of the prisms from the eyepiece, so that we can pass the -rays from a star or planet through one of these compound crystals and -measure the position of the crystal and so the separation of the stars, -and then we shall have the means of doing the same that we did by -dividing our object-glass, and in a less expensive way, for to take a -large object-glass of eight or ten inches in diameter and cut it in two -is a brutal operation, and has generally been repented of when it has -been done. - -[Illustration: - - FIG. 110.—Crystals of Iceland Spar showing, A A´, the optic axis. -] - -It is obvious that a Barlow lens, cut in the same manner as the -object-glass of the heliometer, will answer the same purpose; the two -halves are of course moved in just the same manner as the halves of the -divided object-glass. Mr. Browning has constructed micrometers on this -principle. - -[Illustration: - - FIG. 111.—Double Image Micrometer. FIG. _a_, _p q_, single image - formed by object-glass. FIG. _b_, _p_{1} q_{1}_, _p_{2} q_{2}_, - images separated by the double refracting prism. FIG. _c_, same, - separated less, by the motion of the prism. -] - -There is yet another double-image micrometer depending on the power of a -prism to alter the direction of rays of light. It is constructed by -making two very weak prisms, _i.e._, having their sides very nearly -parallel, and cutting them to a circular shape; these are mounted in a -frame one over the other with power to turn one round, so that in one -position they both act in the same direction, and in the opposite one -they neutralise each other; these are carried by radial arms, and are -placed either in front of the object-glass or at such a distance from it -inside the telescope that they intercept one half of the light, and the -remaining portion goes to form the usual image, while the other is -altered in its course by the prism and forms another image, and this -alteration depends on the position of the movable prism. - ------ - -Footnote 10: - - Grant’s _History of Physical Astronomy_, p. 454. - -Footnote 11: - - More accurately the time of transit is to be multiplied by the cosine - of the star’s declination. - -Footnote 12: - - So called because the contrivance was first used to measure the - diameter of the sun. - - - - - BOOK IV. - _MODERN MERIDIONAL OBSERVATIONS._ - - - - - CHAPTER XVI. - THE TRANSIT CIRCLE. - - -We are now, then, in full possession of the stock-in-trade of the modern -astronomer—the telescope, the clock, and the circle,—and we have first -to deal with what is termed astronomy of position, that branch of the -subject which enables us to determine the exact position of the heavenly -bodies in the celestial sphere at any instant of time. - -Before, however, we proceed with modern methods, it will be well, on the -principle of _reculer pour mieux sauter_, to refer back to the old ones -in order that we can the better see how the modern instruments are -arranged for doing the work which Tycho, for instance, had to do, and -which he accomplished by means of the instruments of which we have -already spoken. - -First of all let us refer to the Mural Quadrant, in which we have the -germ of a great deal of modern work, its direct descendant being the -Transit Circle of the present time. - -We begin then by referring to the hole in the wall at which Tycho is -pointing (see Fig. 112), and the circle, of which the hole was the -centre, opposite to it, on which the position of the body was observed, -and its declination and right ascension determined. This then was -Tycho’s arrangement for determining the two co-ordinates, right -ascension and declination, measured from the meridian and equator. It is -to be hoped that the meaning of right ascension and declination is -already clear to our readers, because these terms refer to the -fundamental planes, and distances as measured from them are the very A B -C of anything that one has to say about astronomical instruments. - -We know that Tycho had two things to do. In the first place he had to -note when a star was seen through the slit in the wall, which was -Tycho’s arrangement for determining the southing of a star, the sun, or -the moon; and then to give the instant when the object crossed the sight -to the other observer, who noted the time by the clocks. Secondly, he -had to note at which particular portion of the arc the sight had to be -placed, and so the altitude or the zenith distance of the star was -determined; and then, knowing the latitude of the place, he got the two -co-ordinates, the right ascension and declination. - -How does the modern astronomer do this? Here is an instrument which, -without the circle to tell the altitude at the same time, will give some -idea of the way in which the modern astronomer has to go to work. In -this we have what is called the Transit Instrument, Fig. 113; it is -simply used for determining the transit of stars over the meridian. It -consists essentially of a telescope mounted on trunnions, like a cannon, -having in the eyepiece, not simple cross wires, but a system of wires, -to which reference has already been made, so that the mean of as many -observations as there are wires can be taken; and in this way Tycho’s -hole in the wall is completely superseded. The quadrant is represented -by a circle on the instrument called the transit circle, of which for -the present we defer consideration. - -[Illustration: - - FIG. 112.—Tycho Brahe’s Mural Quadrant. -] - -[Illustration: - - FIG. 113.—Transit Instrument (Transit of Venus Expedition). -] - -[Illustration: - - FIG. 114.—Transit Instalment in a fixed Observatory. -] - -Now there are three things to be done in order to adjust this instrument -for observation. In the first place we must see that the line of sight -is exactly at right angles to the axis on which the telescope turns, and -when we have satisfied ourselves of that, we must, in the second place, -take care, not only that the pivots on which the telescope rests are -perfectly equal in size, but that the entire axis resting on these -pivots is perfectly horizontal. Having made these two adjustments, we -shall at all events be able, by swinging the telescope, to sweep through -the zenith. Then, thirdly, if we take care that one end of this axis -points to the east, and the other to the west, we shall know, not only -that our transit instrument sweeps through the zenith, but sweeps -through the pole which happens to be above the horizon—in England the -north pole, in Australia the south pole. That is to say, by the first -adjustment we shall be able to describe a great circle; by the second, -this circle will pass through the zenith; and by the third, from the -south of the horizon to the north, through the pole. Of course, if the -pole star were at the pole, all we should have to do would be to adjust -the instrument (having determined the instrument to be otherwise -correct) so as simply to point to the pole star, and then we should -assure ourselves of the east and west positions of the axis. Some -details may here be of interest. - -The first adjustment to be made is that the line of sight or collimation -shall be at right angles to the axis on which the instrument moves: to -find the error and correct it, bring the telescope into a horizontal -position and place a small object at a distance away, in such a position -that its image is bisected by the central wire of the transit, then lift -the instrument from its bearings or Ys, as they are called, and reverse -the pivots east for west, and again observe the object. If it is still -bisected, the adjustment is correct, but if not, then half the angle -between the new direction in which the telescope points and the first -one as marked by the object is the collimation error, which may be -ascertained by measuring the distance from the object to the central -wire, by a micrometer in the field of view, and converting the distance -into arc. To correct it, bring the central wire half way up to the -object by motion of the wire, and complete the other half by moving the -object itself, or by moving the Ys of the instrument. This of course -must be again repeated until the adjustment is sensibly correct. - -The second adjustment is to make the pivots horizontal. Place a striding -level on the pivots and bring the bubble to zero by the set screws of -the level, or note the position of it; then reverse the level east for -west, and then if the bubble remains at the same place the axis of -motion is horizontal, but, if not, raise or lower the movable Y -sufficiently to bring the bubble half way to its original position, and -complete the motion of the bubble, if necessary, by the level screw -until there is no alteration in the position of the bubble on reversing -the level. - -[Illustration: - - FIG. 115.—Diagram explaining third adjustment, H, R, plane of the - horizon; H, Z, A, P, B, R, meridian; A and B places of circumpolar - star at transit above and below pole P. -] - -The third adjustment is to place the pivots east and west. Note by the -clock the time of transit of a circumpolar star, when above the pole, -over the central wire, and then half a day later when below it, and -again when above it; if the times from upper to lower transit, and from -lower to upper are equal, then the line of collimation swings so as to -bisect the circle of the star round the pole, and therefore it passes -through the pole, and further it describes a meridian which passes -through the zenith by reason of the second adjustment. This is therefore -the meridian of the place, and therefore the pivots are east and west. -If the periods between the transits are not equal, the movable pivot -must be shifted horizontally, until on repeating the process the periods -are equal. - -In practice these adjustments can never be made quite perfect, and there -are always small errors outstanding, which when known are allowed for, -and they are estimated by a long series of observations made in -different manners and positions. The error of the first adjustment is -called the collimation error, that of the second the level error, and -that of the third the deviation error. When the errors of an instrument -are known the observations can be easily corrected to what they would -have been had the instrument been in perfect adjustment. - - * * * * * - -Now what does the modern astronomer do with this instrument when he has -got it? It is absolutely without circles, but the faithful companion of -the Transit Instrument is the Astronomical Clock—and the two together -serve the purpose of a circle of the most perfect accuracy, so that by -means of these two instruments we shall be able to determine the right -ascensions of all the stars merely by noting the time at which the -earth’s rotation brings them into the field of view. The clock having -been regulated to sidereal time, a term fully explained in the sequel, -it will show 0_h._ 0_m._ 0_s._ when the first point of Aries passes the -meridian, and instead of dividing the day into two periods of twelve -hours each, the clock goes up to twenty-four hours. If now a star is -observed to pass the centre of the field of view (that is the meridian) -at 1_h._ by the clock, or one hour after the first point of Aries, it -will be known to be in 1_h._ of right ascension; or if it passes at -12_h._ it will be 12_h._ right ascension, or opposite to the first point -of Aries, and so on up to the twenty-four hours, the clock keeping exact -time with the earth. The transit instrument thus gives us the right -ascension of a star, or one co-ordinate: and now we want the other—the -declination. - - - THE TRANSIT CIRCLE. - -This is given by the Transit Circle, which is a transit instrument with -a circle attached, to ascertain the angle between the object and the -pole or equator. - -[Illustration: - - FIG. 116.—The Mural Circle. -] - -The combination of the circle with the transit, forming the transit- or -meridian-circle, is of comparatively recent date, and the earlier method -was to use a circle with a telescope attached, fixed to a pivot moving -on bearings in a wall, and called therefore the Mural Circle, Fig. 116. -Since it is supported only on one side it cannot move so truly in the -meridian as the transit, but, having a large circle, it gives accurate -readings. - -[Illustration: - - FIG. 117.—Transit Circle, showing the addition of circles to the - transit instrument. -] - -[Illustration: - - FIG. 118.—Perspective view of Greenwich Transit Circle. -] - -Fig. 117 shows in what respect the Transit Circle is an advance upon the -transit instrument and the mural circle, for in addition to the transit -instrument we have the circle. This is a perspective view of the -transit, and the telescope is represented sweeping in the vertical plane -or meridian. In addition to the instrument resting with its pivots on -the massive piers, we have the circle attached to the side of the -telescope. We see at once that by means of this circle we are able to -introduce the other co-ordinate of declination. If the clock goes true -with the earth—if they both beat in unison and keep time with each -other—and further if the clock shows 0_h._ 0_m._ 0_s._ when the first -point of Aries passes the centre of the field, that is through the -meridian plane, then, if we observe a star at the moment it passes over -the meridian, the clock will give its right ascension and the circle its -declination, when the latitude of the place is known. - -The construction of the transit circle will repay a more detailed -examination. A system of weights suspended over pulleys (Fig. 118) -reduces the weight of the instrument on the pivots, in order that their -form shall not be altered by too much friction, and on the right-hand -side of one of the piers the eyepieces of the microscopes for reading -the circle are shown. This is shown better in section in Fig. 119. One -of the solid stone piers is pierced through diagonally, as shown at (m) -(m), so that light proceeding from a gas-lamp (q) placed opposite the -pivot of the telescope is allowed to fall through the openings, and is -condensed by means of the lens (n) on the graduations of the circle of -five minutes each, already referred to. By the side of each illuminating -hole is another hole (o) (o) through which the reading microscopes, six -in number, two of which are shown at (q) (p), having their eye-ends -arranged in a circle at the end of the pier, are focussed on to the -graduations of the circle. There is also another reading microscope, -besides the six just mentioned, of less power for reading the degrees, -or larger divisions of the circle. Hence from the side of the pier close -to the lamp the observer can read the circle with accuracy, and measure -the angle, to which we have alluded, made by the telescope when pointed -to any particular star. We have now seen how the circle is illuminated, -and now we will inquire further as to the arrangements that are -necessary in order to bring this instrument into use. - -[Illustration: - - FIG. 119.—Plan of the Greenwich Transit Circle. -] - -We must defer giving more explanation of the practical working of the -instrument until we have considered the clock used in connection with -it, and we shall then show how the observations are made. One important -point to which attention should be given is the method of illuminating -the wires in the eyepiece. This is the arrangement. There is a lamp at -the end of one of the pivots which is hollow, the light falls on a -mirror, placed in the centre of the telescope, of such a shape and in -such a position that it will not intercept the light from the -object-glass falling through the diaphragms on to the eyepiece. The -mirror is ring-shaped, something like the brim of a hat, and is carried -on two pivots, so that it can be placed diagonally in the tube, or at -right angles to it; it is arranged just outside the cone of rays from -the object-glass, so that when the mirror is diagonally placed the light -will be grasped directly from the lamp at the end of the axis and -reflected down and mixed up with the light coming from the star into the -eyepiece. - -In this way of course the wires can be rendered visible at night, and -without such a method they would be invisible. This arrangement gives a -bright field and dark wires; but there is also a method of reversing -matters; for near the edge of the ring-shaped reflector are fixed prisms -for reflecting the light, and when the reflector is placed square with -the axis of the telescope the small prisms on the reflector send the -light down through apertures in the diaphragms, so that the mirror in -this position no longer sends the light down with the rays from the -star, but through holes in the diaphragms themselves, to two small -reflecting prisms, one on each side of the wires in the eyepiece. What -has that light to do? It has simply to do this, it has to fall sideways -on the wires themselves in such a manner that it does not fall on the -eye except by reflection from the wires. In this way we have the means -of getting a bright system of wires on a dark field, in which the wires -and objects to be measured are the only things to be seen. - -As with the pivots of the transit circle, and in fact of any -astronomical instrument, so with the circles, certain fundamental points -have to be borne in mind; and, although it is absolutely impossible to -ensure perfection, still, to go as near to it as possible, the -astronomer has to observe a great many times over in all sorts of -positions in order to bring the error down to its minimum. - -First, the circle must be placed exactly at right angles to the axis of -the telescope, so that it is in the plane of the meridian. Secondly, the -error of centering must be found. For instance, if the Greenwich circle -were to be read by only one microscope, an error in the pivot or any -part of the axis round which the circle turns would vitiate the -readings; but we could get rid of that error, due to a fault of the -axis, or to a want of centering, by means of two readings, at the -extremities of a diameter; but even then we should not get rid of the -possible error due to graduation, for even if the divisions on the -circle were accurate at first, they would not long remain so, for the -metal of which these circles are made is liable, like other metals, to -certain changes due to temperature; and if a circle is very large the -weight of the circle itself, supposing its form perfect when horizontal, -will, when vertical, sag it down and deflect it out of shape, so that at -Greenwich the method adopted is to use six reading microscopes. Fig. -120, which shows the Cambridge Transit Circle, indicates the arrangement -of the five microscopes in use there, set round the circumference of the -circle, much in the same manner as in the case of the Greenwich -instrument, where there are holes through the pier in which the -microscopes are placed with the eye-ends arranged in a circle at the -side of it. - -[Illustration: - - FIG. 120.—Cambridge (U.S.) meridian circle. -] - -When, therefore, the transit is pointed to any particular star, not only -is the time noted in order to determine the right ascension of the star, -in a careful and elaborate way, but the readings of the circle are made -by every one of these microscopes—reading from the next five minutes -division of the circle which happens to be visible,—and there is an -additional microscope giving the rough reading of the larger divisions -of the circle from a certain zero. - -And what, then, is this zero? There is no doubt about the reading of the -zero of right ascension, it is the intersection of the two fundamental -planes at the first point of Aries; but what zero shall be used in the -case of the vertical circle? - -[Illustration: - - FIG. 121.—Diagram illustrating how the pole is found. -] - -Let the circle, H, Z, R, Fig. 121, represent a great circle of the -heavens, the meridian in fact, and let the centre of this circle -represent the centre of the transit instrument. Now what we want is, not -only to be able to measure degrees of arc along this circle, but to -determine some starting-point for those degrees. One arrangement is to -observe the reflection of the wires in the eyepiece of the transit -circle, from the surface of mercury in a vessel which is placed below -the telescope, turned with its object-glass downwards; the vessel -containing the mercury is out of sight, between the two piers, but in -Fig. 118 are seen the two parallel bars, with weights at the ends, -carrying it, by which it may be brought into any position for the -purpose referred to, so that the light from the wires in the eyepiece -may pass through the tube and be reflected back by the mercury (the -surface of which is of course perfectly horizontal), up through the tube -again to the eyepiece. When the telescope is absolutely in the vertical -position the images of the cross wires will be superposed over the cross -wires themselves; and then an observation will give the actual reading -of the circle when the instrument is pointing at 180° from the zenith; -deduct 180° from this reading, and we get the reading when the -instrument is pointing at the zenith—the zero required. This should be -0°, and the quantity by which it differs from 0° must be applied to the -observed position of stars, so that the distance of a star from the -zenith can be at once determined. - -But this is not all. If we assume for the moment that the observer is at -the north pole, the pole star will be exactly over head, and therefore, -supposing the pole star to absolutely represent the pole of the heavens, -all the observer has to do is simply to take a reading of the pole star -on the arc of his circle—call it 0° O´ 0˝—and then use it as another -zero to reckon polar distance from, seeing that every particular star or -body we observe has so many degrees, minutes, seconds, or tenths of -seconds, from the pole star. - -But we are not at the north pole. Still we are in a position where the -pole is well above the horizon, and from that fact we can determine the -polar distance, although the absolute place of the pole is not pointed -out by the pole star. Thus, if we suppose any star, A, Fig. 121, to be a -certain distance from the pole, and the earth carrying the instrument to -be in the centre of the circle H, Z, R, we can observe the zenith -distance of that star, Z, A, when it transits our meridian above the -pole, P; and we can then observe its distance, Z, B, when it transits -below the pole; and it is clear that the difference between those two -measures will give the distance A, B, or double the polar distance of -that star, and the mean of the readings will give the distance, Z, P, -the zenith distance of the pole, so that it is perfectly easy to -determine the distance between the pole and the zenith, which, -subtracted from ninety degrees, gives us the latitude of the place. It -is therefore perfectly easy by means of this instrument to determine -either the zenith or polar distance, and, knowing the polar distance, we -get the declination, or distance from the equator, by subtracting it -from ninety degrees. - -In our case it is the north polar distance or declination of any object -in the heavens that we record; and if we take the precaution to do so -with this instrument at the time given by the clock, when the object -passes the meridian, we have the actual apparent place of that body in -the sky; and in this way all the positions of the stars and other -bodies, and their various changes, and the courses of the planets, have -been determined. - -The transit circle is the most important instrument of astronomy, and -such is the perfection of the Greenwich instrument that nothing could be -more unfortunate for astronomy than that that instrument should be in -any way damaged. And though many of us are admirers of physical -astronomy, we have yet to find the instrument that is as important to -physical astronomy as the transit circle at Greenwich is to astronomy of -position. - -The room in which these transit circles are worked—the transit room—is -required to be of special construction. A clear space from the southern -horizon through the zenith to the north must at any time be available; -this entails the cutting of a narrow slit in the roof and both walls, -without the intervention of any beams across the room. This slit is -closed by shutters or windows which are made to open in sections, so -that any part of the meridian can be observed at pleasure. - - - - - CHAPTER XVII. - THE TRANSIT CLOCK AND CHRONOGRAPH. - - -We have now to consider the way in which the transit instrument is used -and the functions which both it and the transit circle fulfil. - -The connection between the transit instrument and the transit clock is -so intimate that either is useless without the other. In the one case we -should note the passage of a star across the meridian without knowing at -what time it took place; while, on the other hand, we should not learn -whether the clock showed true time or not, unless we could check its -indications in the manner rendered possible by transit observations. In -what has been already said of time we referred to it as measured by our -ordinary clocks, _i.e._ reckoning it from noon to midnight and midnight -to noon, and regulated entirely by the length of the solar day. It would -at first sight seem that it should be twelve o’clock by a clock so -regulated when the sun passes the meridian; but the earth’s orbit is not -circular, and the sun’s course is inclined to the equator, so that, as -determined by such a clock, sometimes he would get to the meridian a -little too late, and sometimes too early, so that we should be -continually altering our clocks if we attempted to keep time with the -sun. - -One of the greatest boons conferred by astronomy upon our daily life is -an imaginary sun that keeps exact time, called the _Mean Sun_, so that -the mean sun is on the meridian at twelve o’clock each day by our -clocks, regulated by the methods we have now to discuss. Such clocks -regulated, as it is called, to mean time are sometimes a few minutes -before, and at others a few minutes behind the true sun, by an amount -called the Equation of Time, which is given in the almanacs. It would -therefore be difficult to regulate our standard clock by the sun, so we -do it through the medium of the stars, which go past our meridian with -the greatest regularity, since their apparent motion depends almost -wholly upon the equable rotation of the earth on its axis, while the -apparent motion of the sun is complicated by the earth’s revolution -round it. - -This method at first sight is complex, and in fact we cannot obtain mean -time directly by such transits of stars. It is accomplished indirectly -by means of a clock set to star- or sidereal-time, and such a clock is -the astronomer’s companion, to which he always refers his observations, -and the indications of which alone are always in his mind. This he calls -the Sidereal Clock. - -[Illustration: - - FIG. 122.—Diagram illustrating the different lengths of solar and - sidereal day. -] - -We have, then, next to consider the difference between the clock used -for the transit, or the sidereal clock, and an ordinary solar clock, or -between a solar and a sidereal day. Let S, Fig. 122, represent the sun, -and the arc a part of the orbit of the earth, the earth going in the -direction of the arrow. Let 2 represent the position of the earth one -day, and let 1 represent the position of the earth on the day before. A -line drawn from the sun through the earth’s centre will give us the -places _a_, _b_, on the earth at which it is midday on the side turned -towards the sun, and midnight on the side turned from the sun. Now when -a revolution of the earth with reference to the stars has been -accomplished the earth comes to the second position, 2; and _c_ is the -point of midday; and there is a certain angle here between _a_ and _c_, -through which the earth must turn before it is noon at _a_, due to the -change of position of the earth, or to the apparent motion of the sun -among the stars, by which the sun comes to the meridian rather later -than the stars each day. Now let us suppose that, while one observer in -England is observing the sun at midday, another is observing the stars -at the antipodes at midnight, the star is seen in the direction ⁎. We -are aware that the stars are so far away, that from any point of the -earth’s orbit they seem to be in absolutely the same place—they do not -change their positions in the same way as the sun appears to do amongst -them—an observer at _b_ therefore sees on his meridian the star ⁎ while -the observer at _a_ sees the sun on his meridian; supposing _b_ to -represent the same observer, on the second day, he will see the star due -south before the other observer at _a_ sees the sun due south. The -result of that is, that the sidereal day is shorter than the solar day, -and the sun appears to lose on the stars. If we wish to have a clock to -show 12 o’clock when the sun is southing, we shall want it to go slower -by nearly four minutes a day than one which is regulated by the stars -and is at 12 o’clock when our starting-point of right ascension—which is -the intersection of those two fundamental planes, the equator and the -ecliptic—passes over the meridian. - -One of the uses of the clock showing sidereal time in connection with -the convenient fiction of the “Mean Sun,” is to give to the outside -world a constant flow of mean time regulated to the average southing of -the sun _in the middle of the period for which the sun is above the -horizon each day in the year_. - -The stellar day, that is the time from one transit of a star to the -next, is shorter than a solar day by 3_m._ 56_s._, so what is called -sidereal time, regulated by the transits of well-known stars, in the -manner we shall presently explain, by no means runs parallel with mean -time so far as the clock indications go. Indeed when we look at a -sidereal clock, we see something different to the clock we are generally -accustomed to see. In the first place, we have twenty-four hours instead -of twelve, and then generally there is one dial for hours, another for -minutes, and another for seconds. That of course might happen in the -case of the mean-time clock; but the mean-time clock is not often -divided into twenty-four hours, although it formerly used to be, as the -dials in Venice still testify. - -We now see the importance of an absolutely correct determination of the -right ascension of stars; for this right ascension, expressed in hours, -minutes, and seconds, is nothing more nor less than the time indicated -by the sidereal clock, by the side of the transit instrument, when a -star passes over, or transits, the central wire of that instrument. -Hence it is the sidereal clock which keeps time with the stars, and -which we keep correct by means of the transit instrument. - -[Illustration: - - FIG. 123.—System of wires in transit eyepiece. -] - -Let us show how this was always done some twenty or thirty years ago, -and how it is sometimes done now. The transit room is kept so quiet that -one can hear nothing but the ticking of the sidereal clock; the star to -be observed is then carefully watched as it traverses the field of view -over the wires, and the time of transit over each wire is estimated to -the tenth of the time between each beat by the observer. - -We reproduce in Fig. 123 a rough representation of what is seen in the -field of view of a transit instrument. Now if we could be perfectly sure -of making an accurate observation by means of the central wire, it is -not to be supposed that astronomers would ever have cared to use this -complicated system of wires in their eyepieces; but so great is the -difficulty of determining accurately the time at which a star passes a -wire, that we have in eyepieces introduced a system of several wires, so -that we may take the transit of the star first at one wire, then at -another, until every wire has been passed over. - -We want one wire exactly in the middle to represent the real physical -middle of the eyepiece so far as skill can do it, and then there is a -similar number of wires on either side at exactly equal distances; so -that the average of all the observations made at each of the wires will -be much more likely to be accurate than a single observation at one -wire. In this way the astronomer gives himself a good many chances -against one to be right. If he lost his chance from any reason when -using only one wire, he would have to wait twenty-four more sidereal -hours before he could make his measure again, but by having five, or -seven, or twenty-five or more wires in the eyepiece of the telescope, he -increases his chances of correctness: and the way in which he works is -this: While the heavens themselves are taking the stars across the wires -he listens to the beating of the clock. If a star crosses one of the -wires exactly as the clock is beating, he knows that it has passed the -wire at some second, and he takes care to know what second that is; but -if, instead of being absolutely coincident with one of the beats of the -clock, it is half-way between one beat and another, or nearer to one -beat than another, he estimates the fraction of a second, and by -practice he has no difficulty at all in estimating divisions of time -equal to tenths of a second, and at each particular wire in the eyepiece -the transit of the star is thus minutely observed. - -Then if the observations are complete and the mean of them is taken, it -should, after the necessary corrections for instrumental errors have -been applied, give the actual observation made at the central wire; if -the astronomer cannot make observations at every wire, he introduces a -correction in his mean to make up for the lost observations. - -This is what is called the “eye and ear” method, because the observer is -placed with his eye to the telescope, and he depends upon his ear to -give him the exact interval at which each beat of the clock takes place, -and he requires an exact power of mentally dividing the distance between -each beat into ten equal parts, which are tenths of seconds. In this -method of observation every observer differs slightly in his judgment of -the instant that the star crosses the wire, and his estimation differs -from the truth by a certain constant quantity which he must always allow -for; this error is called his _personal equation_. - -In this way then the transit instrument enables us, having true time, to -determine the right ascension of a heavenly body as it transits the -meridian, and, knowing the right ascension of a heavenly body, we have -only to watch its transit in order to know the true time; so if the -observer knows at what time a known star ought to transit, he has an -opportunity of correcting his clock. - -So much for the eye and ear method of transit observation. There is -another which has now to a very large extent superseded it. This is -called the “chronographic method”; we owe it to Sir Charles Wheatstone, -who made it possible about 1840. - -Figs. 124-7 are from drawings of the chronograph in use at Greenwich, -and by their means we hope to make the principle of the instrument -clear. In this chronograph, _g_ is a long conical pendulum which -regulates the driving clock in the case below it, through the gearing of -wheel-work, as it turns the cylinder, E, gently and regularly round. On -the cylinder is placed paper to receive the mark registering the -observations; along the side of the cylinder or roller run two long -screws, K and N, Fig. 125, which are also turned by the clock, and on -them are carried electro-magnets, A, B, Fig. 125, and prickers, 35, Fig. -126; as the screws turn, the magnets and prickers are moved along the -roller, and, as the roller turns, the pointer, 36, Fig. 127, traces a -fine line on the paper like the worm of a screw on the surface; and it -is close to this line, which serves as a guide to the eye, that the -prickers make a mark each time a current is sent through the -electro-magnets; this turns each of them into a magnet, and they then -attract a piece of iron which, in moving upwards, presses down its -pricker by means of a lever, and registers the instant the current is -sent. - -The different wires are brought, first from the transit circle to work -one pricker, and then from the clock to work the other, the clock -sending a current and producing a prick on the roller every second. - -[Illustration: - - FIG. 124.—The Greenwich chronograph. General view. -] - -The observer, instead of depending upon the eye and ear as he had to do -before, has then the means of impressing a mark at any instant upon the -same cylinder, in exactly the same way that the pendulum of the clock -impresses the mark of any second, so that as each wire in the eyepiece -of the transit instrument is passed by the star, he is able, by the same -method as the clock, to record on this same revolving surface each -observation, which can afterwards be compared with the marks -representing the seconds, and so the exact time of each observation is -read off more accurately and with less trouble than by the old method. -Let us suppose we are making a transit observation: the clock will be -diligently pricking sidereal seconds, while we, by a contact-maker held -in the hand, are as diligently recording the moments at which the star -passes each wire. - -[Illustration: - - FIG. 125.—Details of the travelling carriage which carries the magnets - and prickers. Side view and view from above. -] - -[Illustration: - - FIG. 126.—Showing how on the passage of a current round the soft iron - the pricker is made to make a mark on the spiral line on the - cylinder. -] - -[Illustration: - - FIG. 127.—Side view of the carriage carrying the magnets and the - pointer that draws the spiral. -] - -This is done by pressing a stud, and sending a current at each transit; -so that we shall have a dot in every other space between the clock dots, -supposing the wires to be two seconds in time apart; supposing them to -be three seconds apart, our dots will be in every third space; supposing -them to be four seconds apart, our dots will be in every fourth space, -and so on; and tenths and hundredths of seconds are estimated, by the -position of each transit dot between those which record the seconds. - -In this way one sees that we have on the barrel an absolute record, by -one of the pointers, of the seconds recorded by the clock, and, by the -other, of the exact times at which a star has been seen at each wire of -the transit instrument. - -Now of course what is essential in this method is that there shall be a -power of determining not only the precise second or tenth of a second of -time, but also the minute at which contact takes place, otherwise there -would be a number of seconds dots without knowing to what minute they -corresponded; it would be like having a clock with only a second-hand -and no minute-hand. - -The brass vertical sliding piece shown at the lower left-hand side in -Fig. 96, carries at its upper end two brass bars, each of which has, at -its right-hand extremity, between the jaws, a slender steel spring for -galvanic contact; the lower spring carries a semicircular piece -projecting downwards, which a pin on the crutch rod lifts in passing, -bringing the springs in contact at each vibration: the contact takes -place when the pendulum is vertical, and the acting surfaces of the -springs are, one platinum, the other gold; an arrangement that has been -supposed to be preferable to making both surfaces of platinum. By means -of the screws _n_ and _o_, which both act on sliders, the contact -springs can be adjusted in the vertical and horizontal directions -respectively. Other contact springs in connection with the brass bars -_p_ and _q_, on the other side of the back plate, are ordinarily in -contact, but the contact is broken at one second in each minute by an -arm on the escape-wheel spindle. The combination of these contacts -permits the clock to complete a galvanic circuit at fifty-nine of the -seconds in each minute, and omit the sixtieth.[13] - -In this way we may suppress the sixtieth second, thus leaving a blank -that marks the minute; and all that the observer has to do after he has -made a record of the transit, is to go quietly to the barrel, and mark -the hour and minute in the vacant space. A barrel of this size will -contain the observations which would be made in some hours; so that at -the end of that time it may be taken off, and it will give, with the -least possible chance of error, a permanent record of the work of the -astronomer. - -It is at once apparent that by the introduction of this application of -electricity, astronomy has been an enormous gainer; but so far we have -simply given a description of one instrument which has been suggested -for that purpose. A few words may be said on other forms. - -In the instrument used in the Royal Observatory at Greenwich the -rotation of the roller is kept uniform, as we have seen, by a conical -pendulum; but there are other methods of attaining this end—there is the -fly-wheel and fan, similar to the arrangement for regulating the -striking part of a clock; there is the governor used for the -steam-engine, and others which give a fairly regular motion—for the -motion need not be absolutely uniform, because the dots, which form the -points from which to measure, are made by the standard clock. - -The particular instant at which each minute occurs may be recorded in -another way. The two steel springs above described may be pressed -together, not by a pin in the crutch, but by cogs on a wheel attached to -the spindle of the escape-wheel of the clock (see Fig. 128); and then -all we have to do to stop the transmission of a current at the sixtieth -second is to remove one of the cogs. - -[Illustration: - - FIG. 128.—Wheel of the sidereal clock, and arrangement for making - contact at each second. -] - -Another simple method for transmitting seconds’ currents has also been -occasionally tried. A wire runs down the whole length of the pendulum, -and ends in a projection of such a length that it swings through a small -globule of mercury in a cup below it, the pendulum being connected with -one wire from the chronograph and the mercury with the other; thus there -will be a making and breaking of contact each time the point of the -pendulum swings through the mercury. It is uncertain which method is the -better; one would prefer that which, under any circumstances, could -disturb the pendulum least: but as to which this is opinions differ. - -We have now described the _modus operandi_ of making time observations -with the transit instrument, the final result of which is that the time -shown by the sidereal clock corresponds with the right ascension of the -“clock stars” as they transit the central wire. - -The great use, as we have already stated, made of the sidereal clock -thus kept right by the stars is to correct the mean-time clock with a -view of supplying mean solar time to the outside world. - -As the sidereal clock is regulated by the stars, it can be corrected by -them at any time by the clock stars given in the “Nautical Almanac,” -whose time of passing the meridian is calculated beforehand much more -accurately than a mean-time clock could be corrected by the sun; we -therefore correct our mean clock by the sidereal, the two agreeing at -the vernal equinox, when the sun is in the first point of Aries, and the -sidereal clock gaining about 3_m._ 56_s._ each day until it has gained a -whole day, and agrees again at the next vernal equinox. - -[Illustration: - - FIG. 129.—Arrangement for correcting mean solar time clock at - Greenwich. -] - -At Greenwich there is, as we have already seen, a _standard, sidereal -clock_, that is, a clock keeping sidereal time; and regulated from this -is the _standard solar time clock_, giving the time by which all our -clocks and watches are governed. In practice at Greenwich the solar -clock is regulated as follows: in the computing room are two -chronometers, _c_ and _b_, Fig. 129, the one, _c_, regulated -electrically by the mean-time clock, and the other, _b_, regulated by -the sidereal clock—the error of the latter being known by transit -observations of stars on the Nautical Almanac list, the difference -between the observed time of transit and the right ascension of the star -being the error required. The proper difference between the two clocks -is then calculated and the error allowed for, which shows whether the -solar clock is fast or slow; to correct it the following method is -adopted: Carried on the pendulum of the solar clock is a slender bar -magnet, about five inches long, and below it, fastened to the -clock-case, is a galvanic coil; the magnet passes at each swing over the -upper end of the coil; if now a current is sent through this coil in one -direction repulsion takes place between the magnet and coil, and the -clock is slowed; if, on the other hand, the current is reversed, the -clock is made to gain. Now between the two chronometers is a commutator, -_d_, which, by moving the handle to one side or the other, sends the -current through the coil in such a manner that the clock is accelerated -or retarded sufficiently to set it right; when the handle of the -commutator is in the position shown in the drawing no action takes -place. As an instance of another method of regulating one clock from -another, we will quote what Professor Piazzi Smyth says of the clock -arrangements at Edinburgh. - -_Correction of Mean-time Clock._—“First get its error on the observing, -_i.e._ sidereal clock. This is always done by _coincidence of beats_, -safe and certain to within one-tenth of a second, and with great ease -and comfort by means of the loud-beating hammer which strikes the -seconds of the sidereal clock on the outside of the case; one can then -watch the neck-and-neck race which takes place every six minutes between -the second of a sidereal clock and the second of a mean-time clock, the -former always winning while you look at the motion of the mean-time -seconds hand, and hear the seconds of the sidereal time. - -Having got the error, say three (0·3)-tenths of a second slow, this is -the arrangement for correcting it. The pendulum is suspended by a spring -extra long, and a long arm goes across the clock pier, and the pendulum -spring passes through a fine slit in the middle of it, and the left end -(of said arm) turns on a pivot, while the right end rests on a cam, -which can be turned by a handle outside the clock-case. Turning the -handle one way raises the arm, and with that lengthens the acting length -of the pendulum spring, and turning the other way, lowers it and -shortens the pendulum, but so slightly that it takes fifteen minutes of -the quickened rate of the pendulum, when shortened, to add the required -0·3 seconds to the indications of the clock.”[14] - -The sidereal clock is used in many ways besides the purpose of giving a -basis from which we can at any time get solar time, the distribution of -which forms the subject of our next chapter. - ------ - -Footnote 13: - - _Nature_, April 1, 1875. - -Footnote 14: - - This plan was devised and executed by Mr. Sang, C.E., Edinburgh. - - - - - CHAPTER XVIII. - “GREENWICH TIME” AND THE USE MADE OF IT. - - -We have now described the method of obtaining and keeping true Greenwich -time by means of transit observations, and the next thing is to -distribute it either by controlling or driving other clocks -electrically, or by sending electric signals at known times for persons -to set their clocks right. - -Nearly all, if not quite the whole, of the mean-time clocks in the -Observatory are driven by a current controlled by the standard clock, as -also is a seconds relay, _a_ Fig. 129. The clock controls, by currents -sent every second by the relay, one or two clocks in London, by special -wires. - -So long ago as the year 1840 Sir Charles Wheatstone read a paper before -the Royal Society in which he described an apparatus for controlling any -number of clocks by one standard clock at a distance away. The principle -was, that at each beat of the standard clock an electric current was -sent from it through a wire to the clocks to be worked by it or -governed; and this current made an electro-magnet attract a piece of -iron each time it was sent; and this piece of iron moved backwards and -forwards two pallets, something like those of an ordinary clock, which -turned a wheel, and so worked the clock. Instead of a spring or weight -being used to work it regulated by the pallets, the pallets moved the -clock themselves, and of course keep time with the standard clock. Sir -Charles Wheatstone in this most valuable pioneer paper, indicates -several modifications of this plan. He proposed to the Astronomer-Royal -to test his method by using the then new telegraph line to Slough, but -the idea was not carried out. - -This method of _driving_ clocks by electricity naturally required -considerable battery power, and in the more modern systems the clocks -are simply _controlled_, and not _driven_, by electric currents. - -A very pretty method of regulating clocks by a standard clock is that in -use at Edinburgh. On the pendulum rod of the clock to be regulated, and -low down on the same, is a coil of fine covered wire wound round a short -tube. Two permanent magnets are placed in line with each other, with -their N or S ends close together and the other ends attached to the -clock-case, in such a manner that the coil, on swinging with the -pendulum, can slide over the magnets without touching. The terminal -wires of the coil are led up to near the point of suspension of the -pendulum, so as not to affect its swing, and the regulating current is -sent through a wire like a telegraph wire from the standard clock, and -from this wire round the coil and then to the earth, or back by another -wire. Currents are sent through the wires in contrary directions during -each successive second, so that the current in the coil flows in one -direction during its swing from, say, right to left, and in the contrary -direction when swinging from left to right; the effect of the current -flowing in one direction is to cause one magnet to repel the coil off -it, and the other to attract it over it, so that there is a tendency to -throw the coil from one side of its swing to the other, and back again -when the current is reversed. A little consideration will make it clear -that if the pendulum tries to go too fast the coil will tend to commence -its return swing before the current assisting the previous swing has -stopped, and it will therefore meet with resistance, and be brought back -to correct time. - -The alternate currents during each second may be sent by having a wheel -of thirty long teeth on the axis of the seconds hand. Above the wheel, -and insulated from each other, are fixed two light springs which descend -side by side on either side of the teeth of the wheel, and at right -angles to each spring there projects sideways a little bar of agate with -sloping sides, which is lifted up by the teeth as they pass; one agate -is fastened a little lower down its spring than the other, so that they -are held one above the other, and half the distance between two teeth -apart: the wheel is so arranged that while at rest one of the teeth -presses against one of the agates and pushes the spring outwards, while -the other agate drops between two teeth. At the next tick of the clock -the wheel will move one-half a tooth’s distance and the other agate will -be raised and the first dropped. At the bottom of each spring is a -little platinum knob that is brought against a platinum plate as each -spring is raised, so as to make electric contact. Two batteries (single -cells of “sawdust-Daniell’s” answer admirably for short distances) are -used, the + pole of one being put in contact with the upper attachment -of one spring and the - pole of the other battery in contact with the -other spring. The other poles are put to earth, or connected to the -return wire from the governed clock. The plate against which the springs -are lifted is put in connection with the line wire going to the -regulated clock. Then, as either spring is lifted up during the swing of -the pendulum from side to side, a + or - current is sent through the -line wire from one of the batteries. It is not absolutely necessary to -use two batteries, one being sometimes sufficient, and in this case one -spring is thrown out of action, and a current sent only during every -other second in the same direction. The battery may in this case be -placed close to the regulated clock, or anywhere in the circuit, so long -as a current flows whenever the standard clock completes the circuit at -the other end. This method has the advantage that the amount of current -sent can be regulated at will by a person at the regulated clock, so -that it is possible by putting on more battery power to get sufficient -current through the wire to work a bell ringing at every other second, -or a galvanometer, showing when the seconds hand of the standard clock -is at the O^s, for there is one tooth cut from the wheel in such a -position that when the seconds hand is at O^s no current is sent for two -or more following seconds according as one or both springs are acting; -knowing this, the observer watches for the first missing current or -“dropped second,” and so finds if his clock is being correctly -regulated. - -We see now the necessity for correcting the standard clock by gradually -increasing or decreasing the rate, for if it were done rapidly, the -controlled clocks would break away from the control, and not be slowed -and accelerated with the standard. At Greenwich the correction, usually -only a fraction of a second, is made a little before the hours of 10 -A.M. and 1 P.M., since at those instants a distribution of time is made -throughout the country. This distribution is made as follows:— - -An electric circuit is broken in two places at the standard clock, one -place of which is connected for some seconds on either side of each -hour, while the other is connected at each sixtieth second; both breaks -can therefore be only connected at the commencement of each hour, and -then only can the current pass. We will call this, therefore, the hourly -current: it acts on the magnet discharging the Greenwich time ball at -one o’clock daily, and on the magnet of the hourly relay shown in Fig. -129, which completes various circuits. One goes to the London Bridge -station of the South-Eastern Railway Co., and the other to the General -Post Office for further distribution. The bell and galvanometer in the -figure marked “S. E. R. hourly signal and Deal ball,” and “Post Office -Telegraphs” show the passage of these signals. We have now got the -hourly signal at the Post Office, and this is distributed by means of -the Chronopher, or rather Chronophers, for there are two, the old one -originally constructed by Mr. Yarley, and brought from Telegraph Street -on the removal to St. Martin’s-le-Grand, and a new one, much larger, -shown in the accompanying Fig. 130. It is to this that the Greenwich -wire is led, and the current transmitted to the different lines. The -lines are divided into four groups, (1) the metropolitan, (2) short -provincial, (3) medium provincial, (4) long provincial; the first being -wires passing to points in London only, the second to places within -about 50 miles of London, the third to more distant places, and the -fourth to the more distant places still, requiring signals. The ends of -each of the four groups are brought together, and each group has its -separate relay. These four relays—the left-hand four shown in Fig. -130—are all acted upon by the Greenwich signal and therefore act -simultaneously, each relay sending a portion of the current of its -battery through each wire of its group. - -[Illustration: - - FIG. 130.—The Chronopher. -] - -The metropolitan group, being used only for time purposes, is always -connected with the relay, but to the country, signals are sent only -twice a day, namely, at 10 A.M. and at 1 P.M., and as the ordinary wires -are used for this purpose, they must be switched into communication with -Nos. 2, 3, and 4 relays. The action at each hour is as follows:—The -wires leading to the respective towns are connected with their speaking -instruments through a contact spring; these contact springs are shown in -the figure in a row, like the keys of a piano; along the keys runs a -flat bar which at a short time before 10 A.M. and 1 P.M. is turned on -its axis by the clockwork above, by so doing it presses back all the -keys from their respective studs, and so cuts off communication with the -speaking instruments, and puts the wires into communication with the -bar, which is divided into three insulated portions, each in -communication with a relay and battery; the batteries and relays become -connected with their respective groups, and a constant current flows -through all the wires to the distant stations serving as a warning. When -the Greenwich current arrives the relays reverse the currents, and this -gives the exact time. Shortly afterwards the clock turns back the rod -and the springs go into contact with their respective instruments, and -all goes on as before. One of the remaining relays of the apparatus -sends a current to Westminster clock tower for the rating of the clock -there, but it is in no way mechanically governed by the current. The -apparatus is entirely automatic, and to judge of the degree of accuracy -obtained an experiment was made. One of the distributing wires was -connected with a return wire to Greenwich, and the outgoing current to -the Post Office and the incoming one were passed round galvanometers, -when no sensible difference could be seen in the indications. - -At 10 A.M. a considerable distribution goes on by hand. At this instant -a sound signal is heard from the chronopher, and the clerks immediately -transmit signals through the ordinary instruments to some 600 places; -these again act as centres distributing the time to railway stations and -smaller places. - -The methods of signalling the time are various; at some places, as at -Edinburgh, Newcastle, Sunderland, Dundee, Middlesborough, and Kendal, a -gun is fired at 1 P.M. The history of the introduction of time-guns is a -somewhat curious one. - -In August 1863, during the meeting of the British Association at -Newcastle, Mr. N. J. Holmes contrived the first electric time-gun. This -gun was fired by the electric current direct from the Royal Observatory -at Edinburgh, 120 miles distant. Time-guns were afterwards -experimentally fired at North Shields and Sunderland; the Sunderland gun -was after a time withdrawn; the Newcastle and North Shields time-guns -are regularly fired every day at 1 P.M. Four time-guns were mounted in -Glasgow, also to be fired by the electric current from Edinburgh; a -large 32-pounder was placed at Port Dundas, on the banks of the Forth -and Clyde Canal; a second small gun was placed near the Royal Exchange; -a third 18-pounder at the Bromielaw, for the benefit of Clyde ships in -harbour; and a fourth twenty-five miles further down the Clyde, at the -Albert Quay, Greenock, for the vessels anchored off the tail of the -bank. These four guns, and the two at Newcastle, were regularly fired -from the Royal Observatory, Edinburgh, for some weeks. A local jealousy -springing up amongst a few of the Glasgow College Professors and the -Edinburgh Observatory, against the introduction of mean-time into -Glasgow from the Royal Observatory Edinburgh, instead of deriving it -from the Glasgow Observatory clock (the longitude of which was -undetermined at that time), the originator of the guns, Mr. Holmes, was -cited before the police-court, charged under the Act with discharging -firearms in the public streets. The jealousy ended in the withdrawal of -the guns, and Glasgow, from then until now, has been without any -practical register of true time.[15] - -Another system of time signalling is to expose a ball to view on the top -of a building, and drop it, as in the case of the ball automatically -dropped at Greenwich every day. We have already mentioned that one of -the wires from the Greenwich Observatory connects it with the London -Bridge Station, and this is used for dropping the time-ball at Deal. In -return for the hourly signals the Company give up the use of the wires -to Deal for two or three minutes about 1 P.M., when the Deal wire is -switched into communication with the Greenwich wire by a clock, just in -the same manner as at the Post Office, and communication is also made at -Ashford and Deal, in order that the current shall go to the time-ball. -In order that they shall know at Greenwich that the ball has fallen -correctly, arrangements are made so that the ball on falling sends a -return current back to Greenwich. It appears that erroneous drops are -rare, but, if such is the case, a black flag is immediately hoisted and -the ball dropped at 2 P.M. - -Hourly signals are distributed on the metropolitan lines and to the -“British Horological Institute” for Clerkenwell; the leading London -chronometer makers also receive them privately. - -We now come to deal with one of the practical uses of the clock and -transit instrument with reference to determining longitudes. - -The earth rotates once every twenty-four hours, and if at any time a -star is directly south of Greenwich it is also due south of all places -on the meridian of Greenwich north of the equator, and north of all -places on the same meridian south of the equator; then, as the earth -rotates, the meridian of Greenwich will pass from under the star, and -others to the west will take its place, and in an hours time, at 1 P.M., -a certain meridian to the west of Greenwich will be under the star, and -in that case all places on this meridian will be an hour west of -Greenwich, and so on through all the twenty-four hours, the meridian -being called so many hours, minutes, or seconds, west, as it passes -under any star that length of time after the meridian of Greenwich. It -is immaterial whether we reckon longitude in degrees or in time, for -since there are 360 degrees or twenty-four hours into which the equator -is divided, each hour corresponds to 15°. We also express the longitude -of a place by its distance east of Greenwich in hours, so instead of -calling a place twenty-three hours west, it is called one hour east. -Suppose we wish to find the longitude of any place, all that is required -to be known to an observer there is the exact time that a certain star -is on the meridian of Greenwich; he then observes the time that elapses -before the star comes to his meridian, and this time is the longitude -required. - -This, of course, only shows the principle, for in practice it is not -absolutely necessary for the star to be on either meridian, provided its -distance on either side is known, when, of course, the difference -between the times when it actually crosses the meridian can be reckoned. - -In practice a difficulty arises in finding out at a distance from -Greenwich what time it is there. It is of course twelve o’clock at -Greenwich when the sun crosses the meridian, and it is also twelve -o’clock at all the other places when the sun crosses their meridian: but -if a place is two hours west of Greenwich, the sun crosses the meridian -two hours later than it does at Greenwich, and consequently their clock -is two hours slower than Greenwich time, hence the term “local time,” -which is different for different places east or west of Greenwich. We -have taken above a star for our fixed point, but obviously the sun -answers the same purpose. - -It will appear from this, that if we know the difference between the -local times of two places, we also know the longitude of one place from -the other, which is the same. A great number of ways have been tried in -order to make it known at one observing station what time it is at the -other. Rockets are sent up, gunpowder fired, and all kinds of signals -made at fixed times for this purpose; but these, of course, only answer -for short distances, so for long ones carefully adjusted chronometers -have to be carried from one station to the other to convey the correct -time; unless telegraph wires are laid from one place to another, as from -England to America; then it is easy to let either station know what time -it is at the other. For ships at sea chronometers answer well for a -short time, but they are liable to variation. - -There are certain astronomical phenomena the instant of occurrence of -which can be foretold—and published in the nautical almanacs—such as the -eclipses of Jupiter’s moons, and the position of our own moon amongst -the stars. Suppose then an eclipse of one of Jupiter’s moons is to take -place at 1 P.M. Greenwich time, and it is observed at a place at 2 P.M. -of the observer’s local time, _i.e._, two hours after the sun has passed -his meridian, then manifestly the clock at Greenwich is at 1 P.M. while -his is at 2 P.M., and the difference of local time is one hour, and the -place is one hour, or 15°, east of Greenwich. If, however, the eclipse -was observed at 12 noon, then the place must be one hour west of -Greenwich. The local time being one hour slower than Greenwich shows -that the sun does not south till an hour after it does at Greenwich, or, -in reality, the place does not come under the sun till after the -meridian at Greenwich has passed an hour before, clearly showing it to -be west of Greenwich. - -We shall now see how easy it is to find the longitude when the two -stations are electrically connected. Suppose we wish to determine the -difference of longitude of two places in England,—this can be determined -with the utmost accuracy in a short time if the observers have a -chronograph, of the kind just described, to record the transit of a star -at these two places. The observers at each station arrange that the -observer at Station A shall observe the transit of a certain star on his -chronograph, and the observer at Station B shall observe the transit of -the same star on his, and then with the faithful clock, beating seconds -and marking them on the surface of both chronographs simultaneously, the -difference of sidereal time between the transit of the same star over -Station A and Station B will be an absolute distance to be measured off -in as delicate a way as possible by comparison of the roller of each -chronograph, and will give exactly how much time elapses between the two -transits. This is the longitude required. There are various methods of -utilizing the same principle, as, for instance, one chronograph only may -be used, and both observers then register their transits on the same -cylinder. But when we have to deal with considerable distances, such as -between England and the United States, then we no longer employ this -method. From Valentia we telegraph to Newfoundland in effect “Our time -is so-and-so,” and then the observer at Newfoundland telegraphs to -Valentia “Our time is so-and-so.” - -In this way the absolute longitude of the West of Ireland and America -and the different observatories of Europe has been determined with the -greatest accuracy. - -So it appears there are two methods, the first showing one time, say -Greenwich time, at both places, and showing the difference in times of -transit of stars; or secondly, having the clock at each place going to -its own local time, so that a certain star transits at the same local -time at each place, and finding the difference between the two clocks. - ------ - -Footnote 15: - - It was found, that between the passing of the spark into the gun, and - the ignition of the powder and discharge of the piece, one tenth of a - second elapsed. - - - - - CHAPTER XIX. - OTHER INSTRUMENTS USED IN ASTRONOMY OF PRECISION. - - -In former chapters we have described the transit circle as it now exists -as the result of the thought of Tycho, Picard, Römer, and Airy. This, -though the fundamental instrument in a meridional observatory, is by no -means the only one, and we must take a glance at the others. - -In Römer’s “Observatorium Tusculaneum,” near Copenhagen, built in 1704, -there was not only a transit circle in the meridian of course, but a -transit instrument in the prime vertical, _i.e._ swinging in a vertical -plane at right angles to the former one, so that while the optical axis -of one always lies in a N.S. plane, that of the other lies in an E.W. -one. Römer did not use this instrument much; it remained for the great -Bessel to point out its value in determinations of latitude. - -This instrument is, so to speak, self-correcting, because between the -transit of a star over its wires while pointing to the east of the -meridian, and that while pointing to the west its telescope can be -reversed in its =Y=s, or one position may be taken for one night’s -observations, and the other for the next, and so on. - -In Struve’s form of this instrument the transit of stars can be observed -at an interval of one minute and twenty seconds, this time only being -required to raise it from the =Y=s, to rotate it through 180°, and lower -it again. This rapid reversal, and consequent elimination of -instrumental imperfections, enable observations of the most extreme -precision to be made in such delicate matters as the slight differences -of declination of stars due to aberration, nutation, and the like. - -The intersection of the meridian with the prime vertical marks the -zenith. To determine this:—first, there is the zenith sector, invented -by Hooke; it consists of a telescope, carried by an axis on one side of -the tube, and at right angles to it, so that the telescope swings -exactly as a transit does, and it is provided with cross wires in the -same manner; instead, however, of having a whole circle, it has only two -segments of a circle; and as it is never required to swing the telescope -far from its vertical position, there is a diagonal reflector at the -eyepiece, so that the observer can look sideways, instead of upwards, in -an awkward position. Its use is to determine the zenith distance of -stars as they pass near that point. These distances are read off on the -parts of the circle by verniers or microscopes, as in the transit -circle. The zenith telescope, chiefly designed by Talcott, is the modern -equivalent of the sector, and both instruments are more used in -geodetical operations than in fixed observatories. At Greenwich, -however, there is an instrument for determining zenith distances of very -special construction. This is called the reflex zenith tube, shown in -Fig. 131. It is a sectional drawing of one of those instruments showing -the path of the rays of light. A, B, is an object-glass, fixed -horizontally, and below it is a trough of mercury, C, the surface of -which is always of course horizontal. The light from a star near the -zenith is allowed to fall through the object-glass, which converges the -rays just so much that they come to a focus at F, after having been -reflected from the surface of the mercury, and also by the diagonal -mirror or prism, G; at F, therefore, we have an image of the star, which -can be examined together with the cross-wires at the eyepiece, M. There -is in this instrument no necessity for the accurate adjustments that -there is in the case of the transit, the surface of the mercury being -always horizontal, and so giving an unaltering datum plane. - -[Illustration: - - FIG. 131.—Reflex Zenith Tube. -] - -When the star is perfectly vertical, its image will fall on a certain -known part in the eyepiece; but, as it leaves the vertical, the angle of -incidence of its light on the mercury alters, and likewise that of -reflection, so that the position of the image changes, and this change -of position in the eyepiece is measured by movable cross-wires and a -micrometer screw, similar to that employed for reading the circle in the -transit circle. - -At the present time γ Draconis is the star which passes very nearly -through the zenith of Greenwich, and observations of this star are -accordingly made at every available opportunity. - -We now pass to an enlargement of the sphere of observation of the -transit circle in order that any object can be viewed at all times when -above the horizon; in this case the transit circle passes into the -alt-azimuth, or altitude and azimuth instrument, astronomical -theodolite, or universal instrument. - -A reference to Fig. 132—a woodcut of an ordinary theodolite—will show -the new point introduced by this construction. - -Imagine the upper part of the theodolite fixed with its telescope and -circle in the plane of the meridian—we have the transit circle; swing -the theodolite round through 90°—we have the prime vertical instrument. -Now instead of having the upper part fixed let it be free to rotate on -the centre of the horizontal circle—we have the alt-azimuth. - -In the description of the instruments used in Tycho’s observatory -(Chapter IV.), we described another instrument by which Tycho and the -Landgrave of Hesse-Cassel endeavoured to make observations out of the -meridian; and we may remember that they almost had to give the matter up -in despair, because they could not find any clocks sufficiently good to -enable them to fix the position of the star. - -[Illustration: - - FIG. 132.—Theodolite. -] - -[Illustration: - - FIG. 133.—Portable Alt-azimuth. -] - -If we refer again to Fig. 18, we see the method by which Tycho tried to -get the two co-ordinates. On the horizontal circle there are the -graduations for azimuth, or the measurement from the south along the -horizon, and on the vertical quadrant are the graduations for altitude. -Now let us turn to the modern equivalent of that instrument. Fig. 133 -shows this in a portable form. The upper part of the instrument is, as -one sees, nothing more than a transit circle exactly equivalent to the -one described. We have a telescope carried on a horizontal axis, -supported by a pillar; we have the reading microscopes, and the like; -but the support of the horizontal axis, instead of being on the solid -ground, as it is in the transit circle, rests on a movable horizontal -circle, which is also read by microscopes arranged round it, so that all -errors may be eliminated. With this instrument we can get the altitude -of an object at any distance from the meridian, and at the same time -measure its distance east and west of it. The arrangements designed by -the Astronomer Royal for observations of the moon at Greenwich are more -elaborate. In the Greenwich alt-azimuth, the telescope is swung on -pivots between two piers, just as in the case of the transit, these -piers being fixed to the horizontal circle. - -The great advantage of this instrument is that the true place of a -heavenly body can be determined whenever it is above the horizon; we -have neither to wait for a transit over the meridian nor over the prime -vertical. Nevertheless its use is not general in fixed observatories. - -Reduce the dimensions of the horizontal circle and increase those of the -vertical one, and we have the _vertical circle_ designed by Ertel, and -largely used in foreign observatories. - - - - - BOOK V. - _THE EQUATORIAL._ - - - - - CHAPTER XX. - VARIOUS METHODS OF MOUNTING LARGE TELESCOPES. - - -We have already gone somewhat in detail into the construction of the -transit circle, which is almost the most important of modern -astronomical instruments. We then referred to the alt-azimuth, in which, -instead of dealing with those meridional measurements which we had -touched upon in the case of the transit circle, we left, as it were, the -meridian for other parts of the sphere and worked with other great -circles, passing not through the pole of the heavens, but through the -zenith. - -We now pass to the “optick tube,” as used in the physical branch of -astronomy, and we have first to trace the passage from the alt-azimuth -to the Equatorial, as the most convenient mounting is called. - -This equatorial gives the observer the power of finding any object at -once, even in the day-time, if it be above the horizon; and, when the -object is found, of keeping it stationary in the field of view. But -although this form is the most convenient, it is not the one universally -adopted, because it is expensive, and because, again, till within the -last few years our opticians were not able to grapple with all its -difficulties. - -Hence it is that some of the instruments which have been most nobly -occupied in investigations in physical astronomy have been mounted in a -most simple manner, some of them being on an alt-azimuth mounting. Of -these the most noteworthy example is supplied by the forty-feet -instrument erected by Sir William Herschel at Slough. - -[Illustration: - - FIG. 134.—The 40-feet at Slough. -] - -Lord Rosse’s six-feet reflector again is mounted in a different manner. -It is not equatorially mounted; the tube, supported at the bottom on a -pivot, is moved by manual power as desired between two high side walls, -carrying the staging for observers, and so allowing the telescope a -small motion in right ascension of about two hours. Our amateurs then -may be forgiven for still adhering to the alt-azimuth mounting for mere -star-gazing purposes. - -[Illustration: - - FIG. 135.—Lord Rosse’s 6-feet. -] - -[Illustration: - - FIG. 136.—Refractor mounted on Alt-azimuth Tripod for ordinary - Stargazing. -] - -We must recollect that, with the alt-azimuth, we are able to measure the -position of an object with reference to the horizon and meridian; but -suppose we tip up the whole instrument from the base, so that, instead -of having the axis of the instrument vertical, we incline it so as to -make the axis, round which the instrument turns in azimuth, absolutely -parallel to the earth’s axis. - -Of course, if we were using it at the north pole or the south pole, the -axis would be absolutely vertical, as when it is used as an alt-azimuth, -or otherwise it would not be absolutely parallel to the axis of the -earth. On the other hand, if we were using it at the equator, it would -be essential that the axis should be horizontal, since to an observer at -the equator the earth’s axis is perfectly horizontal; but, for a middle -latitude like our own, we have to tip this axis about 51½° from the -horizontal, so as to be in proper relationship with, _i.e._ parallel to, -the earth’s axis. Having done this, we can, by turning the instrument -round this axis, called the polar axis, keep a star visible in the field -of view for any length of time we choose by exactly counteracting the -rotation of the earth, without moving the telescope about its upper, or -what was its horizontal, axis. The lower circle of the instrument will -then be in the plane of the celestial equator, and the upper one, at -right angles to it, will enable us to measure the distance from that -plane, or the declination of an object, while the lower circle will tell -us the distance of the object from the meridian in hours or degrees. - -With the aid of good circles and good clocks, we can thus determine a -star’s position. Fig. 137 shows an Equatorial Stand, one of the first -kind of equatorials used by astronomers. We see at once the general -arrangements of the instrument. In the first place, we have a horizontal -base, D, and on it, and inclined to it, is a disc of metal, C; again on -this disc lies another disc, A, B, which can revolve round on C, being -held to it by a central stud, so that when A B is in the plane of the -earth’s equator its axis points to the pole and is parallel to the axis -of the earth. On the upper disc there are two supports for the axis of -the telescope, E, which is at right angles to the polar axis and is -called the declination axis of the telescope; round it the telescope has -a motion in a direction from the pole to the equator. - -[Illustration: - - FIG. 137.—Simple Equatorial Mounting. -] - -In the equatorial mounting, clockwork is introduced, and after the -instrument has been pointed to any particular star or celestial body, -the clock is clamped to the circle moving round the polar axis, and so -made to drive it round in exactly the time the earth takes to make a -rotation. By a clock is meant an instrument for giving motion, not with -reference to time, but so arranged that, if it were possible to use it -continuously, the motion would exactly bring the telescope round once in -the twenty-four sidereal hours which are necessary for the successive -transits of stars over the meridian. - -There is an objection to the form of instrument given above,—the -telescope cannot be pointed to any position near the pole, since the -stand comes in the way. This is obviated in the various methods of -mounting, which we shall now pass under review. - - - _The German Mounting._ - -This is the form now almost universally adopted for refractors and -reflectors under 20 inches aperture. - -The polar axis has attached to it at right angles a socket through which -the declination axis passes, and this axis carries the telescope at one -end and a counterweight at the other. The polar axis lies wholly below -the declination axis, and both are supported by a central pillar -entirely of iron, or partly of stone and partly of iron. - -By the courtesy of Messrs. Cooke and Sons, Mr. Howard Grubb, and Mr. -Browning, we are enabled to give examples of the various forms of this -mounting now in use in this country for instruments of less than 20 -inches aperture. - -In Fig. 138, we have the type form of Equatorial Refractor introduced -some 30 years ago by the late Mr. Thomas Cooke. The telescope is -represented parallel to the polar axis, which is inclosed in the casing -supported by the central pillar, and carries one large right ascension -circle above and another smaller one below, the former being read by -microscopes attached to the casing. - -The socket or tube carrying the declination axis is connected with the -top of the polar axis. To this the declination circle is fixed, while an -inner axis fixed to the telescope carries the verniers. - -[Illustration: - - FIG. 138.—Cooke’s form for Refractors. -] - -[Illustration: - - FIG. 139.—Mr. Grubb’s form applied to a Cassegrain Reflector. -] - -The clock is seen to the north of the pillar. While this is driving the -telescope, rods coming down to the eyepiece enable the observer to make -any small alterations in right ascension or declination; indeed in all -modern instruments everything except winding the clock is done at the -eyepiece, so that the observer when fairly at work is not disturbed. The -lamp to illuminate the micrometer wires is shown near the finder. The -friction rollers, which take nearly all the weight off the surfaces of -the polar axis, are connected with the compound levers shown above the -casing of the polar axis. - -In Fig. 139 we have Mr. Grubb’s revision of the German form. The pillar -is composite, and the support of the upper part of the polar axis is not -so direct as in the mounting which has just been referred to. There are, -however, several interesting modifications to which attention may be -drawn. The lamp is placed at the end of the hollow polar axis, and -supplies light not only for the micrometer wires, but for reading the -circles; the central cavity of the lower support is utilised for the -clock, which works on part of a circle, instead of a complete one, as in -the instrument already described. - -In the case of Newtonian reflectors the observer requires to do his work -at the upper end of the tube; this therefore should be as near the -ground as possible. This is accomplished by reducing the support to a -minimum. Figs. 140 and 141 show two forms of this mounting, designed by -Mr. Grubb and Mr. Browning. - -The two largest and most perfectly mounted refractors on the German form -at present in existence are those at Gateshead and Washington, U.S. The -former belongs to Mr. Newall, a gentleman who, connected with those who -were among the first to recognise the genius of our great English -optician, Cooke, did not hesitate to risk thousands of pounds in one -great experiment, the success of which will have a most important -bearing upon the astronomy of the future. - -[Illustration: - - FIG. 140.—Grubb’s form for Newtonians. -] - -[Illustration: - - FIG. 141.—Browning’s mounting for Newtonians. -] - -In the year 1860 the largest refractors which had been turned out of the -Optical Institute at Munich under the control, first, of the great -Fraunhofer, and afterwards of Merz, were those of 177 square inches area -at Poulkowa and Cambridge (U.S.). Our own Cooke, who was rapidly -bringing back some of the old prestige of Dollond and Tulley’s time to -England—a prestige which was lost to us by the unwise meddling of our -excise laws and the duty on glass,[16] which prevented experiments in -glass-making—had completed a 9⅓ inch for Mr. Fletcher and a 10 inch for -Mr. Barclay; while in America Alvan Clarke had gone from strength to -strength till he had completed a refractor of 18½ inches for Chicago. -The areas of these objectives are 67, 78·5, and 268 inches respectively. - -Those who saw the great Exhibition of 1862 may have observed near the -Armstrong Gun trophy two circular blocks of glass some 26 inches in -diameter and about two inches thick standing on their edges. These were -two of the much-prized “discs” of optical glass manufactured by Messrs. -Chance of Birmingham. - -At the close of the Exhibition they were purchased by Mr. Newall, and -transferred to the workshops of Messrs. Cooke and Sons at York. - -The glass was examined and found perfect. In time the object-glass was -polished and tested, and the world was in possession of an astronomical -instrument of nearly twice the power of the 18½ inch Chicago -instrument—485 inches area to 268. - -Such an achievement marks an epoch in telescopic astronomy, and the -skill of Mr. Cooke and the munificence of Mr. Newall will long be -remembered. - -The general design and appearance of this monster among telescopes will -be gathered from the general view given in the frontispiece, for which -we are indebted to Mr. Newall. It is the same as that of the well-known -Cooke equatorials; but the extraordinary size of all the parts has -necessitated the special arrangement of most of them. - -The length of the tube, including dew-cap and eye-end, is 32 feet, and -it is of a cigar shape, the diameter at the object-end being 29 inches, -at the centre of the tube 34 inches, and at the eye-end 22 inches. The -cast-iron pillar supporting the whole is 19 feet in height from the -ground to the centre of the declination axis, when horizontal; and the -base of it is 5 feet 9 inches in diameter. The trough for the polar axis -alone weighs 14 cwt., the weight of the whole instrument being nearly 6 -tons. - -The tube is constructed of steel plates riveted together, and is made in -five lengths screwed together with bolts. The flanges were turned in a -lathe, so as to be parallel to each other. It weighs only 13 cwt., and -is remarkably rigid. - -Inside the outer tube are five other tubes of zinc, increasing in -diameter from the eye to the object-end; the wide end of each zinc tube -overlapping the narrow end of the following tube, and leaving an annular -space of about an inch in width round the end of each for the purpose of -ventilating the tube, and preventing, as much as possible, all -interference by currents of warm air with the cone of rays. The zinc -tubes are also made to act as diaphragms. - -The two glasses forming the object-glass weigh 144 lb., and the brass -cell weighs 80 lb. The object-glass has an aperture of nearly 25 inches, -or 485 inches area, and in order as much as possible to avoid flexure -from unequal pressure on the cell, it is made to rest upon three fixed -points in its cell, and between each of these are arranged three levers -and counterpoises round a counter-cell, which act through the cell -direct on to the glass, so that its weight in all positions is equally -distributed among the twelve points of support, with a slight excess -upon the three fixed ones. The focal length of the lens is 29 feet. - -Attached to the eye-end of the tube are two finders, each of 12·5 inches -area; they are fixed above and below the eye-end of the main tube, so -that one may be readily accessible in all positions of the instrument. -It is also supplied with a telescope having an object-glass of 33 inches -area. This is fixed between the two finders, and is for the purpose of -assisting in the observations of comets and other objects for which the -large instrument is not so suitable. This assistant telescope is -provided with a rough position circle and micrometer eyepieces. - -Two reading microscopes for the declination circle are brought down to -the eye-end of the main tube; the circle—38 inches in diameter—is -divided on its face and edge, and read by means of the microscopes and -prisms. - -The slow motions in declination and R. A. are given by means of tangent -screws, carrying grooved pulleys, over which pass endless cords brought -to the eye-end. The declination clamping handle is also at the eye-end. - -The clock for driving this monster telescope is fixed to the lower part -of the pillar, and is of comparatively small proportions, the instrument -being so nicely counterpoised that a very slight power is required to be -exerted by the clock, through the tangent screw, on the driving-wheel -(seven feet in diameter), in order to give the necessary equatorial -motion. - -The declination axis is of peculiar construction, necessitated by the -weight of the tubes and their fittings, and corresponding counterpoises -on the other end, tending to cause flexure of the axis. This difficulty -is entirely overcome by making the axis hollow, and passing a strong -iron lever through it having its fulcrum immediately over the bearing of -the axis near the main tube, and acting upon a strong iron plate rigidly -fixed as near the centre of the tube as possible, clear of the cone of -rays. This lever, taking nearly the whole weight of the tubes, &c., off -the axis, frees it from all liability to bend. - -The weight of the polar axis on its upper bearing is relieved by -anti-friction rollers and weighted levers; the lower end of the axis is -conical, and there is a corresponding conical surface on the lower end -of the trough; between these two surfaces are three conical rollers -carried by a loose or “live” ring, which adjust themselves to equalize -the pressure. - -The hour-circle on the bottom of the polar axis is 26 inches in -diameter, and is divided on the edge, and read roughly from the floor by -means of a small diagonal telescope attached to the pillar; a rough -motion in R. A. by hand is also arranged for, by a system of cogwheels, -moved by a grooved wheel and endless cord at the lower end of the polar -axis, so as to enable the observer to set the instrument roughly in R. -A. by the aid of the diagonal telescope. It is also divided on its face, -and read by means of microscopes. The declination and hour-circle will -probably be illuminated by means of Geissler tubes, and the dark and -bright field illuminations for the micrometers will be effected by the -same means. - -[Illustration: - - FIG. 142.—The Washington Great Equatorial. -] - -So soon as the success of the Newall experiment was put beyond all -question by Cooke, Commodore B. F. Sands, the superintendent of the U.S. -Naval Observatory, sent a deputation, consisting of Professors S. -Newcomb, Asaph Hall, and Mr. Harkness, accompanied by Mr. Alvan Clarke, -to examine and report upon the Newall telescope, and the result was that -they commissioned Alvan Clarke to construct a large telescope for that -country. - -In the Washington telescope the aperture of the object-glass is 26 -inches—that is, one inch larger than the English type-instrument. The -general arrangements are shown in the accompanying woodcut. - -It will be seen that the mounting is much lighter than in the English -instrument, and a composite pillar gives place for the clock in the -central cavity. - - - _The English Mounting._ - -In the _English mounting_ the telescope, like a transit instrument, has -on each side a pivot, and these pivots rest on a frame somewhat larger -than the telescope, pointing to the pole and supported by two pivots, -one at the bottom resting on bearings near the ground, and the other -carried by a higher pillar clear of the observer’s chair. The motions of -the telescope are similar to those given by the German mounting in all -essentials; the Greenwich equatorial is mounted in this manner. It is -carried in a large cylindrical frame, supported at both ends by two -pillars—above by a strong iron pillar, while the other end rests on a -firm stone pillar, going right to the earth, independently of the -flooring. This mounting, though preferred for the large instrument at -Greenwich, has been discarded generally, as the long polar axis is -necessarily a serious element of weakness; the telescope is supported on -its weakest part, and it is liable to great changes from contraction and -expansion of the frame. - - - _The Forked Mounting._ - -It is now getting more usual to mount Newtonians of large dimensions -equatorially, in spite of the immense weight to be carried. One of the -first methods was to use a polar axis in the same manner as for a -refractor, only that it bifurcated at the top, forming there a fork, and -between this fork the telescope is swung, after the same manner as a -transit. This method of mounting was adopted by M. Foucault in the case -of his first large silvered-glass reflector. The height of the -bifurcation is dependent on the distance between the centre of gravity -of the tube and the speculum, and if we use an extremely light tube, or -if,—as it is the fashion to abolish them now altogether for -reflectors,—we use a skeleton tube of iron lattice work, this -bifurcation of the polar axis need not be of any great length. The polar -axis being entirely below the telescope and being driven by the clock, -we have a perfect method of mounting a speculum of any weight we please. -This arrangement was first suggested and carried into effect by Mr. -Lassell for his four-foot Newtonian, which was mounted at Malta. The -polar axis was a heavy cone-shaped casting resting on its point below, -and moving on its largest diameter just below the base of the fork. Lord -Rosse has recently much improved upon the original idea. - -As the observer must be at the mouth of the tube, he is in a very bad -position as far as comfort goes, especially as the eye-end changes its -position rapidly in consequence of the great length of the tube from its -centre of gravity outwards. The platform on which he stands is raised on -supports, extending from the floor and going up to the opening through -which the telescope points to the heavens, and the whole platform is -sometimes fixed to the dome of the observatory, so that it travels round -with it. - -With Mr. Lassell’s four-foot the observer stood in a gigantic reading -box, about thirty feet high, with openings in it at different -elevations. This structure was supported on a circular platform movable -on rails round the base of the mounting. Almost continual variations, -both of the observing height and of the circular platform, were -necessary, as the distance from the centre of motion of the tube and the -eyepiece was no less than 34 feet. - -In Lord Rosse’s recent adaptation of this form the observer is placed in -a swinging basket, at the end of an arm almost as long as the telescope -tube. He is here counterpoised, and moves round a railway which -surrounds the mounting at the height of the tip of the fork. - - - _The Composite Mounting._ - -[Illustration: - - FIG. 143.—General view of the Melbourne Reflector. -] - -There is still another form of mounting which promises to be largely -used for reflectors in the future, whether the tube be lightened by its -being constructed of only a framework of iron or not. This mounting is -neither German nor English, but in part imitates both of these methods: -hence I give it the name of Composite. There is a short polar axis -supported at both ends. - -[Illustration: - - FIG. 144.—The mounting of the Melbourne Telescope. C, polar axis (cube - 1 yard square, cone 8 feet long); D, Clock sector; U, Counterpoise - weights (2¼ tons). -] - -Within the last few years two large reflectors have been erected, -equatorially mounted in this composite manner—the great Melbourne -Equatorial, constructed by Mr. Grubb, and the new Paris Equatorial, -constructed by Mr. Eichens. - -Of the former, Fig. 143 gives a general view, showing how the -construction of this instrument differs from other equatorials which we -have seen. Fig. 144 shows the mounting in more detail. C is the polar -axis, T P is the declination axis, and T the small portion of the tube -of the telescope, the remainder of the tube being represented by -delicate lattice work, which is as light as possible, and used merely -for supporting the reflector, by means of which the light is thrown back -again, according to the suggestion of Cassegrain, and comes through the -hole in the centre of the speculum into the eyepiece, which is seen at -_y_, so that the observer stands at the bottom of the telescope in -exactly the same way as if he were using a refractor. - -In this enormous instrument, the tube and speculum of which alone weigh -nearly three tons, the system of counterpoises is so perfect that we -describe the method adopted in order to give an idea of the general -arrangement of the bearing and anti-frictional apparatus. The series of -weights hanging behind the support of the upper end of the polar axis -are intended to take a great part of the weight of that axis off the -lower support; beside which there are friction-rollers pressed upwards -against the axis by the weights inside the support. - -All the bearings are constructed on the same principle as the Y bearings -of a theodolite—that is, the pivots rest on two small portions of their -arc, 90° or 100° apart. - -If allowed to rest on these bearings without some anti-frictional -apparatus, the force required to move such an instrument would render it -simply unmanageable and destroy the bearings. - -The plan adopted by Mr. Grubb is to allow the axis to rest in its -bearings with just a sufficient portion of its weight to insure perfect -contact, and to support the remainder by some anti-frictional apparatus. -Generally 1/50 to 1/100 of the weight is quite sufficient to allow the -axis to take its bearing, and the remainder 49/50 to 99/100 can thus be -supported on friction rollers, and reduced to any desired extent, -without injuring in the slightest degree the perfection of steadiness -obtained by the use of the Y’s. This is the plan used in the bearings of -the polar axis, and the result is that the instrument can be turned -round this axis by a force of 5 pounds at a leverage of 20 feet. The -bearings of the declination axis are supported on virtually the same -principle; but the details of that construction are necessarily much -more complicated, on account of the variability of direction of the -resolved forces with respect to the axis. - -We may now turn to the four-foot silver-on-glass Newtonian now in course -of completion at the Paris Observatory. - -The illustration which we give represents the telescope in a position -for observation. The wheeled hut under which it usually stands, a sort -of waggon seven metres high by nine long and five broad, is pushed back -towards the north along double rails. The observing staircase has been -fitted to a second system of rails, which permits it to circulate all -round the foot of the telescope, at the same time that it can turn upon -itself, for the purpose of placing the observer, standing either on the -steps or on the upper balcony, within reach of the eyepiece. This -eyepiece itself may be turned round the end of the telescope into -whatever position is most easily accessible to the observer. - -[Illustration: - - FIG. 145.—Great Silver-on-Glass Reflector at the Paris Observatory. -] - -The tube of the telescope, 7·30 metres in length, consists of a central -cylinder, to the extremities of which are fastened two tubes three -metres long, consisting of four rings of wrought-iron holding together -twelve longitudinal bars also of iron. The whole is lined with small -sheets of steel plate. The total weight is about 2,400 kilogrammes. At -the lower extremity is fixed the cell which holds the mirror; at the -other end a circle, movable on the open mouth of the telescope, carries -at its centre a plane mirror, which throws to the side the cone of rays -reflected by the great mirror. - -The weight of the mirror in its barrel is about 800 kilogrammes; the -eyepiece and its accessories have the same weight.[17] - -It will be quite clear from what has been said that the manipulation of -these large telescopes at present entails much manual and even bodily -labour, and when we come in future to consider the winding of the clock, -the turning of the dome, and the adjustment of the observing chair, it -will be seen that the labour is enormous. To save this, in all the best -instruments everything is brought to the eye-end of the telescope, -movements both in right ascension and declination, reading of circles, -and adjustment of illumination. Mr. Grubb has suggested that everything -should be brought to this point, and that, by the employment of -hydraulic power, “the observer, without moving from his chair, might, by -simply pressing one or other of a few electrical buttons, cause the -telescope to move round in right ascension, or declination, the dome to -revolve, the shutters to open, and the clock to be wound.” He very -properly adds, “This is no mere Utopian idea. Such things are done, and -in common use in many of our great engineering establishments, and it is -only in the application that there would be any difficulty encountered.” - - - _The Driving Clock._ - -In a previous chapter it was stated that in all large telescopes used -for the astronomy of position, whether a transit circle or the -alt-azimuth, what we wanted to do was to note the transit of the star -across the field—the transit due to the motion of the earth; but that -when we deal with other phenomena, such, for instance, as those a large -equatorial is capable of bringing before us, we no longer want these -objects to traverse the field, we want to keep them, if possible, -absolutely immovable in the field of view of the eyepiece, so that we -may examine them and measure them, and do what we please with them. - -Hence it was that we found driving clocks applied to equatorials; and -our description would not be complete did we fail to explain the general -principles of their construction. They are instruments for counteracting -the motion of the earth by supplying an exactly equal motion to the tube -of the telescope in an opposite direction. - -Without such a clock we may get an image of the object we wish to -examine; but before we should be able to do anything with it, either in -the way of measurement or observation, it would have gone from us. A -glimpse of a planet or star with a large telescope will give a general -notion of the extreme difficulty which any observer would have to deal -with if he wanted to observe any heavenly body without a driving clock. - -We can easily see at once that it would not do to have an ordinary clock -regulated by a pendulum for driving the telescope, it would be driven by -fits and starts, which would make the object viewed jump in the field at -each tick of the pendulum. The most simple clock is therefore one in -which the conical pendulum is used in the form of the governor of a -steam-engine, so that when the balls A A, Fig. 146, fly up by reason of -the clock driving too fast, they rub against a ring, B, or something -else that reduces their velocity. - -[Illustration: - - FIG. 146.—Clock Governor. -] - -[Illustration: - - FIG. 147.—Bond’s Spring Governor. -] - -There is another form made by Alvan Clarke, in which a pendulum -regulates the clock, but not quite in the ordinary way. The drawing will -perhaps make it clear: A A, Fig. 147, is one of the wheels of the -clock-train driving a small weighted fan, B, which is regulated so as to -allow the clock to drive a little too fast. Now let us see how the -pendulum regulates it. On the axis of A A is placed an arm, C, which is -of such a length that it catches against the studs S S, and is stopped -until the pendulum, P, swings up against one of the studs, R, which -moves the piece D, like a pendulum about its spring at E, until the -stud, S, is sufficiently removed to let the arm, C, pass, so that the -clock is under perfect control. If, however, the arm C were fixed -rigidly to the axis of the wheel A A, there would be a jerk every time C -touched one of the studs. The wheel is therefore attached to the axis -through the medium of a spring, F, so that when the arm is stopped the -wheel goes on, but has its velocity retarded by the pressure of the -spring. The pendulum is kept going in the following manner:—There is a -pin fixed to the axis on the same side of the centre as C, which, as the -arm approaches either stud S, raises the piece D, but not sufficiently -to liberate the arm; the pendulum has then only a very little work to do -to raise D and disengage the arm, C; but as soon as it is free it starts -off with a jerk, due to the tension of the spring on the axis, and -leaves D by means of its stud, R, to exert its full force on the -pendulum and accelerate its return stroke, so that the pendulum is kept -in motion by the regulating arrangement itself. - -The late Mr. Cooke of York constructed a very accurately-going driving -clock. This differs in important particulars from Bond’s form, though -the control of the pendulum is retained. - -The following extracts from a description of it will show the principal -points in its construction:— - - The regulator adopted is the vibrating pendulum, because amongst the - means at the mechanician’s command for obtaining perfect - time-keeping there is none other by which the same degree of - accuracy can be obtained. The difficulty in this construction is the - conversion of the jerking or intermittent motion produced by such - pendulums into a uniform rotatory motion which can be available with - little or no disturbing influence on the pendulum itself, when the - machine is subject to varying frictions and forces to be overcome in - driving large equatorials. - - The pendulum is a half-second one, with a heavy bob, adjusted by - sliding the suspension through a fixed slit. It is drawn up and let - down by a lever and screw, the acting length of the pendulum being - thus regulated. - - The arrangement of the wheels represents something like the letter - U. At the upper end of one branch is the scape-wheel. At the upper - end of the other branch is an air-fan. The large driving-wheel and - barrel are situated at the bottom or bend. All the wheels are geared - together in one continuous train, which consists of eight wheels and - as many pinions. The scape-wheel and the two following wheels have - an intermittent motion; all the others have a continuous and uniform - one. - - The change from one motion to the other is made at the third wheel, - which, instead of having its pivot at the end of the arbor where the - wheel is fixed—fixed to the frame like the others—is suspended from - above by a long arm having a small motion on a pin fixed to the - frame; the pivot at the other end of the arbor is fixed to the frame - as the others are, but its bole and its pivot are arranged so as to - permit a very small horizontal angular motion round them, as a - centre, without interfering with the action of the gearing of the - wheel itself. - - If the weight is applied to the clock, and the pendulum is made to - vibrate, the moment it begins to move, the scape-wheel moves its - quantity for a beat; the remontoire wheel, by the very small force - outwardly caused by the reaction of the break-spring, relaxes its - pressure against a friction-wheel, and sets at liberty the train of - the clock. - - The spring is now driven back to the break-wheel, but before it can - produce more than the necessary friction to keep the train in - uniform motion, another beat of the clock again releases it. The - repetition of these actions produces a series of impulses on the - break-wheel of such a force and nature as to keep the train freely - governed by the pendulum. - - The uniform rotatory motion obtained by this clock as far as - experiments can be made by applying widely different weights, and - comparing the times with a chronometer, is perfectly satisfactory. - - A clock constructed on the same principle, connected, and giving - motion to a cylinder, will, it is presumed, make an excellent - chronograph. - -[Illustration: - - FIG. 148.—Foucault’s governor. -] - -The form of governor most usually employed will be seen in figures -previously given. The governor raises a plate and thus becomes a -frictional governor, by which all overplus of power is used up in -frictions, or by that doubling the driving power no, or only a small, -difference should be brought about in the rate. - -Other forms of driving clocks or governors invented by Foucault and Yvon -Villarceau are now being largely employed. In them the rapid motion of a -fan and other devices are introduced. - -A driving clock adjusted to sidereal time requires adjustments for -observations of the sun and moon. This (as at _z_ in Fig. 144) is -sometimes done once for all by differential gearing thrown into action -by levers when required. - -Mr. Grubb has lately made a notable improvement upon the usual form by -controlling the motion of the governor by a sidereal clock and an -electric current. - -There are various methods of attaching the clock to the polar axis. One -is to make the clock turn a tangent screw, gearing into a screw-wheel on -the axis of the telescope, which can be thrown in and out of gear for -moving the telescope rapidly in right ascension. Another method is to -have a segment of a circle on the polar axis which can be clamped or -unclamped at pleasure by means of a screw attached to it. A strip of -metal is attached to each end of the segment and is wound round a drum -turned by the clock, so that the two are geared together just as wheels -are geared by an endless strap passing round them. This arrangement -gives a remarkably even motion to the telescope. When the strap is wound -up to the end of the segment, which is done in about two or three hours’ -work, the drum is thrown out of gear and the arc pushed back to its -starting-place again. - - - _THE LAMP._ - -[Illustration: - - FIG. 149.—Illuminating lamp for equatorial. -] - -In the description of the transit circle we saw how the Astronomer-Royal -had contrived to throw light into the axis of the telescope, so that the -wires were either rendered visible in a bright field, or, the field -being kept dark, the wires were visible as bright lines in a dark field. -That is the difference between a bright field, and a dark field of -illumination. Now a bright field of illumination in the case of -equatorials is managed by an arrangement as follows.—A A, Fig. 149, is a -section of the tube of the telescope. Near the eyepiece is a small lamp, -D, swung on pins on either side which rest on a circular piece of brass -swinging on a pin at C, and a short piece of tube at E, through which -the light passes into the telescope and falls on a small diagonal -reflector, F. This reflects the rays downwards into the eyepiece. When -the telescope is moved into any position the lamp swings like a -mariner’s compass on its gimbals, and still throws its light into the -tube, and the light mixes up with that coming from the star, but spreads -all over the field of view instead of coming to a point, so that the -star is seen on a bright field, and the wires as black lines. Now if the -star which is observed is a very faint one, we defeat our own object, -for the light coming from the lamp puts out the faint star. - -[Illustration: - - FIG. 150.—Cooke’s illuminating lamp. -] - -We have seen how the illumination of the wires, instead of the field, is -carried out in the Greenwich transit. The same method can be adopted in -the case of equatorials, the light from the diagonal reflector being -thrown on other diagonal reflectors or prisms on either side the wires -in the micrometer so as to illuminate them. Messrs. Cooke and Sons have -devised a lamp of very great ingenuity, Fig. 150. It is a lamp which -does for the equatorial, in any position, exactly what the fixed lamp -does for the transit circle. It is impossible to put it out of order by -moving the telescope. There is a prism at P reflecting the light into -the telescope tube, and at whatever different angle of inclination, or -whatever may be the size of the telescope on which this lamp is placed, -it is obvious that the lamp never ceases to throw its light into the -reflector inside the telescope; and any amount of light, or any colour -of light required can be obtained by turning the disc containing glass -of different colours or the other having differently sized apertures, in -order to admit more or less light, or give the light any colour. - -In both these arrangements the lamp is hung on the side of the -telescope, while Mr. Grubb prefers to hang it at the end of the -declination axis, as shown in Figs. 139 and 140. - -The function of the lamp then is to illuminate the wires of the -micrometer eyepiece, of which more presently; but Mr. George Bidder -places the micrometer itself outside the tube of the telescope, the -light of a lamp being thrown on the wires. - -This is done as follows:—On the same side of the wires as the lamp is a -convex lens and reflector so arranged that the rays from the wires are -reflected through a hole in the tube, and again down the tube to the -eyepiece, where the images of the wires are brought to a focus at the -same place as the stars to be measured, so that any eyepiece can be -used. The wires show as bright lines in the field, and they are worked -about in the field just as real wires might be by moving the wires -outside the tube. A sheet of metal can be moved in front of the -distance-wires so as to obstruct the light from them at any part of -their length, and their bright images appear then abruptly to terminate -in the field of view, so that faint stars can be brought up to the -terminations of the wires and be measured without being overcome by -bright lines. - ------ - -Footnote 16: - - It is not too much to say that the duty on glass entirely stifled, if - indeed it did not kill, the optical art in England. We were so - dependent for many years upon France and Germany for our telescopes, - that the largest object-glasses at Greenwich, Oxford, and Cambridge - are all of foreign make. - -Footnote 17: - - These details are given from the _Forces of Nature_ (Macmillan). - - - - - CHAPTER XXI. - THE ADJUSTMENTS OF THE EQUATORIAL. - - -As the equatorial is _par excellence_ the amateur’s instrument, and as -in setting up an equatorial it is important that the several adjustments -should be correctly made, they are here dwelt upon as briefly as -possible. They are six in number. - -1. The inclination of the polar axis must be the same as that of the -pole of the heavens. - -2. The declination circle must read 0° when the telescope is at right -angles to the polar axis. - -3. The polar axis must be placed in the meridian. - -4. The optic axis of the telescope, or line of collimation must be at -right angles to the declination axis, so that it describes a great -circle on moving about that axis. - -5. The declination axis must be at right angles to the polar axis, in -order that the telescope shall describe true meridians about that axis. - -6. The hour circle must read 0h. 0m. 0sec. when the telescope is in the -meridian. - -When these are correctly made the line of collimation will, on being -turned about the declination axis, describe great circles through the -pole, or meridians, and when moved about the polar axis, true parallels -of declination; and the circles will give the true readings of the -apparent declination, and hour angles from the meridian. - -To make these adjustments, the telescope is set up by means of a compass -and protractor, or otherwise in an approximately correct position, the -declination circle put so as to read nearly 90° when the telescope -points to the pole, and the hour circle reading 0h. 0m. 0sec. when the -telescope is pointing south. - -First, then, to find the error in _altitude_ of the polar axis. - -Take any star from the Nautical Almanac of known declination on or near -the meridian, and put an eyepiece with cross wires in it in the -telescope, and bring the star to the centre of the field as shown by the -wires. Then read the declination circle, note the reading down and -correct it for atmospheric refraction, according to the altitude[18] of -the star by the table given in the Nautical Almanac, turn the telescope -on the polar axis round half a circle so that the telescope comes on the -other side of the pier. The telescope is then moved on its declination -axis until the same star is brought to the centre of the field, and the -circle read as before and corrected. The mean of the two readings is -then found, and this is the declination of the star as measured from the -equator of the instrument, and its difference from the true declination -given by the almanac is the error of the instrumental equator and of -course, also of the pole at right angles to it. - -It is obvious that if the declination circle were already adjusted to -zero, when the telescope was pointing to the equator of the instrument, -one observation of declination would determine the error in question; -and it is to eliminate the _index error_ of the circle, as it is called, -that the two observations are taken in such a manner that the index -error increases one reading just as much as it decreases the other, so -that the mean is the true instrumental declination. - -_Index Error._—From what has just been stated it follows that half the -difference of the two readings is the index error, which can be at once -corrected by the screws moving the vernier, giving correction No. 2. - -To correct the error in altitude of the pole, the circle is then set to -the declination of the star given by the almanac, corrected for -refraction, and the telescope brought above or below the star as the -error may be, and the polar axis carrying the telescope is moved by the -setting screws, until the star is in the centre of the field. - -3rd Adjustment.—A single observation of any known star, about 6 hours to -the east or west will give the error of the polar axis east and west, -the difference between the observed and true declination being this -error, and it can be corrected in the same manner as the last. These -observations should be repeated, and stars in different parts of the -heavens observed, in order to eliminate errors of division of the circle -until the necessary accuracy is obtained. - -For example: - - Observed dec. of Capella 43° 50´ 30˝ Telescope west. - 47° 0´ 0˝ Telescope east. - ——— ——— ——— - 2) 90° 50´ 30˝ - ——— ——— ——— - 45° 25´ 15˝ 47° 0´ 0˝ - Error due to refraction 0° 0´ 7˝ 43° 50´ 30˝ - ——— ——— ——— ——— ——— ——— - Instrumental declination 45° 25´ 8˝ 2) 3° 9´ 30˝ - True declination 45° 52´ 0˝ ——— ——— ——— - ——— ——— ——— Index error 1° 34´ 45˝ - 26´ 52˝ - -This indicates that the pole of the instrument is pointing below the -true pole, and index error 1° 34´ 45˝. - - Observed declination of Pollux 6h. west 28° 19´ 18˝ - Refraction 0° 0´ 46˝ - ——— ——— ——— - 28° 18´ 3˝ - True declination 28° 20´ 10˝ - ——— ——— ——— - 0° 1´ 38˝ - -This shows the pole to be 1´ 38˝ east of true pole. - -4th Adjustment.—For the estimation and correction of the third error, -that of collimation, an equatorial star is brought to the centre of the -field of the telescope, the time by a clock noted, and the hour circle -read. The polar axis is then turned through half a circle, and the star -observed with the telescope on the opposite side (say the west) of the -pier, the time noted, and the hour circle read. Subtract the first -reading from the second (plus twenty-four hours if necessary) and -subtract the time elapsed between them, and the result should be exactly -twelve hours, and half the difference between it and twelve hours is the -error in question. If it is more than twelve hours the angle between the -object end of the telescope and the declination axis is acute, and if -less then it is obtuse. This error can then be corrected by the proper -screws. A little consideration will show, that if the angle between the -object end of the telescope and the declination axis be acute, and the -telescope is on the east side of the pier, and pointing to a star, say -on the meridian, the hour circle will not read so much as it would do if -the line perpendicular to the declination axis were pointing to the -meridian. When the telescope is on the wrest side of the pier, the -circle will read higher for the same reason, and therefore the -difference between the angle through which the hour circle is moved and -180° is equal to double the angle between the line perpendicular to the -declination axis and the collimation axis of the telescope; allowance -being made for the star’s motion. - -For example γ Virginis, Dec. 0° 46´·5. - - Time by clock. Hour circle reading. - 11h. 23m. 52s. 11h. 55m. 30s. Telescope east. - 11h. 31m. 55s. 24h. 8m. 24s. Telescope west. - ———— ———— ———— ———— ———— —————— - 8m. 3s. 12h. 12m. 54s. - 8m. 3s. - ———— —————— - 2) 4m. 51s. - ———— —————— - Collimation error at 2m. 25·5s. - dec. 46´·5 - angle between object glass and declination axis acute. - -If this error is not corrected, it must be added when the telescope is -on the east side of the pier, and subtracted when on the west.[19] - -5th Adjustment.—Place a striding level on the pivots of the declination -axis and bring the bubble to zero by turning the polar axis; read off -the hour circle and note it; then reverse the declination axis east and -west and replace the level; bring the bubble to zero and again read the -circle. The readings should show the axis to be turned through half a -circle, and the difference shows the error. - -If the second reading minus the first be more than half a circle or 12 -hours, it shows that the pivot at the east at the first observation is -too high, and therefore in bringing the declination axis level, the -first reading of the hour circle is diminished from its proper amount -and increased on the axis being reversed. - -To adjust the error, find half the difference of circle readings and -apply it, with the proper sign, to each of the two circle readings, -which will then differ by exactly twelve hours; bring the circles to -read one of the corrected readings and alter the declination axis until -the bubble of the level comes to zero. If the pivots of the declination -axis are not exposed, so that the level can be applied, the following -method must be adopted:—Fasten a small level on any part of the -declination axis or its belongings, say on the top of the counterpoise -weight; bring the axis apparently horizontal and the bubble to zero; -turn the telescope on the declination axis, so that by the turning of -the counterpoise the level comes below it; if then the bubble is at -zero, the axis of the level is parallel to the declination axis, and -both are horizontal, and if not it is clear that neither of these -conditions holds; therefore bring the bubble to zero by the two motions -of the level with reference to the counterpoise and the motion of the -declination axis on the polar axis, so that the error is equally -corrected between them; repeat the proceeding until the level is -parallel with the axis, when it will show when the axis is horizontal as -well as the striding level. - -For example:— - - Hour circle reading when } 11h. 57m. 57s. Telescope east. - declination axis is horizontal. } 23h. 59m. 47s. Telescope west. - ———— ———— ———— - 12h. 1m. 50s. - Error 0h. 1m. 50s. - -Or this error can be found and corrected without a level by taking two -observations of a star of large declination in the same manner as in -estimating the collimation error, for example:— - - Η URSÆ MAJORIS. - - Time by clock. Hour circle reading. - 12h. 8m. 57s. 0h. 28m. 44s. Telescope east. - 12h. 18m. 53s. 12h. 46m. 42s. Telescope west. - ———— ———— ———— ———— ———— ———— - 9m. 56s. 12h. 17m. 58s. - 9m. 56s. - ———— ———— - 2) 8m. 2s. - ———— ———— - Error of hour circle due to error of 4m. 1s. - inclination of axes[20] - -6th Adjustment.—Bring the declination axis to a horizontal position with -a level and set the hour circle to zero, or obtain the sidereal time -from the nearest observatory, or again find it from the solar time by -the tables, and correct it for the longitude of the place (subtracting -the longitude reduced to time when the place is west and adding when -east of the time-giving observatory) and set a clock or watch to it. -Take the time of transit of a known star near the meridian and then the -sidereal time by the clock at transit minus the right ascension of the -star will give the hour angle past the meridian, and its difference from -the circle reading is the index error, which is easily corrected by the -vernier. If the star is east of the meridian the time must be subtracted -from the right ascension to give the circle reading. - -In the above examples we have assumed, for the sake of better -illustration, that the hour circle is divided into twenty-four hours, -but more usually they are divided into two halves of twelve hours each. -A movement through half a circle, therefore, brings the hour circle to -the same reading again instead of producing a difference of twelve -hours, as in the above example. - -When the equatorial is once properly in adjustment, not only can the -co-ordinates of a celestial body be observed with accuracy when the time -is known, but a planet or other body can easily be found in the -day-time. The object is found by the two circles—the declination circle -and the hour or right-ascension circle. The declination of the required -object being given, the telescope is set by the circle to the proper -angle with the equator. The R.A. of the object is then subtracted from -the sidereal time, or that time plus twenty-four hours, which will give -the distance of the object from the meridian, and to this distance the -hour-circle is set. The object should then be in the field of the -telescope, or at least in that of the finder. We subtract the star’s -R.A. from the sidereal time because the clock shows the time since the -first point of Aries passed the meridian, and the star passes the -meridian later by just its R.A., so that if the time is 2_h._, or the -first point of Aries has passed 2_h._ ago, a star of 1_h._ R.A., or -transiting 1_h._ after that point, will have passed the meridian 2_h._ - -1_h._ = 1_h._ ago; so if we set the telescope 1_h._ west of the meridian -we shall find the star. The moment the object is found the telescope is -clamped in declination, and the clock thrown into gear, so that the star -may be followed and observed for any length of time. - ------ - -Footnote 18: - - The altitude of the star in this case is its declination plus the - co-latitude of the place, but this only applies when the star is on - the meridian. When the altitude of a star in another situation is - required, it is found sufficiently accurately by means of a globe. A - sextant, if at hand, will of course give it at once. - -Footnote 19: - - Since the velocity of the star varies as the cosine of the - declination, the error of collimation at the equator = 2m. 25·5s. cos. - 0° 45´·5 = 2m. 25·08s.; and for non-equatorial stars, 2m. 25·08s. sec. - dec. - -Footnote 20: - - This error varies as the tangent of the declination, and therefore to - find the constant for the instrument, in case the parts do not admit - of easy adjustment, we divide 4m. 1s. by 1·18 the tan. of Dec. of η - Ursæ Majoris, giving 3 min. 28 sec. - - - - - CHAPTER XXII. - THE EQUATORIAL OBSERVATORY. - - -We have now considered the mounting and adjustment of the equatorial, be -it reflector or refractor. If of large dimensions it will require a -special building to contain it, and this building must be so constructed -that, as in the case of the Melbourne and Paris instruments, it can be -wheeled away bodily to the north, leaving the instrument out in the -open; or the roof must be so arranged that the telescope can point -through an aperture in it when moved to any position. This requirement -entails (1) the removal of the roof altogether, by having it made nearly -flat, and sliding it bodily off the Observatory, or (2) the more usual -form of a revolving dome, with a slit down one side, or (3) the -Observatory maybe drum-shaped, and may run on rollers near the ground. -The last form is adopted for reflectors whose axis of motion is low; but -with refractors having their declination axis over six or seven feet -from the ground, the walls of the Observatory can be fixed, as the -telescope, when horizontal, points over the top. The roof, which may be -made of sheet-iron or of wood well braced together to prevent it -altering in shape, is built up on a strong ring which runs on wheels -placed a few feet apart round the circular wall, or, instead of wheels, -cannon balls may be used, rolling in a groove with a corresponding -groove resting on them. A small roof, if carefully made, may be pulled -round by a rope attached to any part of it, but large ones generally -have a toothed circle inside the one on which the roof is built, or this -circle itself is toothed, so that a pinion and hand-winch can gear into -it and wind it round. If the roof is conical in shape the aperture on -one side can be covered by two glazed doors, opening back like -folding-doors; but if it is dome-shaped, the shutter is made like a -Venetian blind or revolving shop-window shutter, and slides in grooves -on either side of the opening. - -[Illustration: - - FIG. 151.—Dome. -] - -[Illustration: - - FIG. 152.—Drum. -] - -[Illustration: - - FIG. 153.—New Cincinnati Observatory—Front elevation, showing exterior - of Drum. -] - -[Illustration: - - FIG. 154.—Cambridge (U.S.) Equatorial, showing Observing Chair and - rails. -] - -The equatorial and the building to contain it have now been described, -but there is another piece of apparatus which is required as much as any -adjunct to the equatorial, and that is the chair or rest for the -observer. Since the telescope may be sometimes horizontal, and at other -times vertical, the observer must be at one time in an upright position, -and at another lying down and looking straight up. A rest is required -which will carry the observer in these or in intermediate positions. A -convenient form of rest for small telescopes consists of a seat like -that of a chair, with a support moving on hinges at the back of the -seat; a rack motion fixes this at any inclination, so that the -observer’s back can be sustained in any position, between upright and -nearly horizontal. The seat with its back slides on two straight bars of -wood, sloping upwards from near the ground at an angle of about 30°, and -about 8ft. long; these are supported at their upper ends by uprights of -wood, and at their lower ends in the same manner by shorter pieces. -These four uprights are firmly braced together, and have castors at the -bottom. A rack is cut on one of the inclined slides, and a catch falls -into it, so as to fix the seat at any height to which it is placed. - -In larger observatories a more elaborate arrangement is adopted, the -rails, on which the seat moves, are curved to form part of a circle, -having the centre of motion of the telescope for its centre; as the seat -with its back is moved up or down on the curved slides, its inclination -is changed, so that the observer is always in a favourable position for -observing. The seat on its frame runs on circular rails round the pier -of the telescope, so that the eyepiece can be followed round as the -telescope moves in following a star. A winch by the side of the -observer, acting on teeth on one of the rails, enables him to move the -chair along, and a similar arrangement enables him to raise or lower the -seat on the slides without removing from his place. A steady mounting -for the telescope, and a comfortable seat for the observer, are the two -things without which a telescope is almost useless. - -The observing chair is well seen in the engravings of Mr. Newall’s and -the Cambridge telescopes. The eyepieces and micrometer can be carried on -the rest, close to the observer, when much trouble is saved in moving -about for things in the dark; and for the same reason there should be a -place for everything in the observatory, and everything in its place. - -[Illustration: - - FIG. 155.—Section of Main Building—United States Naval Observatory, - showing support of Equatorial. -] - -The very high magnifying power employed upon equatorials in the finest -states of the air necessitates a very firm foundation for the central -pillar. The best position for such an instrument is on the ground, but -it is almost always necessary to make them high in order to be able to -sweep the whole horizon. The accompanying woodcut will give an idea of -the precautions that have to be taken under these circumstances. A solid -pillar must be carried up from a concrete foundation, and there must be -no contact between this and the walls or floors of the building, when -the dome thus occupies the centre of the observatory. The other rooms, -generally built adjoining the equatorial room, radiate from the dome, -east and west, not sufficiently high to interfere with the outlook of -the equatorial. In one of these the transit is placed; an opening is -made in the walls and roof, so that it has an unimpeded view when swung -from north through the zenith to south, and this is closed when the -instrument is not in use by shutters similar to those of the dome. - - - - - CHAPTER XXIII. - THE SIDEROSTAT. - - -At one of the very earliest meetings of the Royal Society, the -difficulties of mounting the long focus lenses of Huyghens being under -discussion, Hooke pointed out that all difficulties would be done away -with if instead of giving movement to the huge telescope itself, a plane -mirror were made to move in front of it. This idea has taken two -centuries to bear fruit, and now all acknowledge its excellence. - -One of the most recent additions to astronomical tools is the -Siderostat, the name given to the instrument suggested by Hooke. By its -means we can make the sun or stars remain virtually fixed in a -horizontal telescope fixed in the plane of the meridian to the south of -the instrument, instead of requiring the usual ponderous mounting for -keeping a star in the field of view. - -It consists of a mirror driven by clockwork so as to continually reflect -the beam of light coming from a star, or other celestial object, in the -same direction; the principle consisting in so moving the mirror that -its normal shall always bisect the angle subtended at the mirror by the -object and the telescope or other apparatus on which the object is -reflected. - -[Illustration: - - FIG. 156.—Foucault’s Siderostat. -] - -It was Foucault who, towards the end of his life, thought of the immense -use of an instrument of this kind as a substitute for the motion of -equatorials; he, however, unfortunately did not live to see his ideas -realized, but the Commission for the purpose of carrying out the -publication of the works of Foucault directed Mr. Eichens to construct a -siderostat, and this one was presented to the Academy of Science on -December 13th, 1869, and is now at the Paris Observatory. Since that -date others have been produced, and they have every chance of coming -largely into use, especially in physical astronomy. Fig. 156 shows the -elevation of the instrument, the mirror of which, in the case of the -instrument at Paris, is thirty centimetres in diameter, and is supported -by a horizontal axis upon two uprights, which are capable of revolving -freely upon their base. The back of the mounting of the mirror has an -extension in the form of a rod at right angles to it, by which it is -connected with the clock, which moves the mirror through the medium of a -fork jointed at the bottom of the polar axis. - -The length of the fork is exactly equal to the distance from the -horizontal axis of the mirror to the axis of the joint of the fork to -the polar axis, and the direction of the line joining these two points -is the direction in which the reflected ray is required to proceed. The -fork is moved on its joint to such a position that its axis points to -the object to be viewed, and, being carried by a polar axis, it remains -pointing to that object as long as the clock drives it, in the same -manner as a telescope would do on the same mounting. Then, since the -distance from the axis of the mirror to the joint of the fork is equal -to the distance from the latter point to the axis of its joint to the -sliding tube on the directing rod, an isosceles triangle is formed -having the directing rod at its base; the angles at the base are -therefore equal to each other. - -Further, if we imagine a line drawn in continuation of the axis of the -fork towards the object, then the angle made by this line and that from -the axis of the mirror to the elbow joint of the fork (the direction of -the reflected ray) will be equal to the two angles at the base of the -isosceles triangle; and, since they are equal to each other, the angle -made by the directing rod and the axis of the fork (or the incident ray) -from the object, is equal to half the angle made by the latter ray and -the direction of the reflected ray; and if lines are drawn through the -surface of the mirror in continuation of the directing rod and the line -from the elbow joint to the axis of the mirror; and a line to the point -of intersection be drawn from the object, this last line will be -parallel to the axis of the fork, and the angle it makes with the -continuation of the directing rod, or normal to the surface of the -mirror, will be half the angle made by it and the line representing the -reflected ray. Therefore the angle made by the incident ray and the -required direction of the reflected ray is always bisected by the -normal, so that the reflected ray is constant in the required direction. - -The clock is driven in the usual manner by a weight. A rod carries the -motion up to the system of wheels by which the polar axis is rotated. As -this axis rotates it carries with it the fork, which transmits the -required motion to the mirror. And as the fork alters its direction the -tube slides upon the directing rod, thus altering the inclination of the -mirror. In order to vary the position of the mirror without stopping the -instrument there are slow motion rods or cords proceeding from the -instrument which may be carried to any distance desirable. - -[Illustration: - - FIG. 157.—The Siderostat at Lord Lindsay’s Observatory. -] - -The polar axis is set in the meridian similarly to an equatorial -telescope, the whole apparatus being firmly mounted upon a massive stone -pillar which is set several feet in the ground, and rests upon a bed of -concrete, if the soil is light. A house upon wheels, running upon a -tramway, is used to protect the instrument from the weather, and when in -use this hut is run back to the north, leaving the siderostat exposed. -In the north wall of the observatory is a window, and the telescope is -mounted horizontally opposite to it: so the observer can seat himself -comfortably at his work, and by his guide rods direct the mirror of the -siderostat to almost any part of the sky, viewing any object in the -eyepiece of his telescope without altering his position. In spectroscopy -and celestial photography its use is of immense importance, for in these -researches the image of an object is required to be kept steadily on the -slit of the spectroscope or on the photographic plate, and for this -purpose a very strongly-made and accurate clock is required to drive the -telescope and mounting, which are necessarily made heavy and massive to -prevent flexure and vibration. The siderostat, on the other hand, is -extremely light, without tube or accessories, and a light, delicate -clock is able to drive it with accuracy, while the heavy telescope and -its adjuncts are at rest in one position. The sun and stars can, -therefore, as it were, be “laid on” to the observer’s study to be viewed -without the shifting of the observatory roof and equatorial, or of the -observing chair, which brings its occupant sometimes into most uneasy -positions. - -We figure to ourselves the future of the physical observatory in the -shape of an ordinary room with siderostat outside throwing sunlight or -rays from whatever object we wash into any fixed instrument at the -pleasure of the observer. There are, however, inconveniences attending -its use in some cases; for instance, in measuring the position of double -stars, the diurnal motion gradually changes their position in the field -of the telescope, so that a new zero must be constantly taken or else -the time of observation noted and the necessary corrections made. - - - - - CHAPTER XXIV. - THE ORDINARY WORK OF THE EQUATORIAL. - - -The equatorial enables us to make not only physical observations, but -differential observations of the most absolute accuracy. - -First we may touch upon the physical observations made with the eyepiece -alone—star-gazing, in fact. The Sun first claims our attention: our -dependence on him for the light of day, for heat, and for in fact almost -everything we enjoy, urges us to inquire into the physics of this -magnificent object. Precautions must however be taken; more than one -observer has already been blinded by the intense light and heat, and -some solar eyepiece must be used. For small telescopes up to two inches, -a dark glass placed between the eye and the eyepiece is sufficiently -safe; for larger apertures, the diagonal reflector, or Dawes’ solar -eyepiece, already described, comes into requisition. Another method of -viewing the sun is to focus the sun’s image with the ordinary eyepiece -on a sheet of paper or card, or, better still, on a surface of plaster -of Paris carefully smoothed. The bright ridges or streaks, usually seen -in spotted regions near the edge, called the faculæ, and the mottled -surface, appearing, according to Nasmyth, like a number of interlacing -willow-leaves—the minute “granules” of Dawes, are best seen with a blue -glass; but for observing the delicately-tinted veils in the umbræ of the -spots a glass of neutral tint should be used. - -The Moon is a fine object even in small telescopes. The best observing -time is near the quarters, as near full moon the sun shines on the -surface so nearly in the same direction as that in which we look, that -there is no light and shade to throw objects into view. Hours may be -spent in examining the craters, rilles, and valleys on the surface, -accompanied with a good descriptive map or such a book as that which Mr. -Neison has recently published. - -The planets also come in for their share of examination. Mercury is so -near the sun as seldom to be seen. Venus in small telescopes is only -interesting with reference to her changes, like the moon, but in larger -ones with great care the spots are visible. Mars is interesting as being -so near a counterpart of our own planet. On it we see the polar snows, -continents and seas, partially obscured by clouds, and these appearances -are brought under our view in succession by the rotation of the planet. -With a good six-inch glass and a power of 200 when the air is pure and -the opposition is favourable, there is no difficulty in making out the -coast-lines, and the various tones of shade on the water surface may be -observed, showing that here the sea is tranquil, and there it is driven -by storms. Up to very lately it was the only planet of considerable size -further off the sun than Venus that was supposed to have no satellite; -two of these bodies have however been lately discovered by Hall with the -large Washington refractor of twenty-six inches diameter, and they -appear to be the tiniest celestial bodies known, one of them in all -probability not exceeding 10 miles in diameter. Jupiter and Saturn are -very conspicuous objects, and the eclipses, transits, and occultations -of the moons, and the belts of the former and rings of the latter, are -among the most interesting phenomena revealed to us by our telescopes, -while the delicate markings on the third satellite of Jupiter furnish us -with one of the most difficult tests of definition. Uranus and Neptune -are only just seen in small telescopes, and even in spite of the use of -larger ones, we are in ignorance of much relating to these planets. The -amateur will do well to attack all these with that charming book, the -Rev. T. W. Webb’s _Celestial Objects for Common Telescopes_, in his -hand. - -To observe the fainter satellites of the brighter planets, or, indeed, -faint objects generally, near very bright ones, the bright object may be -screened by a metallic bar, or red or blue glass placed in the common -focus. - -So much with regard to our own system. When we leave it we are -confounded with the wealth of nebulæ, star-clusters, and single or -multiple systems of stars, which await our scrutiny. With the stars, not -much can be done without further assistance than the eyepiece alone. The -colours of stars may however be observed, and for this purpose a -chromatic scale has been proposed, and a memoir thereon written, by -Admiral Smyth, for comparison with the stars. The colour of a star must -not be confused with the colours—often very vivid—produced by -scintillations, these rapid changes of brightness and colour depending -on atmospheric causes. Of the large stars, Sirius, Vega and Regulus are -white, while Aldebaran and Betelgueux are red. In many double and -multiple stars however the contrast of colours shows up beautifully; in -β Cygni for instance we have a yellow and blue star, in γ Leonis, a -yellow and a green star; and of such there are numerous examples. - -Interesting as all these observations are, a new life and utility are -thrown into them when instead of using a simple eyepiece the wire -micrometer is introduced. This, as we have before stated, generally -consists of one wire, or two parallel wires, fixed, and one or two other -wires at right angles to these, movable across the field. This -micrometer is used in connection with a part of the eyepiece end of the -telescope, which has now to be described. This is a circle, the fineness -of the graduation of which increases with the size of the telescope, -read by two or four verniers. The circle is fixed to the telescope, -while the verniers are attached to the eyepiece, carrying the -micrometer, which is rotated by a rack and pinion. - -The whole system of position circle (as it is called) and wire -micrometer, is in adjustment when (1) the single or double fixed wires -and the movable ones cross in the centre of the field, and (2) when with -a star travelling along the single fixed or between the two fixed wires, -the upper vernier reads 180 and the lower one reads zero. - -This motion across the field gives the direction of a parallel of -declination; that is to say, it gives a line parallel to the celestial -equator, and, knowing that, one will be able at once, by allowing the -object to pass through the field of view, to get this datum line. For -instance, supposing the whole instrument is turned round on the end of -the telescope, so that one of the two wires _x_ and _y_, Fig. 104, at -right angles to the thin wires for measuring distance, shall lie on a -star during all its motion across the field of view; then those two -wires, being parallel to the star’s motion, will represent two parallels -of declination; and we use the direction of the parallels of declination -to determine the datum point at right angles to them, that is, the north -point of the field. We have then a _position micrometer_, that is, one -in which the field of view is divided into four quadrants, called north -preceding, north following, south preceding, and south following, -because if there be an object at the central point it will be preceded -and followed by those in the various quadrants. The movable wires lie on -meridians and the fixed ones on parallels when adjusted as above. - -[Illustration: - - FIG. 158.—Position Circle. -] - -The position circle is often attached to, and forms part of, the -micrometer instead of being fixed to the telescope, and in screwing it -on from time to time, the adjustment of the zero changes, and the index -error must be found each time the micrometer is put on the telescope. - -In practice it is usual to take the north and south line as the datum -line, and positions are always expressed in degrees from the north round -by east 90°, south 180°, and west 270°, to north again in the direction -contrary to that of the hands of a clock. - -The angle from the east and west line being found by the micrometer, 90° -is either added or subtracted, to give the angular measurement from -north. But to make these measurements we want a clock; a clock which, -when we have got one of these objects in the middle of the field of -view, shall keep it there, and enable the telescope to keep any object -that we may wish to observe fixed absolutely in the field of view. But -in the case of faint objects this is not enough. We want not only to see -the object, but also the wires we have referred to. Now then the -illuminating-lamp and bright wires, if necessary, come into use. - -The following, Fig. 159, will show how we proceed if we merely wish to -measure a distance, the value of the divisions of the micrometer screw -having been previously determined by allowing an equatorial star to -transit. It represents the position of the central and the movable wire -when the shadow thrown by the central hill of the the lunar crater -Copernicus is being measured to determine the height of the hill above -the floor of the crater. It has been necessary to let the fixed wire lie -along the shadow; this has been done by turning the micrometer; but -there is no occasion to read the vernier. - -[Illustration: - - FIG. 159.—How the Length of a Shadow thrown by a Lunar Hill is - measured. -] - -Except on the finest of nights the stars shake in the field of view or -appear woolly, and even on good nights the readings made by a practised -eye often differ, _inter se_, more than would be thought possible. In -measuring distances we have supposed for simplicity that we find the -distance that one wire has to be moved from coincidence with the fixed -wire from one point to another, and theoretically speaking the pointer -should point to O on the screw head when the wires are over each other, -and then when the wires are on the points, the reading of the screw head -divided by the number of divisions corresponding to 1˝ will give the -distance of the points in seconds of arc. But in practice it is -unnecessary to adjust the head to O when the wires coincide, and the -unequal expansion of the metals of the instrument, due to changes of -temperature, would soon disarrange it. It is also somewhat difficult to -say when the wires exactly coincide, and an error in this will affect -the distance between the points. It is therefore found best to only -roughly adjust the screw head to O, and then open out the wires until -they are on the points and take a reading, say twenty-two; the screw is -then turned, in the opposite direction and the movable wire passed over -to the other side of the fixed one, and another reading taken, say -eighty-two; now the screw has to be moved in the direction which -decreases the readings on its head from one hundred downwards, as the -distance of the wires increases, so that we must subtract the reading -eighty-two from a hundred to give the number of divisions from the O -through which the screw is turned, and the reading in this direction we -will call the indirect reading, in contradistinction to the direct -reading taken at first. So far we have got a reading of twenty-two -direct and eighteen indirect, which means that we have moved the screw -from twenty-two on one side of O to eighteen on the other side, or -through forty divisions, and in doing so the movable wire has been moved -from the distance of the two points on one side of the fixed wire to the -same distance on the other, or through double the distance required. -Therefore forty divisions is the measure of twice the distance, and the -half of forty, or twenty divisions, is the measure of the distance -itself between the two points to which our attention has been directed, -whether stars, craters in the moon, spots on the sun, and the like. - -Let us consider what is gained by this method over a measure taken by -coincidence of the wires as a starting-point, and opening out the wires -until they cut the points. In the method we have just described there -are two chances of error in taking the measurements—the direct and -indirect; but the result obtained is divided by two, so that the error -is also halved in the final result. Now by taking the coincidence of the -wires as the zero, or starting-point, the measure is open to two errors, -as in the last case—the error of measurement of the points, _plus_ the -error of coincidence of wires, an error often of considerable amount, -especially as the warmth of the face and breath causes considerable -alteration in the parts of the instrument, making a new reading of -coincidence necessary at each reading of distance. As the result is not -divided by two, as in the first case, the two errors remain undivided, -so we may say that there is the half of two errors in one case and two -whole errors in the other. - -Here then we use the micrometer to measure distances; but from a very -short acquaintance with the work of an equatorial it will at once be -seen that one wants to do something else besides measure distances. For -instance, if we take the case of the planet Saturn, it would be an -object of interest to us to determine how many turns, or parts of a -turn, of the screw will give the exact diameter of the different rings; -but we might want to know the exact angle made by the axis with the -direction of the planet’s motion, across the field, or with, the north -and south line. - -If we have first got the reading when the wires are in a parallel of -declination, and then bring Saturn back again to the middle of the field -and alter the direction of the wires until they are parallel to the -major axis of the ring, we can read off the position on the circle, and -on subtracting the first reading from this, we get the angle through -which we have moved the wires, made by the direction of the ring with -the parallel of declination, which is the angle required. We are thus -not only able to determine the various measurements of the diameter of -the outer ring by one edge of the ring falling on one of the fine wires, -and the other edge on the other wire, but, by the position circle -outside the micrometer we can determine exactly how far we have moved -that system, and thus the angle formed by the axis of the ring of the -planet at that particular time. - -[Illustration: - - FIG. 160.—The Determination of the Angle of Position of the axis of - Saturn’s Ring. -] - -The uses of the position micrometer as it is called are very various. In -examination of the sun it is used to ascertain the position of spots on -the surface, and the rate of their motion and change. The lunar craters -require mapping, and their distances and bearing from certain fixed -points measuring, for this then the position micrometer comes into use. - -The varying diameters and the inclinations of the axes of the planets -and the periods of revolution of the satellites are determined, and the -position of their orbits fixed, in like manner. When a comet appears it -is of importance to determine not only the direction of its motion among -the stars, but the position of its axis of figure, and the angles of -position and dimensions of its jets. The following diagram gives an -example of the manner in which the position of its axis of figure is -determined. First the nucleus is made to run along the fixed wire, so -that it may be seen that the north vernier truly reads zero under this -condition; if it does not its index error is noted. The system of wires -is then rotated till one of the wires passes through the nucleus and -fairly bisects the dark part behind the nucleus. - -[Illustration: - - FIG. 161.—Measurement of the Angle of Position of the Axis of Figure - of a Comet, _a a_, positions of fixed wire when the north vernier is - at zero; _d d_ position of movable wire under like conditions; _a´ - a´_, _d´ d´_, positions of these wires which enable the angle of - position of the comet’s axis to be measured. The angle _a a´_ or _d - d´_ is the angle required. -] - -It need scarcely be said that these observations are also of importance -with reference to the motion of the binary stars, those compound bodies, -those suns revolving round each other, the discovery of which we owe to -the elder Herschel. We may thus have two stars a small distance apart; -at another time we may have them closer still; and at another we may -have them gradually separating, with their relative position completely -changed. By means of the wire micrometer and the arrangement for turning -the system of wires into different positions with regard to the parallel -of declination, we have a means of determining the positions occupied by -the binary stars in all parts of their apparent orbit, as well as their -distances in seconds of arc. It is found, however, by experience that -the errors of observation made in estimating distances are so large, -relatively to the very small quantities measured, that it is absolutely -necessary to make the determination of the orbit depend chiefly on the -positions. And this is done in the following way. - -[Illustration: - - FIG. 162.—Double Star Measurement, _a a_, _b b_, first position of - fixed, double wire when the vernier reads 0°, and the star runs - between the wires; _c c_, _d d_, first position of movable wires. - _a´ a´_, _b´ b´_, new position of fixed double wire which determines - the angle of position; _c´ c´_, _d´ d´_, new positions of the - movable wires which measure the distance. -] - -It is possible, by knowing the position angles at different dates, to -find the angular velocity, and since the areas described by the radius -vector are equal in equal times, the length of the radius vector must -vary inversely as the square root of the angular velocity, and by taking -a number of positions on the orbit of known angular velocity, we can set -off radii vectores, and construct an ellipse, or part of one, by drawing -a curve through the ends of the radii vectores; and from the part of the -ellipse so constructed it is possible to make a good guess at the -remainder. The angular size of this ellipse is obtained from the average -of all the measures of distance of the stars. This ellipse is then the -apparent ellipse described by the star, and the form and position of the -true ellipse can be constructed from it from the consideration of the -position of the larger star (which must _really_ be the focus), with -reference to the focus of the _apparent_ ellipse; for if an ellipse be -seen or projected on a plane other than its own, its real foci will no -longer coincide with the foci of the projected ellipse. - -The methods adopted in practice, for which we must refer the reader to -other works on the subject, are, however, much more laborious and -lengthy than the above outline, which is intended merely to show the -possibility, or the faint outline of a method of constructing the real -ellipse. When the real ellipse or orbit is known, it is then of course -possible to predict the relative positions of the two components. Let us -consider in some little detail the actual work of measuring a double -star. - -A useful form for entering observations upon, as taken, is the -following, which is copied from one actually used. - - - TEMPLE OBSERVATORY. - - No. 1. _April 12, 1875·276._ - - DOUBLE STARS. - - STRUVE 1338. - - R.A.—9h. 13m. 28s. DECL. 38° 41´ 20˝. - - Magnitudes—6·7, 7·2. - - POSITION. - - Zero, 109·8. - -[Illustration] - - DISTANCE. - - Direct. Indirect. ½ Diff. - 17 97 10 - 16 97 9·5 - ——————— - 9·75 mean. - - Readings. - 170·1 - 170· - 169·5 - 169·8 - ————— - 4) 679·4 - ————— - 169·8 - 109·8 - 90·0 - ————— - 19·8 - 169·8 Position = 150° - 19·8 - ————— Distance = 1˝·828. - 150 - - * * * * * - - No. 2. _Feb. 5th, 1875·09._ - - DOUBLE STARS. - - STRUVE 577. - - R. A.—4h. 34m. 9s. DECL. 37° 17´ - - Magnitudes—7, 8. - - POSITION. - - Zero, 88·9. - -[Illustration] - - DISTANCE. - - Direct. Indirect. ½ Diff. - 12·5 99·5 6·5 - 12·6 99·2 6·7 - ——————— - 6·6 mean. - - Readings. - - 79·5 - 81·5 - 81·2 - ————— - 3) 242·2 - ————— - 81·1 mean. - - 88·9 - 90·0 - ————— - -1·1 - 81·1 - -1·1 - ————— - 82·2 Position = 262°·2. - 180·0 - ————— Distance = 1´·237. - 262·2 - -The star having been found, the date and decimal of the year are entered -at the top, and a position taken by bringing the thick wires parallel to -the stars. A distance—say direct—is then taken, and the degrees of -position 170°·1, and divisions of the micrometer screw seventeen, read -off with the assistance of a lamp and entered in their proper columns. -The micrometer is then disarranged and a new measure of position and an -indirect distance taken, and so on. At the end of the readings, or at -any convenient time, the zero for position is found by turning the -micrometer until the wires are approximately horizontal, and then -allowing a star to traverse the field by its own motion, or rather that -of the earth, and bringing the thick wires parallel to its direction of -motion; this may be more conveniently done by means of the slow-motion -handle of the telescope in R. A., which gives one the power of -apparently making the star traverse backwards and forwards in the field. -The position of the wires is altered until the star runs along one of -them. The position is then read off and entered as the zero. In -describing the adjustments of the position circle we made the vernier -read 0° when the star runs along the wire, for that is practically the -only datum line attainable; since, however, the angles are reckoned from -the north, it is convenient to set the circle to read 90° when the star -runs along the wire, so that it reads 0° when the wires are north and -south. - -Now as positions are measured from north 0° in a direction contrary to -that of the hands of a watch, and an astronomical telescope inverts, we -repeat the bottom of the field is 0°, the right 90°, and so on; now the -reading just taken for zero is the reading when the wires are E. and W., -so that we must deduct 90° from this reading, giving 19°·8 as the -reading of the circle when the wires were north and south, or in the -position of the real zero of the field. Of course theoretically the -micrometer ought to read 0° when the wires are north and south, but in -screwing on the instrument from night to night it never comes exactly to -the same place, so that it is found easier to make the requisite -correction for index error rather than alter the eye end of the -telescope to adjustment every night. The readings of position must -therefore be corrected by the number of degrees noted when the wires are -at the real zero, which in the case in point is 19°·8, which may be -called the index error. - -It is also obvious that the micrometer may be turned through 180° and -still have its wires parallel to any particular line. The position of -the stars also depends upon the star fixed on for the centre round which -our degrees are counted; for in the case of two stars just one over the -other in the field of view, if we take the upper one as centre, then the -position of the system is 0°, but if the lower one, then it is 180°; in -the case of two equal or nearly equal stars, it is difficult to say -which shall be considered as centre, and so the position given by two -different persons might differ by 180°. There are also generally two -verniers on the position circle, one on each side, and these of course -give readings 180° different from each other, so that 180° has often to -be added or subtracted from the calculated result to give the true -position. All that is really measured by the position micrometer is the -relative position of the line joining the stars with the N. and S. line. -In order, therefore, to find, whether 180° should be added or not, a -circle is printed on the form, with two bars across for a guide to the -eye, and the stars as seen are roughly dotted down in their apparent -position—in the case in point about 150°. Our readings being now made, -we first take a mean of those of position, which is 169°·8, nearly, and -the zero is 109°·8; deduct 90° from this to give the reading of the N. -and S. line 19°·8, then we deduct this from the mean of position, 169·8, -giving us 150° as the position angle of the stars. - -It often happens that the observed zero is less than 90°, and then we -must add 360° to it before subtracting the 90°, or what is perhaps best, -subtract the observed zero from 90°, and treat the result as a minus -quantity, and therefore add it to the mean of position readings instead -of subtracting as usual. The observations of the second star give a case -in point: the zero is 88°·9, and subtracting this from 90°, we get 1°·1; -we put this down as -1°·1 to distinguish it from a result when 90° is -subtracted from the zero; it is then added to the mean of position -readings 81°·1, giving 82°·2, but on reference to the dots showing the -approximate position of the stars, it is seen that 180° must be added to -their result, giving 262°·2 as the position of the stars. - -Now as to distance, take the case of the second star. Subtract the first -indirect reading from 100°, giving 0·5, and add this to the direct -reading, 12·5, making 13·0, which is the difference between the two -readings taken on either side of the fixed wire; the half of this, 6·5, -is placed in the next column, and the same process is repeated with the -next two readings: a mean of these is then taken, which is 6·6 for the -number of divisions corresponding to the distance of the stars. In the -micrometer used in this case, 5·3 divisions go to 1˝, so that 6·6 is -divided by 5·3, giving 1˝·237 as the distance. A table showing the value -in seconds of the divisions from one to twenty or more, saves much time -in making distance calculations; the following is the commencement of a -table of this kind where 5·3 divisions correspond to 1˝. - - ┌──────┬─────┬────┬────┬────┬────┬────┬────┬────┬────┬────┐ - │Divi- │ 0 │ ·1 │ ·2 │ ·3 │ ·4 │ ·5 │ ·6 │ ·7 │ ·8 │ ·9 │ - │sions │ │ │ │ │ │ │ │ │ │ │ - │ of │ │ │ │ │ │ │ │ │ │ │ - │micro-│ │ │ │ │ │ │ │ │ │ │ - │meter.│ │ │ │ │ │ │ │ │ │ │ - ├──────┼─────┼────┼────┼────┼────┼────┼────┼────┼────┼────┤ - │ 0 │0·000│·018│·037│·056│·075│·093│·112│·131│·150│·168│ - ├──────┼─────┼────┼────┼────┼────┼────┼────┼────┼────┼────┤ - │ 1 │0·187│·205│·224│·243│·262│·280│·299│·318│·337│·356│ - ├──────┼─────┼────┼────┼────┼────┼────┼────┼────┼────┼────┤ - │ 2 │0·375│·393│·412│·431│·450│·468│·487│·506│·525│·543│ - └──────┴─────┴────┴────┴────┴────┴────┴────┴────┴────┴────┘ - -In the first column are the divisions, and in the top horizontal line -the parts of a division, and the number indicated by any two figures -consulted is the corresponding number of seconds of arc. In the case of -a half difference of 2·3 we look along the line commencing at 2 until we -get under 3, when we get 0˝·431 as the seconds corresponding to 2·3 -divisions. - -It is necessary to adjust the quantity of light from the lamp in the -field, so that the wires are sufficiently visible while the stars are -not put out by too much illumination; for the majority of stars a red -glass before the lamp is best. This gives a field of view which renders -the wires visible without masking the stars, but a green or blue light -is sometimes very serviceable. A shaded lamp should be used for reading -the circles on the micrometer, so as not to injure the sensitiveness of -the eye by diffused light in the observatory. A lamp fixed to the -telescope, having its light reflected on the circles, but otherwise -covered up, is a great advantage over the hand-lamp. In very faint -stars, which are masked by a light in the field sufficient to see the -wires, the wires can be illuminated in the same manner as in the -transit, but there is this disadvantage—the fine wires appear much -thickened by irradiation, so that distances, especially of close stars, -become difficult to take. - - * * * * * - -We come now to the differential observations made with the equatorial. -Let us explain what is meant. Suppose it is desired to determine with -the utmost accuracy the position of a new comet in the sky. If we take -an ordinary equatorial, or an extraordinary equatorial (excepting -probably the fine equatorial at Greenwich), and try to determine its -place by means of the circles, its distance from the meridian giving its -right ascension and its distance from the equator giving its -declination, we shall be several seconds out, on account of want of -rigidity of its parts; but if we do it by means of such an instrument as -the transit circle at Greenwich, we wait till the comet is exactly on -the meridian, and determine its position in the way already described. - -As a matter of fact, however, the transit circle is not the instrument -usually used for this purpose, but the equatorial. We do not however -just bring the comet or other object into the middle of the field and -then read off the circles, but we differentiate from the positions of -known stars; so that all that has to be done in order to get as perfect -a place for the comet as can be got for it by waiting till it comes to -the meridian—which perhaps it will do in the day-time, when it will not -be visible at all—is to determine its distance in right ascension and -declination from a known star, by means of a micrometer. Of course one -will choose the brightest part of the comet and a well-known star, the -place of which has been determined either by its appearance in one of -the catalogues, or by special transit observations made in that behalf. -We then by the position micrometer determine its angle of position and -distance from the known star at a time carefully noted, or we measure -the difference in right ascension and the difference in declination. - -[Illustration: - - FIG. 163.—Ring Micrometer. -] - -Continental astronomers have another way of doing this which we will -attempt to explain. Suppose we wish to find the difference in -declination of a star and Jupiter, we place the ring, A D, Fig. 163, in -the eyepiece of the telescope and watch the passage of Jupiter and the -star over this ring micrometer. It will be clear that, as the motion of -the heavens is perfectly uniform, it will take very much less time for -the star to travel over the ring from B to C than it will for Jupiter to -travel over the ring from _b_ to _c_, because the star is further from -the centre; and by taking the time of external and internal contact at -each side of the ring, the details of which we need not enter upon here, -the Continental astronomers are in the habit of making differential -observations of the minutest accuracy by means of this ring micrometer, -whilst we prefer to make them by the wire micrometer. - - - - - BOOK VI. - _ASTRONOMICAL PHYSICS._ - - - - - CHAPTER XXV. - THE GENERAL FIELD OF PHYSICAL INQUIRY. - - -We have now gone down the stream of time, from Hipparchus to our own -days. We find now enormous telescopes which enable us to see and examine -celestial bodies lying at distances so great that the mention of them -conveys little to the mind. We find also perfect systems of determining -their places. The following chapters will show, however, that modern -astronomy has not been contented with annexing those two branches of -physics which have enabled us to make the object-glass and the clock, -and another still which enables us to make that clock record its own -time with accuracy. - -These applications of Science have been effected for the purpose either -of determining with accuracy the motion and positions of the heavenly -bodies or of enabling us to investigate their appearances under the best -possible conditions. The other class of observations to which we have -now to refer, have to do with the quantity and the quality of the -vibrations which these bodies impart to the ether, by virtue of which -vibrations they are visible to us. - -We began by measurement of angles, we end with a wide range of -instruments illustrating the application of almost every branch of -physical as well as of mathematical science. In modern observatories -applications of the laws of Optics, Heat, Chemistry and Electricity, are -met with at every turn. - -Each introduction of a new instrument, or of a new method of attack, has -by no means abolished the preexisting one; accretion rather than -substitution has been the rule. On the one hand, measurement of angles -goes on now more diligently than it did in the days of Hipparchus, but -the angles are better measured, because the telescope has been added to -the divided arc. Time is as necessary now as it was in the days of the -clepsydra, but now we make a pendulum divide its flow into equal -intervals and electricity record it. On the other hand, the colours of -the stars are noted as carefully now as they were before the -spectroscope was applied to the telescope, but now we study the spectrum -and inquire into the cause of the colour. The growth of the power of the -telescope as an instrument for eye observations has gone on, although -now almost all phenomena can be photographically recorded. - -The uses to which all astronomical instruments may be put may be roughly -separated into two large groups:— - - I. They may be used to study the positions, motions, and sizes of - the various masses of matter in the universe. Here we are - studying celestial mechanics or mechanical astronomy, and with - these we have already dealt. - - II. They maybe used to study the motions of the molecules of which - these various masses are built up, to learn their quality, - arrangement, and motions. Here we are studying celestial - physics, or physical astronomy. - -It is with this latter branch that we now have to do. - -First we have to deal with the quantity and intensity of the ethereal -vibrations set up by the constituent molecules of these distant bodies. -We wish to compare the quantity of light given out by one star with that -given out by another. We wish, say, to compare the light of Mars with -the light of Saturn; we are landed in the science of photometry, which -for terrestrial light-sources has been so admirably investigated by -Rumford, Bouguer, and others. - -Here we deal with that radiation from each body _which affects the -eye_—but by no means the total radiation. This is a point of very -considerable importance. - -Modern science recognises that in the radiation from all bodies which -give us white light there is so great a difference of length of wave in -the vibrations that different effects are produced on different bodies. -Thus white light is a compound thing containing long waves with which -heat phenomena are associated, waves of medium length to which alone the -eye is tuned, and short waves which have a decided action on some -metallic salts which are unaffected by the others. - -To thus examine the constituents of a beam of light a lantern, with a -lime-light or electric light, may be used for throwing a constant beam; -we may then produce an image of the cylinders of lime or the carbon -points in the lantern on a piece of paper or a screen, and our eyes will -tell us that this is an instance of how the radiations from any -incandescent substance are competent to give us light. We receive all -the rays to which our eyes are tuned and we see a white image on the -screen. We shall see also that the light is more intense than that of a -candle, in other words that the radiation from the light-sources we have -named is very great. - -[Illustration: - - FIG. 164.—Thermopile and Galvanometer. -] - -Now let us insert in front of the lantern a piece of deep red glass, -that is, glass which allows only the red constituents of the white light -to pass. Now if a thermo-electric pile, Fig. 164, be introduced into the -beam we shall see that the needle of the galvanometer will alter its -position. Now, why does the needle turn? This is not the place for -giving all the details of this instrument, but it is sufficient to say -(1) that the needle moves whenever a current of electricity flows -through the coil of wire surrounding the needles, and (2) that the pile -consists of a number of bars of antimony and bismuth joined at the -alternate ends, and whenever one end of the pile is heated more than the -other, a current of electricity is caused to flow. Such is the delicacy -of the instrument, that the heat radiated from the hand, held some yards -away from it, is sufficient to set the needle swinging violently; this -then acts as a most delicate thermometer. In this case it shows that -heat effects are produced by the red constituents of the light from the -lamp. - -Now replace the thermopile by a glass plate coated with a salt of silver -in the ordinary way adopted by photographers. No effect will be -produced. - -Replace the red glass by a blue one. If the light is now allowed to fall -on the photographic plate, its effect is to decompose, or alter the -arrangement of, the atoms of silver, so that on applying the developing -solution, the silver compound is reduced to its metallic state on the -places where the light has acted; and thus, if the image of the -light-source has been focussed on the plate, a photograph of it is the -result. If the thermopile is brought into the beam it will be now as -insensitive to the blue light as the photographic plate was to the red -light in the former case. We have therefore three kinds of effects -produced, viz., light, heat, and chemical or actinic action, and when -light is passed through a prism, these three different radiations, or -energies, are most developed in three different portions of the -spectrum. - -If indeed a small spectrum be thrown on the screen and the different -colours are examined with the thermopile, it will be found that as long -as we allow it to remain at the blue end of the spectrum, there will be -no effect on the galvanometer, but if instead of holding it at the blue -end we bring it towards the red, the galvanometer needle is deflected -from its normal position, to that it had when the red rays fell on it, -showing that it is beyond all doubt the red rays and not the blue to -which it is sensitive. Where then in the spectrum are the rays which -affect the photographic plate? We can at once settle this point. If one -be placed in the spectrum for a short time, and then developed, it will -be found to be affected only in the part on which the blue rays have -fallen. Indeed to demonstrate this no lamp is necessary. - -If for half-an-hour or so two pieces of sensitive paper are placed in -the daylight, one covered with red glass, and the other with violet, so -that the sunlight is made to travel, in the one case, through red glass, -and in the other through violet, it will be found that the violet light -will act, and produce a darkening of the paper, while the red glass will -preserve the paper below it from all action. This is a proof that the -blue end of the spectrum has another kind of energy, a chemical energy, -by means of which certain chemicals are decomposed, this is the basis of -photography. - -These different qualities of light have been utilized by the astronomer. -He attaches a thermopile to his telescope and establishes a celestial -thermometry. The radiations repay a still more minute examination, and -aided by the spectroscope, he is able to study with the utmost certitude -the chemical condition of the heavenly host, while the polariscope -enables him to acquire information in still another direction. Nor does -he end here. He replaces his eye by a sensitive plate, which not only -enables him to inquire into the richness of the various bodies in these -short waves, but actually to obtain images of them of most marvellous -beauty and exactness. - -These various lines of work we have to consider in the remaining -chapters. - - - - - CHAPTER XXVI. - DETERMINATION OF THE LIGHT AND HEAT OF THE STARS. - - -One branch of observatory work is that of determining the relative -_magnitude_ of stars, the word magnitude being of course used in a -conventional sense for brightness. There are, moreover, stars which vary -in brightness or _magnitude_ from time to time; these are called -variable stars, and the investigation of the amount and period of -variation opens up another use for the equatorial, and an instrument is -required for finding the value of the amount of light given by a star at -any instant; in fact, a photometer is necessary. The methods of -determining the brilliancy of stars are so similar in principle to those -employed for ordinary light-sources that the ordinary methods of -photometry may be referred to in the first instance. We may determine -the relative brilliancy of two or more lights, or we may employ a -standard light and refer all other lights to that. - -Rumford’s photometer, Fig. 165, is based upon the fact that if the -intensity of the shadows of an opaque body be equal, the lights throwing -the shadows are equal. Hence the lights are moved towards or from a -screen until the shadows are equal; then if the distances from the -screen are unequal the lights are unequal, and the intensities vary in -the inverse ratio of the squares of the distances. - -This method is practically carried out in the telescope by reducing the -aperture till the stars become invisible, and noting the apertures at -which each vanishes in turn. - -The most simple method of doing this is that used by Dawes, which is -simply an adjustable diaphragm limiting the available area of the -object-glass; we can thus view a star, and gradually reduce the aperture -until the star is _just visible_, or until it _just disappears_, the -latter limit being perhaps the most accurate and most usually used; the -aperture is read off on the scale attached. - -[Illustration: - - FIG. 165.—Rumford’s Photometer. -] - -The photometer of Mr. Knobel is, however, a very handy one; it consists -of a plate of metal having a large V-shaped piece with an angle of 60° -cut out of it; another plate slides over the first in such a manner that -its edge forms a base for the V-shaped opening, thus forming an -equilateral triangular hole, which is adjustable at pleasure by moving -the second plate. The edge of the moveable plate is divided so that the -size of the base of opening is known at once, and its area easily -calculated. - -The annexed woodcut will give an idea of the second method which is -possible. - -[Illustration: - - FIG. 166.—Bouguer’s Photometer. -] - -Let the gas flame be supposed to represent a constant light at constant -distance; then the intensity of the light to be experimented upon -(represented by the candle) is determined by moving it towards or from -the mirror till the illumination of both the halves of the porcelain -screen is equal. The instrument by which this kind of investigation is -carried out by astronomers has been introduced by Zöllner, and is called -the Astrophotometer. - -In this the star is compared with a small image of a portion of the -flame of a lamp attached to the telescope. It being found that, though -the total light emitted by the flame varies with its size, the -_intensity_ of the brightest part does not, appreciably. Two artificial -stars are formed by means of a pin-hole, a double concave lens, and a -double convex lens. These appear in the field by reflexion from the -front and back faces of a plate of glass alongside the image of the real -star, the light of which passes through the plate. The intensity of the -artificial star is varied, first by changing the pin-hole, and finally -by two Nicol’s prisms, the colour being first matched with that of the -star by means of a third Nicol, with a quartz plate between it and the -first of the other two Nicols. The instrument is provided with -object-glasses of various sizes (and diaphragms) up to 2¾ inches, and, -if fainter stars are to be examined, it can be screwed on to the -eyepiece of an equatorial instrument. A second arrangement, like the -first, but without the quartz plate arrangement, forms an artificial -star from moonlight, for comparison of the light of that body with the -artificial star. - -So far there is no difficulty, but this measure must be interpreted into -magnitude, and we must know what magnitude a star is which just -disappears with a given aperture of, say, one inch, and secondly, the -ratio of light between the magnitudes, or how much less light is -received from a star of the next magnitude in proportion to the given -one. If now we were able to start a new scale of magnitude, it would be -easy to say that a star just visible with an inch aperture on a fine -night shall be called a ninth magnitude star, and fix a certain number -of ninth magnitude stars for reference, so that the errors induced by -hazy nights and variable eyes might be eliminated. An observer on a bad -night could limit his aperture on a known star, when he might find that -double the area given by an aperture of one inch was required as a limit -for one of the stars of reference, and in that case he would know that -half the usual amount of light from every star was stopped by -atmospheric causes, and he would make the requisite corrections -throughout his observations. We might also say that a star of a whole -magnitude, greater or less than another, shall give us half or double -the amount of light—in fact, that _this_ shall be the ratio between -magnitudes. We are not, however, able to make these rules, for an -arbitrary scale has been adopted for years, and we can only reduce this -scale to a law, in such a manner as not to interfere greatly with the -generally received magnitudes. - -Amongst the brighter stars there is a close agreement in the estimate of -magnitude by different observers, but amongst the higher magnitudes a -difference appears. Sir J. Herschel and Admiral Smyth, for instance, go -into much higher numbers of magnitudes than Struve; the limit of Admiral -Smyth’s vision with his 6-inch telescope was a 16th magnitude, while the -limit of Struve’s vision with a 9½-inch telescope he calls a 12th -magnitude; the estimates of the latter observer are, however, gaining -greater adoption. In order to reduce the relative magnitude to a law, -Mr. Pogson[21] took stars differing largely in magnitude, and compared -the amount of light from each, and so reduced the ratio between the -magnitudes given by Knott and all the best observers. - -From this he found that a mean of 2·4 represented the ratio, and for -reasons given he adopted the quantity 2·512 as a convenient ratio; as he -states, “the reciprocal of ½ log. R (in his paper R = the ratio 2·512), -a constant continually occurring in photometric formulæ, is in this case -exactly 5.” - -So far the ratio is established. The next thing is the basis from which -to commence reckoning; this Mr. Pogson fixed by reference to -Argelander’s catalogued stars, estimated by him at about the 9th -magnitude, and with these, comparison is made with the star whose light -is measured, and the above constant of ratio applied, which at once -gives the magnitude of the measured star. To do this, in Mr. Pogson’s -words: “If then any observer will determine for himself the smallest of -Argelander’s magnitudes, just visible by fits, on a fine moonless night, -with an aperture of one inch, and call this quantity L, or the limit of -vision for one inch, the limit _l_, for any other aperture, will be -given by the simple formula, _l_ = L + 5 × log. aperture.” The value of -L founded by Mr. Pogson is 9·2; that is, a star of 9·2 magnitude, -according to Argelander, is limited by 1-inch aperture, with Mr. -Pogson’s eye. On different nights and with different eyes, this number, -or the magnitude limited, must vary, and it varies from exactly the same -causes that produce variation in the light of the stars to be measured, -so that we are independent of transparency of the air, at least within -considerable limits. Having found the value of L for any night, we turn -the telescope on a star to be measured, then alter the aperture if we -employ the first method, until the limit is found, and insert the value -in the equation, the value of _l_, or the star’s magnitude, then at once -appears. By this means a number of well-known stars of all magnitudes -may be settled for future reference and comparison with variable stars. - -The comparison stars then being fixed upon, and their magnitude -accurately known, there is not much difficulty in comparing any variable -star with one or more of those of approximately the same magnitude. By -this means a number of independent estimates of the magnitude of the -variable is obtained free from errors from the disturbing effects of -mist or moonlight, which affects both the stars of comparison and -variable alike. If we call the stars of comparison A B C D, we enter the -comparisons somewhat as follows; (variable) 2 > A, 4 < B, 1 < C, 7 > D, -the number showing how many tenths of a magnitude the variable is more -or less bright than each comparison star, and the magnitude of the -latter being known, we get several values of the magnitude of the -variable, a mean of which is taken for the night. In order to show -clearly to the eye the variations of a star, and to compute the periods -of maximum and minimum, a graphical method is adopted: a sheet of -cross-ruled paper is prepared, on which the dates of observation are -represented by the abscissæ, and the corresponding observed magnitudes -by the ordinates. Dots are then made representing the several -observations, and a free-hand curve drawn amongst the dots, which at -once gives the probable magnitude at any epoch in the period of -observation, the change of the curve from a bend upwards to downwards, -or _vice versâ_, indicating a maximum or minimum of magnitude. - -So much then for the method of determining the intensity of the visible -radiation. The next point to consider is the intensity of the thermal -radiations—we pass from photometry to thermometry. The thermopile will -in the future be an astronomical instrument of great importance. We need -not go into its uses in other branches of physics, we shall here limit -ourselves to the astronomical results which have been already obtained. -Lord Rosse used a pile of this kind, made of alternate bars of bismuth -and antimony. He attacked the moon, and by observing it from new to -full, and from full to new, he got a distinct variation of the amount of -heat, according as the moon was nearest to the epoch of full moon, or -further from that epoch. As the moon was getting full, he found the -needle moved, showing heat, and, after the full, it went down again and -found its zero again at new. By differential observations Lord Rosse -showed that this little instrument, at the focus of his tremendous -reflector, was able to give some estimate of the heat of the moon, which -may be 500 degrees Fahr. at the surface. - -It may be said that the moon is very near us, and we ought to get a -considerable amount of heat from it; but the amount is scarcely -perceptible without delicate instruments. Still the instrument is so -delicate, that the heat of the stars has been estimated. A pile of very -similar construction to the one just mentioned has been attached by Mr. -Stone to the large equatorial at Greenwich. The instrument consists of -two small piles about one-tenth of an inch across the face; the wires -from each are wound in contrary directions round a galvanometer, so that -when equal currents of electricity are passing they counteract each -other, and the needle remains stationary. It only moves when the two -currents are unequal; we have then a differential galvanometer, showing -the difference of temperature of the faces of the two piles; the image -of a star is allowed to fall half-way between the two piles—then on one -pile and then on another; then matters are reversed, and a mean of the -galvanometer readings taken, beginning with zero when the image of a -star was exactly between the two piles. The result was this, that the -heat received from Arcturus, when at an altitude of 25°, was found to be -just equal to that received from a cube of boiling water, three inches -across each side, at the distance of 400 yards. - -Arcturus is not the only star which has been observed in this way; in -another star, Vega, which is brighter than Arcturus, it has been -demonstrated that the amount of heat which it gives out, when at an -altitude of 60°, is equal to that from the same cube at 600 yards, so -that Mr. Stone shows beyond all question, that Arcturus gives us more -heat than Vega. - -This opens a new field, for if we get heat effects different from the -effects on the eye, the stars ought to be catalogued with reference to -their thermal relations as well as their visual brightness. Another -valuable application of this method is due to Professor Henry, of -Washington. Professor Henry imagined that, by means of a thermo-electric -pile placed at the eyepiece of the telescope, so that a sun-spot, or a -part of the ordinary surface, could be brought on the face of the pile, -he could tell whether there was a greater, or less radiation of heat -from a spot, than from any other part; and he was able with the -thermopile to show that there was a smaller radiation of heat from the -spots than from the other parts of the sun’s surface. - ------ - -Footnote 21: - - Monthly Notices, R.A.S., vol. xvii., p. 17. - - - - - CHAPTER XXVII. - THE CHEMISTRY OF THE STARS: CONSTRUCTION OF THE SPECTROSCOPE. - - -In the addition of chemical ideas to astronomical inquiries, we have one -of the most fruitful and interesting among the many advances of modern -science, and one also which has made the connection between physics and -astronomy one of the closest. - -To deal properly with this part of our book, as the constitution of one -of the heavenly bodies can be studied in the laboratory as well as in -the observatory, we have to describe physical instruments and methods, -as well as the more purely astronomical ones. - -In a now rare book published in London in the year 1653, that is to say, -some years before Sir Isaac Newton made his important observations on -the action of a prism on the rays of light—observations which have been -so very rich in results—is given Kepler’s treatise on Dioptrics. From -this one finds that the great Kepler had done all he could to try to -investigate the action of a three-cornered piece of glass. - -It has been considered, that, because Newton was the first to teach us -much of its use, he was the first to investigate the properties of the -prism. This is not so. Fig. 167 is an illustration taken from this book, -by which Kepler shows that if we have a prism and pass light through it, -we get three distinct results when a ray (F) falls on the prism. He -shows that the first surface reflects a certain amount of light, (D I), -and that this is uncoloured, because it does not pass through the glass, -and that the remainder is refracted by the glass and part emerges at E, -coloured like the rainbow. Then he goes on to show that the second -surface of the prism also reflects some light internally, and that there -is a certain amount of light leaving the prism at M, and going to K. - -[Illustration: - - FIG. 167.—Kepler’s Diagram. -] - -By means of a very few experiments Newton was able to show how much -knowledge could be got by examination of the prism. The first -proposition in Newton’s _Optics_ is an attempt to prove that light, -which differs in colour, differs also in degree of refrangibility. We -shall recollect from the fifth chapter what this term means, for it was -there shown that whenever a ray of light enters obliquely a medium -denser than that in which it had been travelling, it is bent towards the -perpendicular to the surface, in fact it is refracted, and those rays -which are most refracted by the same substance with the same angle are -said to be more refrangible than others. Newton’s experiment was very -simple. He took a piece of paper, one half of which was coloured red and -the other half blue; and this was placed on a stand horizontally, in the -light from a window, with a prism between it and the eye. - -[Illustration: - - FIG. 168.—Newton’s Experiment showing the different Refrangibilities - of Colours. -] - -He went on to show, that when he allowed the beam of sunlight to fall -upon the paper, strongly illuminating the red and blue portions, making -at the same time all the rest of the room as dark as possible (so that -the operation was not impeded by extraneous light), when he held a prism -in a particular way, he found that the red and the blue occupied -different positions when looked at through the prism. When the prism is -held as shown, the red is seen below and the blue above. If the prism be -turned with the refracting edge downwards, the red is seen above and the -blue below. When the refracting edge is upwards, it is very clear that -if the violet is seen uppermost it must be because the violet ray is -more refracted, and when the red ray is uppermost, with the refracting -edge of the prism downwards, it is because the red ray is the least -refracted. - -There are other experiments to which he alludes, and by which Sir Isaac -Newton considered he had proved that lights which differ in colour -differ also in degrees of refrangibility. - -Newton at one step went to the sun, and his second theorem is “The light -of the sun consists of rays of different refrangibility,” and then he -enters into the proof by experiment. The light from the sun passes -through a hole in the window-shutter and through the prism which throws -a spectrum on a screen. We now see the full meaning of the different -degrees of refrangibility. There he had a long band of light of all -colours, the red at one end and the blue at the other, showing that the -different colours are unequally refracted, or turned from their course. -In this way Sir Isaac Newton determined whether the law, that light -which differed in colour differed also in refrangibility, held true with -regard to the sun; and he clearly showed that in this case also the -light differs in refrangibility, in exactly the same way as the red -light and the blue light had done in his experiment with the pieces of -paper. He was soon able to prove to himself that the circular aperture -was not the best thing he could use, because in the spectrum he had a -circle of colour representing every ray into which the light could be -broken up. If we put a bit of red glass in the path of the rays we get -an image of the hole in red; if we use other coloured glasses, we have a -circle for each particular colour; all these images overlap, and the sum -total gives us an extremely mixed spectrum, something quite different -from what is seen when we introduce a slight alteration, which curiously -enough was delayed for a great many years. - -Sir Isaac Newton recognised the difficulties there were in getting a -pure spectrum by means of a circular aperture, but although he used -afterwards an oblong opening instead of a circular aperture, in which we -had something more or less like what we now use, namely, a “slit”—a -narrow line of light; he does not seem to have grasped the point of the -thing, because in one of his theorems he says he also tried triangular -openings. We shall show how important it is that we should not only have -an oblong opening as proposed by Newton, but that that oblong opening -should be of small breadth. - -The moment we exchange the circular aperture for the oblong opening of -Newton, we get a spectrum of greater purity, and, as in the case of the -circular opening the purity depended on the size of the circle, so also -in the case of the oblong opening the purity of the spectrum depends -very much on the breadth of the oblong opening. - -We thus sort out the red, orange, yellow, green, blue, and violet; they -are no longer mixed as they are when we employ a circular opening. If we -attempt the same experiment with red glass interposed we get something -more decided than before; we have no longer a circular patch of light, -but an oblong one in the red; in fact, the exact form of the aperture, -or slit, through which we have allowed the light to pass through the -prism and lens to form an image. - -[Illustration: - - FIG. 169.—Wollaston’s first Observation of the Lines in the Solar - Spectrum. -] - -Now although Newton made these important observations on sunlight, he -missed one of the things, in fact we may say _the_ thing, which has made -sunlight and starlight of so much importance to Astronomy. The oblong -opening which Newton used varied from one-tenth to one-twentieth of an -inch in width; but Dr. Wollaston in 1812—we had to wait from 1672 till -1812 to get this apparently ridiculously small extension—used such a -narrow slit as we have mentioned, and he found that when he examined the -light of the sun with a prism before the eye, he got results of which -Newton had never dreamt. - -Dr. Wollaston not only found the light of the sun differing in -refrangibility; but in the different colours of the solar light he found -a number of dark lines, which are represented by the black lines across -the spectrum in Fig. 169. - -[Illustration: - - FIG. 170.—Copy of Fraunhofer’s first Map of the Lines in the Solar - Spectrum. -] - -[Illustration: - - FIG. 171.—Student’s Spectroscope. -] - -In the year 1814 Fraunhofer examined the spectrum by means of the -telescope of a theodolite, directing it towards a distant slit, with a -prism interposed. In this manner he observed and mapped 576 lines, the -appearance of the spectrum to him being represented in Fig. 170. From -this time they were called the “Fraunhofer lines.” It need scarcely be -said that from the time of Wollaston until a few years ago these strange -mysterious lines were a source of wonder to all observers who attempted -to attack the problem. The difference between the simple prism and slit -which Newton, Wollaston, and Fraunhofer used to map these lines, and the -modern spectroscope, as used with or without the telescope, is due to a -suggestion of Mr. Simms in 1830. - -Let us refer to a modern spectroscope. Fig. 171 represents a form -usually used for chemical analysis. The only difference between the -spectroscope and the simple prism in Newton’s experiment is this, that -in the one case the light falls directly from the slit through the prism -on a screen and is viewed there; and in the other the eye is placed -where the screen is, and looks through the prism and certain lenses at -the slit. - -The great improvement which Mr. Simms suggested was this simple one. He -said, “It would surely be better that the light which passes through the -prism or prisms independently of the number I use, should, if possible, -pass through them as a parallel beam of light; and therefore, instead of -putting the slit merely on one side of a prism and the eye on the other, -I will, between the slit and the prism, insert an object-glass,” as -shown in Fig. 172; so that the slit of the spectroscope is the -representative of the hole in the shutter. - -[Illustration: - - FIG. 172.—Section of a Spectroscope, showing the Path of the Ray from - the Slit. -] - -The slit is exactly in the focus of the little object-glass, C, or -collimating lens, as it is called; so that naturally the light is -grasped by this lens, and comes out in a parallel beam, and travels -among the prism or prisms, quite irrespective of course of their number. -This parallel beam, in order to be utilized by the eye after it has -passed through the system of prisms, is again taken up by another -object-glass and reduced from its parallel state into a state of -convergence, and brought to a focus which can be examined by means of an -eyepiece. - -The red rays from the slit come to a focus at R, and the blue at B, -forming there their respective images of the slit, and between B and R -are a number of other images of the slit, painted in every colour that -is illuminating it, thus forming a spectrum which is viewed by the -eyepiece. In fact, the object-glass and eyepiece constitute a telescope, -through which the slit is viewed, and the collimating lens makes the -light parallel, just as if it had come from a distant object, and fit to -be utilized in the telescope. This is the principle to be observed in -the construction of every spectroscope. - -We have now given an idea of the general nature of the instrument -depending on this important addition made by Mr. Simms, which is the -basis of the modern spectroscope, and it is obvious that if we want -considerable dispersion, we can either increase the number of prisms, or -increase their dispersive power. - -We have already shown in a previous chapter that the dispersion depends -on the angle of the prisms, and that the calculations necessary for -making the object-glass of a telescope were based upon an observation -made by passing light through a prism of a particular angle made of the -same glass as that of which the proposed object-glass was to be -constructed. Then, again, we took the opportunity of showing that with -very dense substances greater dispersion could be obtained. We showed -how the prism of dense flint glass overpowered the dispersion of the -prism of the crown glass, and how the combination gave us refraction -without dispersion. - -[Illustration: - - FIG. 173.—Spectroscope with Four Prisms. -] - -Fig. 173 is a drawing of a spectroscope containing four prisms. It is a -representation of that used by Bunsen and Kirchhoff when they made their -maps of the solar spectrum: it is so arranged that the light after -passing through the slit goes through the collimating lens, and then -through the prisms; it is afterwards caught by the telescope lens and -brought to a focus in front of the eyepiece. It is very important, when -we have many prisms, to be able to arrange them so that whether we use -one part of the spectrum or the other, each prism shall be in the best -condition for allowing the light to traverse it; that is to say, that it -shall be in the position of _minimum deviation_, when the angles of -incidence and emergence are equal, and each surface refracts the ray -equally. They can be arranged so, that as the telescope is moved to -observe a new part of the spectrum, every prism will be automatically -adjusted. - -To insure this the prisms are united to form a chain so that they all -move together, and each has a radial bar to a central pin which keeps -them at the proper angle. - -[Illustration: - - FIG. 174.—Automatic Spectroscope (Grubb’s form). -] - -There is another arrangement which is very simple, in which we get the -condition of minimum deviation by merely mounting the prisms on a -spring, and then moving the spring with the telescope, in the same way -as the telescope moves the other automatic arrangement. - -[Illustration: - - FIG. 175.—Automatic Spectroscope (Browning’s form). -] - -For some observations, especially solar observations, in which the light -is very intense, it is extremely important, in fact essential, to reduce -the brilliancy of the spectrum; and of course this enables us, in the -case of the sun especially, to increase the dispersion almost without -limit, by having a great number of prisms, or even using the same twice -over, in the following manner: - -On the spectroscope there is a number of prisms so arranged that the -light comes from the slit, and travels through the lower portion of the -prisms; it then strikes against the internal reflecting surface of a -right-angled prism at the back of the last prism, Fig. 176, and is sent, -up to another reflecting surface, and then comes back again through the -same prisms along an upper storey, and then is caught by means of a -telescope above the collimator, on the slit of which the sun’s image is -allowed to fall. - -[Illustration: - - FIG. 176.—Last Prism of Train for returning the Rays. -] - -This contrivance, suggested by the author and Prof. Young independently, -is now largely used. Fig. 177 shows an ordinary spectroscope so armed. -The light from the slit traverses the upper portions of the prisms; it -is then thrown down by the reflecting prism seen behind the collimator, -then, returning along the lower part, it is received by a right-angled -prism in front of the object-glass of the observing telescope. - -Instead of the rays of light being reflected back through the upper -storey of the prisms, another method has been adopted; the last prism is -in this case a half prism, and the last surface on which the rays of -light fall is silvered; the rays then are returned on themselves, and, -when the instrument is adjusted, come to a focus on the inside of the -slit plate, forming there a spectrum, any part of which can, by moving -the prisms, be made to fall on a small diagonal reflecting prism on one -side of the slit, by which it is reflected to the eyepiece. In this -arrangement the collimating lens becomes its own telescope lens on the -return of the ray. - -[Illustration: - - FIG. 177.—Spectroscope with returning Beam. -] - -There is another form of spectroscope, called the _direct vision_, which -is largely used for pocket instruments. The principle of it is that the -light passing through it is dispersed but not turned from its course, -just the reverse of the achromatic combination of the object-glass; a -crown-glass prism is cemented on a flint one of sufficient angle that -their deviative powers reverse each other but leave a certain portion of -the flint-glass dispersion uncorrected; since, however, the dispersive -power of the flint-glass is to a great extent neutralized, therefore, in -order to make the instrument as powerful as one of the ordinary -construction, a number of flint-glass prisms are combined with -crown-glass ones, as shown in Fig. 178. - -[Illustration: - - FIG. 178.—Direct Vision Prism. -] - -There is another form of direct-vision prism, called the -Herschel-Browning, in which the ray is caused to take its original -course on emerging by means of two internal reflections. - - - - - CHAPTER XXVIII. -THE CHEMISTRY OF THE STARS (CONTINUED): PRINCIPLES OF SPECTRUM ANALYSIS. - - -We have next to say something about the principles on which the use of -the spectroscope depends; if we look through one we can readily observe -how each particular ray of light paints an image of the slit. Thus, if -we are dealing with a red ray of light, that ray, after passing through -the prisms, will paint a red image of the slit; if the light be violet, -the ray will paint a violet image of the slit, and these images will be -separated, because one colour is refracted more than the other. Now it -follows from this that when the slit is illuminated by white light, -white light being white because it contains all colours, we get an -infinite number of images of slits touching or overlapping each other, -and forming what is called a _continuous spectrum_. - -Hence it is that if we examine the light of a match or candle, or even -the electric light, we get such a continuous spectrum, because these -light sources emit rays of every refrangibility. Modern science teaches -us that they do so because the molecules—the vibrations of which -produce, through the intermediary of the ether, the sensation of light -on our optic nerve—are of a certain complexity. - -In the preceding list of light sources the sun was not mentioned, -because its light when examined by Wollaston and Fraunhofer, was found -to be discontinuous. Now it is clear that if in a beam of light there be -no light of certain particular colours, of course we shall not find the -image of the slit painted at all in the corresponding regions of the -spectrum. This is the whole story of the black lines in the spectrum of -the sun and in the spectra of the stars. - -Here and there in the spectrum of these there are colours, or -refrangibilities, of light which are not represented in light which -comes from those bodies, and therefore there is nothing to paint the -image of the slit in that particular part of the spectrum; we get what -we call a dark line, which is the absence of the power of painting an -image. - -But then it may be asked, How comes it that the prism and the -spectroscope are so useful to astronomers? In answer we may say, that if -we knew no more about the black lines in the spectra of the sun and -stars than we knew forty years ago, the spectroscope ought still to be -an astronomical instrument, because it is our duty to observe every fact -in nature, even if we cannot explain it. But these dark lines have been -explained, and it is the very explanation of them, and the flood of -knowledge which has been acquired in the search after the explanation, -which makes the spectroscope one of the most valuable of astronomical -instruments. - -Many of us are aware of the magnificent generalizations by which our -countrymen, Professors Stokes and Balfour Stewart, and Ångström, -Kirchhoff and Bunsen, were enabled to explain those wonderful lines in -the solar spectrum. - -These lines in the solar spectrum are there because something is at work -cutting out those rays of light which are wanting, and they explained -this want by showing to us that around the sun and all the stars there -are absorbing atmospheres containing the vapours of certain substances -cooler than the interior of the sun or of the stars. - -These philosophers also showed us, that we can divide radiation and -absorption into four classes, and that we can have general radiation and -selective radiation, and general absorption and selective absorption, so -that the phenomena that we see in our chemical and physical laboratories -and our observatories may all be classed as general and selective -radiation, or general and selective absorption. - -Let us explain these terms more fully. Kirchhoff showed us that from -incandescent solid and liquid bodies we get a continuous spectrum; thus -from the carbon poles of an electric lamp we get a complete spectrum. -That is called a continuous spectrum, and it is an instance of -continuous radiation, which we get from the molecular complexity of -solids or liquids, and likewise, from dense gases or vapours. When we -examine vapours or gases which are not very dense we get an indication -of selective radiation—that is to say, the light one gets from these -substances, instead of being spread broadcast from the red to the -violet, will simply fall here and there on the spectrum; in the case of -one vapour we may get a yellow line—a yellow image of the slit—and in -the case of another vapour, we may get a green one; the light selects -its point of appearance, and does not appear all along the spectrum. - -[Illustration: - - FIG. 179.—Electric Lamp. _y_, _z_, wires connecting battery of 50 - Grove or Bunsen elements; G, H, carbon holders; K, rod, which stops - a clockwork movement, which when going makes the poles approach - until the current passes; A, armature of a magnet which by means of - K frees the clockwork when not in contact; E, electro-magnet round - which the current passes when the poles are at the proper distance - apart, causing it to attract the armature A. -] - -This selective radiation is due to a simplification of the molecular -structure of the vapours, the simpler states are less rich in -vibrations, and therefore instead of getting rays of _all_ -refrangibilities we only get rays of _some_. - -[Illustration: - - FIG. 180.—Electric Lamp arranged for throwing a spectrum on a screen. - D, lens; E E´, bisulphide of carbon prisms. -] - -Very striking experiments showing the spectra of bodies may be made with -an electric lamp armed with a condenser and a narrow slit; by means of a -lens this slit is magnified on a screen. Then one or two prisms of glass -containing bisulphide of carbon are placed in the beam after it has -traversed the lens, which draw out the image of the slit into a -spectrum. We can then place a piece of sodium on the lower carbon pole, -and when the poles are brought together it will be volatilized, and its -vapour rendered luminous. Its spectrum on the screen will be seen to -consist of four lines only, the yellow line being for more brilliant -than the rest. Sodium was selected on account of the simplicity of its -spectrum. - -[Illustration: - - FIG. 181.—Comparison of the line spectra of Iron, Calcium, and - Aluminium, with Common Impurities. Copy of a photograph, in which by - dividing the slit of the spectroscope into sections, and admitting - light from the various light sources through them in succession, - spectra of different elements are recorded on the same photographic - plate. -] - -If we put another metal, say calcium, in the place of the sodium, there -will appear on the screen the characteristic lines of that metal. A -number of distinct images of the slit in different colours is seen; if -we are well acquainted with the spectrum of any metal, and see it with -the spectroscope, it is easy to at once recognise it. Fig. 181 shows at -one glance the spectra (1) of iron, (2) of calcium, and (3) of -aluminium; and will clearly indicate the great difference there is -between the radiation spectra of the rare vapours of each of the -metallic elements. - -[Illustration: - - FIG. 182.—Coloured Flame of Salts in the flame of a Bunsen’s Burner. -] - -The electric light is only required where great brilliancy is essential, -as for showing spectra on a screen. A Bunsen’s burner is the best -instrument for studying the spectra of metallic salts. By its means the -nature of a salt can be easily studied with a hand spectroscope, and in -this way an almost infinitesimal quantity can be detected. - -These are instances of selective radiation. We will now turn to -absorption. If we first get a continuous spectrum from our lantern and -then interpose substances in the path of the beam, we can examine their -effects on the light. If we first use a piece of neutral-tinted glass, -which is a representative of a great many substances which do, for -stopping light, what solids and liquids do for giving light—namely, it -cuts off a portion of every colour; the spectrum on the screen will be -dimmed; here we have a case of general absorption. If, instead of this, -we hold in the beam a vessel containing magenta, a dark band in the -spectrum is seen, and if we put a test-tube in its place containing -iodine vapour, a number of well-defined lines pervading the spectrum is -observed. In these cases clearly, the magenta in one case, and the -iodine vapour in the other, have cut off certain colours, and so the -slit is not painted in these colours, and dark lines or bands appear. -These are instances of _selective absorption_, certain rays are selected -and absorbed, while others pass on unheeded. The easiest method of -performing these absorption experiments in the case of liquids is to -place the substance in a test-tube in front of the slit of the -spectroscope, as shown in Fig. 183, and point the collimator to a strong -light. - -Besides the absorption by liquids, the vapours of the metals also absorb -selectively, and if a tube containing a piece of sodium and filled with -hydrogen (so that the metal will not get oxidized) is placed in the path -of the rays, and the sodium heated, the spectrum is at first unaffected, -but as the sodium gets hot and its vapour comes off, we can mark its -effect on the spectrum. We see a dark line beginning to appear in the -yellow, finally the whole light of that particular colour is absorbed, -and we have a dark line in its place. To sum up then:— - -We get from solids, when heated, general radiation, and when they act as -absorbers, we get general absorption; from gases and vapours we get -selective radiation and selective absorption. - -[Illustration: - - FIG. 183.—Spectroscope arranged for showing Absorption. -] - -Now it at once strikes any one performing these experiments that the -dark line of yellow sodium appears in the same place in the spectrum as -the bright one, and this is so. When the absorption by sodium vapour is -examined by the spectroscope, it is then seen to consist of two -well-defined lines close together, and when the radiation is examined, -it is found to consist of two bright ones, and the absorption and -radiation lines, the dark and bright ones, are found to exactly agree in -position in the spectrum, showing that the substance that emits a -certain light is able to absorb that same light, so that it matters not -whether a body is acting as an absorber or radiator, for still we -recognize its characteristic lines. In 1814 Fraunhofer strongly -suspected the coincidence of the two bright sodium lines with the dark -lines in the sun; afterwards Brewster, Foucault, and Miller showed -clearly the absolute coincidence; and Professor Stokes in 1852 came to -the conclusion that the double line D, whether bright or dark, belonged -to the metal sodium, and that it absorbed from light passing through it -the very same rays which it is able, when incandescent, to emit. The -phenomena rendered visible to us by the spectroscope have their origin, -as we have said, in molecular vibration, and the reason of the identical -position of the light and dark lines, and indeed the whole theory of -spectrum analysis, may be shortly stated as follows:— - -The spectroscope tells us that when we break a mass of matter down to -its finest particles, or, as some people prefer to call them, ultimate -molecules, the vibrations of these ultimate parts of each different kind -of matter are absolutely distinct; so that if we get the ultimate -particle, say of calcium, and observe its vibrations we find that the -kind of vibration or unrest of one substance—of the calcium, for -instance—is different from the kind of unrest or mode of vibration—which -is the same thing—of another substance, let us say sodium. Mark well the -expression, ultimate molecule, because the vibrations of the larger -molecular aggregations are absolutely powerless to tell us anything -about their chemical nature. When we bring down a substance to its -finest state, and observe, by means of the prism, the vibrations it -communicates to the ether, we find that, using a slit in the -spectroscope and making these vibrations paint different images of the -slit, we get _at once_ just as distinct a series of images of the slit -for each substance as we should get a distinct _sequence_ of notes if we -were playing different tunes on a piano. - -Next, this important consideration comes into play—whenever any element -finds itself in this state of fineness, and therefore competent to give -rise to these phenomena, it will give rise to them in different degrees -according to certain conditions. The intensest form is observed when we -employ electricity. In a great many cases the vibrations may be rendered -very intense by heat. The heat of a furnace or of gas will, for -instance, in a great many cases, suffice to give us these phenomena; but -to see them in all their magnificence—their most extreme cases—we want -the highest possible temperatures, or better still, the most extreme -electric energy. What we get is the vibration of these particles -rendered visible to our eye by the bright images of the slit or by their -bright “lines.” - -But that is not the only means we have of studying these states of -unrest. We can study them almost equally well if, instead of dealing -with the radiation of light from the particles themselves, we interpose -them between us and a light source of more complicated molecular -structure, and hotter or more violently excited than the particles -themselves. From such a source the light would come to us absolutely -complete; that is to say, a perfectly complete gamut of waves of light, -from extreme red to extreme violet. When we deal with these particles -between us and a light-source competent to give us a continuous -spectrum, _then we find that the functions of these molecules are still -the same, but that their effect upon our retinas is different_. They are -not vibrating strongly enough to give us effectively light of their own, -but they are eager to vibrate, and, being so, they are employed, so to -speak, _in absorbing the light which otherwise would come to our eyes_. -So that whether we observe the bright spectrum of calcium or any other -metal, or the absorption spectrum under the conditions above stated, we -get lines exactly in the same part of the chromatic gamut, with the -difference that when we are dealing with radiation we get bright lines, -and when dealing with absorption we get dark ones. - -It was such considerations as these by which the presence of sodium was -determined in the sun. Soon followed the discovery of coincidence of -other dark lines with the bright lines of numbers of our elements, and -we had maps made by Kirchhoff, and Bunsen, and Ångström, in which almost -every dark line is mapped with the greatest accuracy. - -The dark lines in the spectra of the stars, and the light ones in -nebulæ, comets, and meteorites have also yielded to us a knowledge more -or less accurate of the elements of which these celestial bodies are -built up. - -These radiations and absorptions are the A B C of spectrum analysis, and -they have their application in every part of the heavens which the -astronomer studies with the spectroscope. But although it is the A B C -it is not quite the whole alphabet. After Kirchhoff and Bunsen had made -their experiments showing that we might differentiate between solids, -liquids, gases, and vapours, by means of their spectra, and say, here we -have such a substance, and there another, either by its spectrum when it -is incandescent or from the absorption lines produced by it on a -continuous spectrum when it is absorbing, Plücker and Hittorf showed -that not only were the spectra very different among themselves, but -there were certain conditions under which the spectrum of the same -substance was not always the same; and although they did not make out -clearly what it was, they showed that it depended either on the pressure -of the gas or vapour, or the density, or the temperature. And other -observations since then indicate that we get changes in spectra which -are due to pressure, and not to temperature _per se_; so that we have -another line of research opened to us by the fact, that not only are the -spectra of different substances different, but that the spectra of the -same substances are different under different conditions. - -[Illustration: - - FIG. 184.—Geissler’s Tube. -] - -Fig. 184 represents a hydrogen tube, called a Geissler’s tube—a glass -tube with hydrogen in it and two platinum wires, one passing into each -bulb, by which a current of electricity can be passed through the gas. -In this case we use hydrogen gas in a state of extreme tenuity. If now -one of these tubes be connected with a Sprengel pump, we can alter the -condition of tenuity at pleasure, either reducing the contents of the -tube or increasing them by admitting hydrogen from a receiver, by a tap -connected to the tubing of the air-pump; we can thus considerably -increase the amount of gas in the tube and bring it to something like -atmospheric pressure. We shall find the colour of the gas through which -the spark passes varies considerably as we increase the pressure of the -hydrogen in the tube. The hydrogen at starting is nearly as rare as it -can be, and if more hydrogen be let in we shall see a change of colour -from greenish white to red; the hydrogen admitted has increased the -pressure and the colour of the spark is entirely changed. It is a very -brilliant red colour, the colour of the prominences round the sun. - -It may be asked, probably, whether there are any applications of this -experiment to astronomical observation. It _is_ of importance to the -astronomer to get the differences of the spectra of the same substance -under different conditions, and it is found as important to get these -differences between the spectra of the same substance, as those between -the spectra of different substances. - -There is another experiment which will show another outcome of this kind -of research. Change of colour in the spark is accompanied by a -considerable difference in the spectrum—that is to say, it is clear, to -refer back to the colour of the hydrogen when the light was green, that -we should get some green in the spectrum, and when the light became red, -there would be some change or increase of light towards the red end of -the spectrum. We see that that is perfectly true; but there is not only -a change produced by the different pressures, as shown by the different -colours; but if we carry the analysis still further—if, instead of -dealing with the whole of the spectrum, we examine particular lines, we -find in some cases that there are very great changes in them. If, for -instance, we examine the bluish-green line given by hydrogen, we shall -find it increase in width as the pressure increases. This kind of effect -can be shown on the screen by means of the electric lamp. We place some -sodium on the carbon poles in the lamp, and have an arrangement by which -we can use either twenty or fifty cells at pleasure. The action of a -number of cells upon the vapour of sodium in the lamp is this: the more -cells we work with, the greater is the quantity of the sodium vapour -thrown out, and associated with the greater quantity of vapour is a -distinct variation of the light—in fact, an increase in the width and -brightness of the yellow lines on the screen. - -[Illustration: - - FIG. 185.—Spectrum of Sun-Spot. -] - -Now just to give an illustration of the profitable application of this: -we know, for instance, from other sources, strengthened by this, that in -certain regions of the sun, called sun-spots, there are greater -quantities of sodium vapour present than in others, or it exists there -at greater pressure. If that be so, we ought to get the same sort of -result from the sun as we get on the screen by varying the density of -the sodium vapour. That is so. We do get changes exactly similar to the -changes on the screen, only of course it is the dark lines we see, and -not the bright ones: the dark lines of sodium are widened out over a -sun-spot, Fig. 185, showing its presence in greater quantity, or at -greater pressure. - -[Illustration: - - FIG. 186.—Diagram explaining Long and Short Lines. -] - -Besides the widening of the lines due to pressure, there is something -else which must be mentioned. While experimenting with the spark taken -between two magnesium wires focussed on the slit of the spectroscope by -a lens, the lines due to the metal were found to be of unequal lengths. -Now, as the lines are simply images of the slit, the lengths of the -lines depend on the length of the slit illuminated, so that in this case -it appeared that the slit was not illuminated to an equal extent by all -the colours given out by magnesium vapour, but that the vapour existed -in layers round the wires, the lower ones giving more colours, and so -also more lines, than the upper ones further from the wire, as is -represented in Fig. 186; this is only meant to give an idea of the -thing, and is not, of course, exactly what is seen. S is the slit of the -spectroscope, P the image of one of the magnesium poles; the other, -being at some little distance away, does not throw its image on the -slit, and therefore does not interfere. The circles shown are intended -to represent the layers of vapour giving out the spectrum; on the right -the lower layers give A, B, and C, the next A and B, and the upper ones -only B. Now we may reason from this that the layers next the poles are -denser than those further off, and give a more complicated spectrum than -the others; and also, if the quantity of vapour of any metal is small, -we may only get just these longest lines. - -Of late, experiments have been made in England on other metals—for -instance, aluminium and zinc, and their compounds; and it is found that, -when the vapour is diluted, as it were, one gets only the longest line -or lines; and in the compounds, where the bands due to the compound -compose the chief part of the spectrum, the longest line or lines of the -metal only appear. Now what is the application of this? In the sun are -found some of the dark lines of certain metals, but not all; for -instance, there are two lines in the solar spectrum corresponding to -zinc, but there are twenty-seven bright lines from the metal when -volatilized by the electric spark. Why should not these also have their -corresponding dark lines in the sun? The answer is, that the -non-corresponding lines of the metal are the short ones, and only exist -close to the metal where the vapour is dense; and in the sun the density -is not sufficient to give these lines. Here, then, we have at once a -means of measuring the _quantity_ of vapour of certain metals composing -the sun. It was thought that aluminium was not in the sun, as only two -lines of the metal out of fourteen corresponded to black lines in the -solar spectrum. It is now known that these two are the longest lines, -and that aluminium probably exists in the sun, and zinc, strontium, and -barium must also be added. These probably exist in small quantities, -insufficiently dense to give all the lines seen from a spark in the air. - -[Illustration: - - FIG. 187.—Comparison of the Absorption Spectrum of the Sun with the - Radiation Spectra of Iron and Calcium, with Common Impurities. -] - -There is also another quite distinct line of inquiry in which the -spectroscope helps us. - -Imagine yourself in a ship at anchor, and the waves passing you, you can -count the number per minute; now let the vessel move in the direction -whence the waves come, you would then meet more waves per minute than -before; and if the vessel goes the other way, less will pass you, and by -counting the increase or decrease in the number passing, you might -estimate the rates at which you were moving. Again, suppose some moving -object causes ripples on some smooth water, and you count the number per -minute reaching you, then if that object approach you, still moving, and -so producing waves at the same rate, the number of ripples a minute will -increase, and they will be of course closer together; for as the object -is approaching you, every subsequent ripple is started, not from the -same place as the preceding one, but a little nearer to you, and also -nearer to the one preceding, on whose heels it will follow closer. By -the increase in the number of ripples, and also the decrease in the -distance between them, one can estimate the rate of motion of the object -producing them, for the decrease in distance between the ripples is just -the distance the object travels in the time occupied between the -production of two waves, which was ascertained when the object was -stationary. - -Now let us apply this reasoning to light. Light, we now hold, is due to -a state of vibration of the particles of an invisible ether, or -extremely rare fluid, pervading all space; and the waves of light, -although infinitesimally small, move among these particles. - -Now we know that it is the length of the waves of light which determines -their refrangibility or colour, and therefore anything that increases or -diminishes their length alters their place in the spectrum; and as waves -of water are altered by the body producing them moving to or from the -observer, so the waves of light are changed by the motion of the -luminous body; and this change of refrangibility is detected with the -spectroscope. By measuring the wave-length of let us say the F line, and -the new wave-length as shown by the changed position, we can estimate -the velocity at which the light source is approaching or receding from -us. - -This application, as we shall see in the next chapter, enables us to -determine the rate at which movements take place in the solar -atmosphere. It also gives us the power of measuring the third -co-ordinate of the motion of stars. We can, by the examination of their -positions, measure the motion at right angles to our line of sight, and -so determine their motion with reference to the two co-ordinates, R.A. -and Dec., or Lat. and Long., and just in the same way as we can measure -the velocity of the solar gases to or from us, so we can measure the -motion of the stars to or from us, thereby giving us the third -co-ordinate of motion. - -It need scarcely be said that by the introduction of the spectroscope a -new method of observation, and a new power of gaining facts, has dawned, -and the sooner it is used all over the world with the enormous -instruments which are required, the better it will be for science. - - * * * * * - -These then are some of the chief points of spectroscopic theory which -makes the spectroscope one of the most powerful instruments of research -in the hands of the modern astronomer. - - - - - CHAPTER XXIX. - THE CHEMISTRY OF THE STARS (CONTINUED): THE TELESPECTROSCOPE. - - -We have now to speak of the methods of using these spectroscopes for the -purpose of astronomical observations. For a certain class of -observations of the sun no telescope is necessary, but some special -arrangements have to be made. - -Thus while Dr. Wollaston and Fraunhofer were contented with simple -prisms, when Kirchhoff observed the solar spectrum, and made his careful -maps of the lines, he used an instrument like Fig. 173, and for the -purpose of comparing the spectrum of the sun with that of each of the -chemical elements in turn, he used a small reflecting prism, covering -one-half of the slit, Fig. 188, so that any light thrown sideways on to -the slit would be caught by this prism, and reflected on to the slit as -if it came from an object near the source of light at which the -spectroscope is pointing, so that one-half of the slit can be -illuminated by the sun, while the other is illuminated by another light; -and on looking through the eyepiece one sees the two spectra, one above -the other; so that we are able to compare the lines in the two spectra. - -The sunlight, whether coming from the sun itself or a bright cloud, is -reflected, into the comparison prism, Fig. 189, of the spectroscope. An -instrument called a heliostat can be used for this, reflecting the light -either directly into the prism or through the medium of other -reflectors. - -[Illustration: - - FIG. 188.—Comparison Prism, showing the path of the Ray. -] - -The heliostat is a mirror, mounted on an axis, which moves at the same -rate as the sun appears to travel, so that wherever the sun is, the -reflector, once adjusted, automatically throws the beam into the -instrument, so that the light of the moving sun can be observed without -moving the spectroscope. - -[Illustration: - - FIG. 189.—Comparison Prism fixed in the Slit. -] - -An average solar spectrum is thus obtained, and, by means of a prism -over one-half of the slit, it was quite possible for Kirchhoff and -Bunsen to throw in a spectrum from any other source for comparison, and -so they compared the spectra of the metals and other elements with the -solar spectrum, and tested every line they could find in the spectra. -They first found that the two lines of sodium corresponded with the two -lines called D in the spectrum, then that the 460 lines of iron -corresponded in the main with dark lines in the solar spectrum; and so -they went on. - -[Illustration: - - FIG. 190.—Foucault’s Heliostat. -] - -There is, however, a method of varying the attack on this body -altogether, by means of the spectroscope and telescope. We saw that -Kirchhoff and Bunsen contented themselves with an average spectrum of -the sun—that is to say, they dealt with the general spectrum which they -got from the general surface of the sun, or reflected from a cloud or -any other portion of the sky to which they might direct the reflector; -but by means of some such an arrangement as is shown in Fig. 192, we can -arrange our spectroscope so that we shall be able to form _an image_ of -the sun by the object-glass of a telescope, on the slit, and allow it to -be immersed in any portion of the sun’s image we may choose. We then -have a delicate means of testing what are the spectroscopic conditions -of the spots and of those brighter portions of the sun which are called -faculæ, and the like. And it is known that, by an arrangement of this -kind, it is even possible to pick up, without an eclipse, those strange -things which are called the red prominences, or the red flames, which -have been seen from time to time during eclipses. - -If we wish to observe any of the other celestial bodies, we must employ -a telescope and form an image on the slit, or else use the heavenly body -itself as a slit. In the former case spectroscopes must be attached to -telescopes, and hence again they must be light and small, unless a -siderostat is employed. - -In the latter case the prism is placed outside the object-glass, and the -true telescope becomes the observing telescope. - -Fraunhofer, at the beginning of the present century, was the first to -observe the spectra of the stars by placing a large prism outside the -object-glass, three or four inches in diameter, of his telescope, and so -virtually making the star itself the slit of the spectroscope; and in -fact he almost anticipated the arrangement of Mr. Simms, and satisfied -the conditions of the problem. The parallel light from the star passed -through the prism, and by means of the object-glass was brought to a -focus in front of the eyepiece, so that the spectrum of the star was -seen in the place of the star itself. - -This system has recently been re-invented, and the accompanying woodcut, -Fig. 191, shows a prism arranged to be placed in front of an -object-glass of four inches aperture. It is seen that the angle of the -prism is very small. The objection to this method of procedure is that -the telescope has to be pointed away from the object at an angle -depending upon the angle of the prism. - -[Illustration: - - FIG. 191.—Object-glass Prism. -] - -In the other arrangement we have the thing managed in a different way: -we have the object-glass collecting the light from the star and bringing -it to a focus on the slit, and it then passes on to the prisms, through -which the light has to pass before it comes to the eye. In this -combination of telescope and spectroscope we have what has been called -the _telespectroscope_; one method of combination is seen in the -accompanying drawing of the spectroscope attached to Mr. Newall’s great -refractor; but any method will do which unites rigidity with lightness -and allows the whole instrument to be rotated with smoothness. - -[Illustration: - - FIG. 192.—The Eyepiece End of the Newall Refractor (of 25 inches - aperture), with Spectroscope attached. -] - -For solar observation, as there is light enough to admit of great -dispersion, many prisms are employed, as shown in Fig. 192; or the -prisms may be made so tall that the light may be sent backwards and -forwards many times by means of return prisms, to which reference has -been already made. - -For the observation of those bodies which give a small amount of light, -fewer prisms must be used, and arrangements are made for the employment -of reference spectra, _i.e._, to throw the light coming from different -chemical elements into the spectroscope, in order that we may test the -lines; whether any line of Sirius, for instance, is due to the vapour of -magnesium, as Kirchhoff tested whether any line in the sunlight was -referable to iron or the other vapours which he subsequently studied. - -[Illustration: - - FIG. 193.—Solar Spectroscope (Browning’s form). -] - -[Illustration: - - FIG. 194.—Solar Spectroscope (Grubb’s form). -] - -[Illustration: - - FIG. 195.—Side view of Spectroscope, showing the arrangement by which - the light from a spark is thrown into the instrument by means of the - reflecting prism, _e_, by a mirror F. (Huggins.) -] - -[Illustration: - - FIG. 196.—Plan of Spectroscope. T, eyepiece end of telescope, B - interior tube, carrying A, cylindrical lens; D, slit of - spectroscope; G, collimating lens; _h h_, prisms; Q, micrometer. - (Huggins.) -] - -[Illustration: - - FIG. 197.—Cambridge Star Spectroscope Elevation. -] - -[Illustration: - - FIG. 198.—Cambridge Spectroscope Plan. -] - -These are shown in Fig. 195. _e_ is a reflecting prism, and F is another -movable reflector to reflect the light from a spark passed between two -wires of the metal to be compared, and to throw it on the prism, which -reflects the light through the slit of the spectroscope to the prisms -and eye; if the instrument were in perfect adjustment and turned on a -star, and a person were to place his eye to the spectroscope, he would -see in one-half of the field of view the spectrum of the star with dark -lines, and in the other half the spectrum of the vapour with its bright -lines; and if he found the bright lines of the vapour to correspond with -any particular dark line of the spectrum of the star, he would know -whether the metal exists at that star or not; so this little mechanical -arrangement at once tells him what there is at the star, whether it be -iron or anything else. - -In Figs. 197 and 198 is shown another form of stellar spectroscope, that -of the Cambridge (U.S.) observatory; it is the same in principle as that -just described. - -A direct vision star spectroscope is shown in Fig. 199. - -[Illustration: - - FIG. 199.—Direct-vision Star Spectroscope. (Secchi.) -] - -A new optical contrivance altogether has to be used when star spectra -are observed. - -The image of a star is a point, and if focussed on the slit will of -course give only an extremely narrow spectrum; to obviate this a -cylindrical lens is employed, which may be placed either before the slit -or between the eyepiece and the eye. If placed before the slit, it draws -out the image of the star to a fine line which just fits the slit, so -that a sufficient portion of the slit is illuminated to give a spectrum -wide enough to show the lines, or the slit may be dispensed with -altogether. - -In stellar observations, when the cylindrical lens is used in front of -the slit, special precautions should be taken so as to secure that the -position of the cylindrical lens and slit in which the spectrum appears -brightest should be used. In any but the largest telescopes the spectra -of the stars are so dim that unless great care is used the finer lines -will be missed. A slit is not at all necessary for merely seeing the -spectra; indeed they are best seen without one. If a slit be used, it -should lie in a parallel and not in a meridian; under these -circumstances slight variations in the rate of the clock are of no -moment. - -In this and in other observational matters it is good to know what to -look for, and there are great generic differences between the spectra of -the various stars. In Fig. 200 are represented spectra from the -observations of Father Secchi. In the spectrum of Sirius, a -representative of Type I., very few lines are represented, but the lines -are very thick; and stars of this class are the easiest to observe. - -Next we have the solar spectrum, which is a representative of Type II., -one in which more lines are represented. In Type III. fluted spaces -begin to appear; and in Type IV., which is that of the red stars, -nothing but fluted spaces is visible, and this spectrum shows that there -is something different at work in the atmosphere of those red stars to -what there is in the simpler atmosphere of the first—of Type I. These -observations were first attempted, and carried on with some success, by -Fraunhofer, and we know with what skill and perseverance Mr. Huggins has -continued the work in later years, even employing reference spectra and -determining their chemical constitution as well as their class. - -[Illustration: - - FIG. 200.—Types of Stellar Spectra (Secchi). -] - -We need scarcely say that the same arrangement, minus the cylindrical -lens, is good for observing the nebulæ and such other celestial objects -as comets and planets. - -For all spectrum work, it has to be borne in mind that the best -definition is to be had when the actual colour under examination is -focussed on the slit. With reflectors, of course, there is no difference -of focus for the different colours. As the best object-glasses are -over-corrected for chromatic aberration, the red focus is generally -inside and the blue one outside the visual one. It is not necessary to -move the whole spectroscope to secure this; all collimators should be -provided with a rack and pinion giving them a bodily movement backwards -and forwards. - -This precaution is of especial importance in the case of solar -observations, to which we have next to refer. - -If in any portion of the sun’s image on the plate carrying the slit we -see a spot, all we have to do is to move the telescope, and with it of -course the sun’s image, so that the slit is immersed in the image of the -spot; if, however, we wish to observe a bright portion of the sun, we -can immerse this slit in the bright portion. Again, if we wish to -examine the chromosphere of the sun, we simply have to cover half the -slit with the sun, and allow the other part of the slit to be covered by -any surroundings of the sun, and, so to speak, to fish round the edge; -the lower half of the slit, say, is covered by the sun itself, and -therefore we shall get from that half the ordinary solar spectrum; the -upper half is, however, immersed in the light reflected from our -atmosphere, giving a weak solar spectrum, so that we get a bright and -feeble spectrum side by side. But besides the atmospheric light falling -on the upper part of the slit, the image of anything surrounding the sun -falls there also, and its spectrum is seen with the faint solar -spectrum, and we find there a spectrum of several bright lines. Now, as -an increase of dispersive power will spread out a continuous spectrum -and weaken it, we may almost indefinitely weaken the atmospheric -spectrum, and so practically get rid of it, still leaving the -bright-line spectrum with the lines still further separated; so that if -it were not for our atmosphere, we should get only the spectrum of the -sun and that of its surroundings; one a continuous spectrum with black -lines, and the other consisting of bright lines only. - -Now if we suppose these observations made—if the precaution to which we -have alluded be not taken, the spectrum of the sun-spot will differ but -little from that of the general surface, and the chromospheric lines -will scarcely be visible. - -If the precaution _be_ taken, in the case of the spot it will be found -that every one of the surrounding pores is also a spot; and if the air -be pure the spectrum will be full of hard lines running along the -spectrum, just like dust lines, but emphatically not dust lines, because -they change with every movement of the sun. The figure of the spot -spectrum on p. 415 will show what is meant. Fig. 201 will show the -appearance of the chromospheric line when the blue-green light is -exactly focussed; the boundary of the spectrum of the photosphere -approaches in hardness that at the end of the slit. - -By measuring the lengths of the lines we can estimate the height of the -vapours producing them; we find from this that magnesium is usually -present to a height of a few hundred miles, and that hydrogen extends to -between 3,000 and 4,000 miles; in some positions of the slit the -hydrogen lines are seen to start up to great heights, showing the -presence of flames or prominences extending in height to sometimes -100,000 miles. - -[Illustration: - - FIG. 201.—Part of Solar Spectrum near F. -] - -If, without changing the focus, we open the slit wider, and throw the -sun’s image just off the slit, so that the very bright continuous -spectrum no longer dazzles the eye, we shall be able to see these flames -whenever they cross the opening, for the image of the slit is focussed -on the eye, and the sun and its flames are focussed on the slit, so if -we virtually remove the slit by opening it wide, we see the flames; -still the limit of opening is soon approached, and the flood of -atmospheric light soon masks them. The red hydrogen line of the spectrum -is the best for viewing them, although the yellow or blue will answer. -We may also place the sun’s image so that the slit is tangential to it, -in which case a greater length of the hydrogen layer, or chromosphere, -as it is called, is visible, although its height is limited by the -opening of the slit. - -By these means we are able to view a small part of the chromosphere at a -time, and to go all round the sun in order to obtain a daily record of -what is going on. If, however, we throw the image of the sun on a disc -of metal of exactly the same size, we eclipse the sun, but allow the -light of the chromosphere to pass the edge of the disc; this of course -is masked by the atmospheric light, but if the annulus, or ring of -chromosphere, be reduced sufficiently small, it can be viewed with a -spectroscope in the place of a slit, in fact it is virtually a circular -slit on which the chromosphere rests. By this means nearly the whole of -the chromosphere can be seen at once. This is accomplished as follows:— - -The image of the sun is brought to focus on a diaphragm having a -circular disk of brass in the centre, of the same size as the sun’s -image, so that the sun’s light is obstructed and the chromospheric light -is allowed to pass. The chromosphere is afterwards brought to a focus -again at the position usually occupied by the slit of the spectroscope; -and in the eyepiece is seen the chromosphere in circles corresponding to -the “C” or other lines. - -A lens is used to reduce the size of the sun’s image, and keep it of the -same size as the diaphragm at different times of the year; and other -lenses are used in order to reduce the size of the annulus of light to -about ⅛ inch, so that the pencils of light from either side of it may -not be too divergent to pass through the prisms at the same time, in -order that the image of the whole annulus may be seen at once. There are -mechanical difficulties in producing a perfect annulus of the required -size, so one ½ inch in diameter is used, and can be reduced virtually to -any size at pleasure. - -From what has been said it is easy to see that we really now get a new -language of light altogether, and a language which requires a good deal -of interpretation. - -[Illustration: - - FIG. 202.—Distortions of F line on Sun. -] - -We have still, indeed, to consider some curious observations which are -now capable of being made every day when anything like a sun-storm is -going on, by means of the arrangement in which the spectroscope simply -deals with the light that comes from a small portion of the sun instead -of from all the sun. If we make the slit travel over different portions -of the sun on which any up-rushes of heated material, or down-rushes of -cold material, or other changes, are going on from change of surface -temperature, the Fraunhofer lines, which we have before shown to be -straight, instead of being so, appear contorted and twisted in all -directions. On the other hand, if we examine the chromosphere under the -same conditions, we find the bright lines contorted in the same manner. -The usually dark lines, moreover, sometimes appear bright, even on the -sun itself; sometimes they are much changed in their relative positions -with reference to the solar spectrum. The meaning of these contortions -has already been hinted at (p. 420). - -It was there shown that every colour, or light of every refrangibility, -is placed by the prisms in its own particular position, so if a ray of -light alters its position in the spectrum it must change its colour or -refrangibility, so the light producing the F line in the one case, and -the absent light producing the dark line in the other, differ slightly -in colour, or are rather more or less refrangible than the normal light -from hydrogen. In the case when the F line is wafted towards the blue -end of the spectrum, the light falling on the slit is rather more -refrangible than usual; and in the middle drawing, Fig. 203, where the F -line bifurcates, the slit is supplied with two kinds of light differing -slightly in refrangibility. Not only does the light radiated by a -substance change in this way, but the light absorbed by that substance -also changes, hence the contortions of the black lines are due to a -similar cause. - -[Illustration: - - FIG. 203.—Displacement of F line on edge of Sun. -] - -Here, therefore, we have evidence of a change of refrangibility, or -colour, of the light coming from the hydrogen surrounding the sun. This -change of refrangibility is due to the motion of the solar gases, as -explained in the last chapter. - -So we find that the hydrogen producing the light giving us one of the -forms of the F line, shown in Fig. 203, is moving towards us at the rate -of 120 miles a second, while that giving the other form is moving away -from us. - -Let us see how these immense velocities are estimated. By means of -careful measurements, Ångström has shown on his map of the solar -spectrum the absolute length of the waves of light corresponding to the -lines; thus the length of the wave of light of hydrogen giving the F -line is 4860/10000000 of a millimeter. In Fig. 203 the dots on either -side of the F line show the positions, where light would fall, if it -differed from the F light by 1, 2, 3, or 4 ten-millionths of a -millimeter, so that in the figure the light of that part of the line -wafted over the fourth dot is of a wave-length of 4 ten-millionths of a -millimeter less than that of the normal F light, which has a wave-length -4860/10000000 of a millimeter. The F light therefore has had its -wave-length reduced by 4/4860 = 1/1215 part; and in order that each wave -may be decreased by this amount, the source of the light must move -towards us with a velocity of 1/1215 of the velocity of light, which is -186,000 miles per second, and 1/1215 of 186,000 is about 150; this then -is the velocity, in miles per second, at which the hydrogen gas must -have been moving towards us in order to displace the light to the fourth -dot, as shown in the figure. - - - - - CHAPTER XXX. - THE TELEPOLARISCOPE. - - -In previous chapters we have considered the lessons that we can learn -from light—from the vibrations of the so-called ether—when we put -questions to it through various instruments as interpreters. There is -still another method of putting questions to these same vibrations, and -the instrument we have now to consider is the Polariscope. - -The spectroscope helped us to inquire into the lengths of the -luminiferous waves; from the polariscope we learn whether there is any -special plane in which these waves have their motion. - -The polariscope is an instrument which of late years has become a useful -adjunct to the telescope in examining the light from a body in order to -decide whether it is reflected or not, and to ascertain indirectly the -plane in which the rays reflected to the eye lie. The action of the -instrument depends upon the fact that light which consists solely of -vibrations perpendicular to a given plane is said to be completely -polarized in that plane. Light that contains an excess of vibrations -perpendicular to a given plane is said to be partially polarized in that -plane. - -It was Huyghens that discovered the action of Iceland spar in doubly -refracting light; and the light which passed the crystal was called -_polarized light_ at the suggestion of Newton, who, it must be -remembered, looked upon light as something actually emitted from -luminous bodies; these projected particles were supposed, after passage -through Iceland spar, to be furnished with poles analogous to the poles -of a magnet, and to be unable to pass through certain bodies when the -poles were not pointing in a certain direction. It was not until the -year 1808 that Malus discovered the phenomenon of polarization by -reflection. He was looking through a double-refracting prism at the -windows of the Luxembourg Palace, on which were falling the rays of the -setting sun. On turning the prism he noticed the ordinary and -extraordinary images alternately become bright and dark. This phenomenon -he at once saw was in close analogy to that which is observed when light -is passed through Iceland spar. At first he thought it was the air that -polarized the light, but subsequent experiments showed him that it was -due to reflection from the glass. - -Let us examine some of the phenomena before we proceed to show the use -astronomers make of them. - -It is the property of some crystals, such as tourmaline, when cut -parallel to a given direction, called the optic axis of the crystal, to -absorb all vibrations or resolved parts of vibrations perpendicular to -this line, transmitting only vibrations parallel to it. - -A similar absorption of vibrations perpendicular to a given direction -may be effected by various other combinations, of which one, Nicol’s -prism, is in most common use. Any of these arrangements may be used as -an analyzer with the telescope, for determining whether the light is -completely or partially polarized, and in either of these cases which is -the plane of polarization. The plane containing the direction of the -rays and the line in the analyzer to which the transmitted vibrations -are parallel, is called the plane of analyzation: all the light which -reaches the eye consists of vibrations in the plane of analyzation. As -we rotate the analyzer, we rotate equally the plane of analyzation. If -we find a position of the plane of analyzation for which the light -received by the eye is a maximum, we know that the light from the object -is partially or completely polarized in a plane perpendicular to the -plane of analyzation when in this position. To determine whether the -polarization is partial or complete, we must turn the analyzer through -an angle of 90° from this position: if we now obtain complete darkness, -we know that there are no vibrations having a resolved part parallel to -the plane of analyzation in this position, or that the light is -completely polarized in this plane: if there be still some light -visible, the polarization is only partial. - -To explain this a little more fully, we may compare the vibrations or -waves of light to waves of more material things: we may have the -vibrating particles of the ether moving up and down as the particles do -in the case of a wave of water, or the particles may move horizontally -as a snake does in moving along the ground. We may consider that -ordinary light consists of vibrations taking place in all planes, but if -it passes through or is reflected by certain substances at certain -angles, the vibrations in certain planes are, as it were, filtered out, -leaving only vibrations in a certain plane. This light is then said to -be polarized, and its plane of polarization is found by its power of -passing through polarizing bodies only when they are in certain -positions. - -If, for instance, a ray of ordinary light is passed through a crystal of -tourmaline, the vibrations of the filtered ray will only lie in one -plane; if then a second crystal of tourmaline be held in a similar -position to the first, the ray will pass through it unaffected; but if -it be turned through a quarter of a circle about the ray as an axis, the -ray will no longer be able to pass, for being in a position at right -angles to the first, it will filter out just the rays that the first -allows to pass. For illustration, take a gridiron: if we attempt to pass -a number of sheets of paper held in all positions through it, only those -in a certain plane, viz., that of the rods forming the gridiron, could -be passed through, and those that would go through would also go through -any number of gridirons held in a similar position. But if another -gridiron be placed so that its bars cross those of the first, the sheets -of paper could no longer pass, and it is evident that if we could not -see or feel the paper, we could tell in what plane it was by the -position in which the gridiron must be held to let it pass, and having -found the paper to be, say horizontal, we know that the bars of the -first gridiron are also horizontal. So with light, we can analyze a ray -of polarized light and say in what plane it is polarized. - -The example of the gridiron, however, does not quite represent the -action of the second crystal; for if the bars of the second gridiron are -turned a very small distance out of coincidence with those of the first, -the sheets of paper would be stopped; but with light, the intensity of -the ray is only gradually diminished, until it is finally quenched when -the axes of the crystals are at right angles to each other. - -[Illustration: - - FIG. 204.—Diagram showing the Path of the Ordinary and Extraordinary - Ray in Crystals of Iceland Spar. -] - -Light is polarized by transmission and by reflection. We have already, -when we were discussing the principle involved in the double-image -micrometer, seen how a crystal of Iceland spar divides a ray into two -parts at the point of incidence. Now these two rays are _oppositely -polarized_, that is to say, the vibrations take place in planes -perpendicular to each other; the vibrations of the incident light in one -plane are refracted more than the vibrations in the opposite plane, and -we have therefore two rays, one called the ordinary ray, and the other -the extraordinary ray. Fig. 204 shows a ray of light, S I, incident on -the first crystal at I; it is then divided up into the ordinary ray I R -and the extraordinary one I R´; a screen is then interposed, stopping -the extraordinary ray and allowing the ordinary one to fall on the -second crystal at I. If then this crystal be in a similar position to -the first, this ray, vibrating only in one plane, will pass onwards as -an ordinary ray, I R; there being no vibrations in the perpendicular -plane to form an extraordinary ray, there will be only one circle of -light thrown on the screen at O by the lens. But, if the second crystal -be turned round the line S S as an axis, the plane of vibration of the -ray falling on its surface will no longer coincide with the plane in -which an ordinary ray vibrates in the crystal, and it therefore becomes -split up into two, one vibrating in the plane as an ordinary ray, and -the other in that of an extraordinary ray; we have therefore the ray I -R´ in addition to the first, and consequently a second circle on the -screen at E´. As the crystal rotates, the plane of extraordinary -refraction becomes more and more coincident with the plane of vibration -of the incident ray, until, when it has revolved through 90°, it -coincides with it exactly; it then passes through totally as an -extraordinary ray, and as the refractive power of the crystal is greater -for vibrations in this plane, we get all the light traversing the -direction I R and falling on the screen at E´, and there being then no -light ordinarily refracted, the circle O disappears. Fig. 205 shows the -relative brightness of the circles E and O as they revolve round the -centre S of the screen, the images produced by the ordinary and the -extraordinary ray becoming alternately bright and dark as the crystal is -rotated. Fig. 206 shows the images on the screen when the ordinary ray -is stopped by the first screen instead of the extraordinary one. - -[Illustration: - - FIG. 205.—Appearance of the Spots of Light on the Screen shown in the - preceding Figure, allowing the ordinary ray to pass and rotating the - second Crystal. -] - -[Illustration: - - FIG. 206.—Appearance of Spots of Light on Screen on rotating the - second Crystal, when the extraordinary ray is allowed to pass - through the first Screen. -] - -A crystal of tourmaline acts in a like manner to Iceland spar, but the -ordinary ray is rapidly absorbed by the crystal, so that the -extraordinary ray only passes. There is an objection to the use of it, -as it is not very transparent, and a Nicol’s prism is now generally used -for polarizing light. It is constructed out of a rhombo-hedron of -Iceland spar cut into two parts in a plane passing through the obtuse -angles, and the two halves are then joined by Canada balsam. The -principle of construction is this: the power of refracting light -possessed by Canada balsam is less than that possessed by Iceland spar -for the ordinary ray, and greater in the case of the extraordinary ray; -in consequence, the ordinary ray is reflected at the surface of -junction, while the extraordinary ray passes onwards through the -crystal. - -[Illustration: - - FIG. 207.—Instrument for showing Polarization by Reflection. -] - -It is manifest then that if two Nicols are used instead of two simple -crystals, represented in Fig. 204, there will be only one spot of light -on the screen, which is due to the extraordinary ray, and as in certain -positions this no longer passes (for the ordinary ray, which appears in -the place of the extraordinary when the crystal is used, cannot pass -through the Nicol), no light at all passes in such positions, so that we -can use the second Nicol as an analyzer to ascertain in what plane the -light is polarized. - -Light is also polarized by reflection from the surface of a transparent -medium. When a ray of ordinary light falls on a plate of glass at an -angle of 54° 55´ with the normal, the reflected ray is perfectly -polarized, and at other inclinations the polarization is incomplete. -Here then is polarization by reflection. Fig. 207 shows an apparatus for -producing this phenomenon. The light foiling on the first mirror from E -is reflected through the tube as a polarized beam, and this is analyzed -by the other mirror (I), whose plane can be rotated round the axis of -the tube. The angle of polarization differs with different substances -according to their refractive power, for polarization of the reflected -ray is perfect only when the angle of incidence is such that the -reflected ray is at right angles to the refracted one. - -As a result of what we have said, the light of the sun reflected from -the surface of water or from the glass of a window is polarized, and -although it may be dazzling to the eye, it is reduced, or even entirely -cut off, when falling at the polarizing angle, by looking through the -transparent Nicol’s prism or plate of glass held in certain positions -and acting as an analyzer. On rotating the analyzer there is an -alternation of intensity, and by looking at the window through a crystal -of Iceland spar as an analyzer, two images would be seen which would -alternate in brightness as the crystal is rotated. So also there is a -difference in the intensity of the light from the sky when the analyzer -is rotated, showing that the light reflected from the watery and dust -particles in the air is polarized, and by the position of the analyzer -we find that it is polarized in the plane we should expect if it be, as -it is, reflected from the sun. - - * * * * * - -It will be asked, however, what is the astronomical use of determining -whether light has an excess of vibrations in any given direction? - -To this we may reply that light that is reflected from any body is -generally partially polarized in the plane of reflection, and that if we -find that the light received from any body is partially polarized in a -given plane, we may conclude that it has very likely been reflected in -that plane. - -Hence then in the case of any celestial body the origin of the light of -which is doubtful, the polariscope tells us whether the light is -intrinsic or reflected. - -It tells us more than this, it tells us the plane in which the -reflection has taken place. As the polarization takes place, when it -does take place, at the celestial body, all we have to do is to attach -an analyzer to the telescope. - -A careful application of the above principles has shown that the light -from the sun’s corona is partially polarized, and in the same plane as -it would be if reflected from small particles in the neighbourhood of -the sun: so also a portion of the light of Coggia’s Comet was found to -be polarized, and therefore we say that it reflected sunlight in -addition to its own proper light. - -In what has been hitherto said we have only considered the use of a -Nicol, or glass plates, or crystal of Iceland spar as an analyzer, and -by the variation of brightness the presence and plane of polarization -have been determined; but unless the polarization is somewhat decided, -it could not be detected by this method. Advantage is therefore taken of -the fact that a plate of quartz rotates the plane of polarization of a -ray passing through it, and it rotates the more refrangible colours more -than the others, and some crystals rotate the plane one way, and others -in the opposite direction: the crystals are therefore called -respectively right- and left-handed quartz; the thicker the quartz the -greater the angle through which the plane of polarization is twisted. - -This supplies us with a most delicate apparatus, which we next describe. -A crystal of right- and a crystal of left-handed quartz are taken and -cut to such thickness that a ray of any colour, say green, has its plane -turned through 90° on passing through each of them. They are then cut -into the form of a semicircle and placed side by side. Any change of the -angle of polarization will now affect each plate differently. In one -plate the colours will change from red to violet, in the other from -violet to red. - -If now a ray of polarized light, say vibrating in a vertical plane, -falls on them, the green rays will have their plane of vibration turned -through 90° by each crystal, and the vibration of the green from both -crystals will then be in the horizontal plane. Nicol’s prism interposed -between the quartz plates and the eye, so as to allow horizontal -vibrations to pass, will show the green from both crystals of equal -intensity; the rays of other colours, being turned through a greater or -less angle than 90°, will not be vibrating horizontally, and will -therefore only partially pass through, so green will be the prevailing -colour. If now the plane of vibration of the original ray be turned a -little out of the vertical, the ray, on the red side of the green, will -appear in one half, and that on the violet side of the green in the -other: so that immediately the plane of polarization changes, the plates -transmit a different colour, and the apparatus must be twisted round -through just the same angle as the polarized ray in order to get the -crystals of the same colour. It is therefore obvious that the angle made -by a polarized ray with a fixed plane is easily ascertained in this -manner. - -There is also another instrument for detecting polarization which is -perhaps more commonly used than the biquartz: it is generally called -Savart’s analyser, and is extremely sensitive in its action. On looking -through it at any object emitting ordinary light, the white circle of -light limited by the aperture of the instrument only is seen; but if any -polarized light should happen to be present, a number of parallel bands, -each shaded from red to violet, make their appearance; on rotating the -instrument a point is found when a very slight motion causes the bands -to vanish and others to appear in the intermediate spaces, and knowing -the position required for the change of bands with light polarized in a -known plane, say the vertical plane, it is easy to find how far the -plane of polarization of any ray is from the vertical, by the number of -degrees through which the instrument must be turned to change the bands. -The construction of the instrument, and especially its action, is not -easy to understand without a considerable knowledge of optics, but it -may be stated that a plate of quartz is cut, in a direction inclined at -45° to its axis, into two parts of the same thickness; one part is then -turned through a right angle and placed with the same surfaces in -contact as before; these are fixed in the instrument so that the light -shall traverse them perpendicularly to the plane of section; the light -then passes through a Nicol’s prism as an analyser to the eye. The lines -observed, “black centred” in one position, and “white centred” in the -position at right angles to this, are always in the direction before -referred to. The delicacy of the test supplied by this arrangement -increases as this direction is more nearly parallel or perpendicular to -the plane of polarization of the ray under examination. - - - - - CHAPTER XXXI. - CELESTIAL PHOTOGRAPHY.—THE WAYS AND MEANS. - - -We come now last of all to that branch of the work of the physical -astronomer which bids fair in the future to replace all existing methods -of observation. - -In the introductory chapter we referred to the introduction of -photographic records of astronomical phenomena as marking an epoch in -the development of the science. In the last ones we have to dwell -briefly on the _modus operandi_ of the various methods by which the eye -is thus being gradually replaced. - -The point of celestial photography is that it not only enables us to -determine form and place, absolutely irrespective of personal equation -so far as the eye is concerned, but that, properly done, it gives us a -faithful and lasting record of the operation, so that it is not -forgotten; Mr. De La Rue has called the photographic plate the _retina -which does not forget_, and an excellent name it is. - -We may pass over altogether the ordinary photographic processes, which -have been carried on with a degree of skill and patience which is beyond -all praise, and confine our attention exclusively to the instrumental -processes. Be it remembered, we have no longer to consider the visual -rays, but the so-called chemical rays, which lie at the violet end of -the spectrum. - -We must also recollect that, in a former chapter, we have seen that the -optician’s business was to throw aside the violet rays altogether—to -discard them, caring nothing for them, because, so far as the visible -form of the objects is concerned, they help very little. But we shall -see in a moment that, if we wish to use refractors for photographing, we -must abolish this idea, and undo everything we did to get a perfect -telescope to see the body, because in the case of the photographic -processes employed at present, the visible rays have as little to do -with building up the image on the photographic plate as the blue rays -have to do with building up the image on the retina of the eye. We shall -see presently how admirably this has been done by Mr. Rutherfurd. If, -however, we use reflectors instead of refractors, we are able to utilize -all the rays by means of the same mirror without alteration, as the -focus is the same for all rays, so that a reflector is equally good for -all classes of observation. - -Let us first consider the cases in which the plate is made to replace -the retina with the ordinary telescope. We shall see in the sequel that -whether the spectroscope, polariscope, or other physical instrument be -added to the telescope—when we pass, that is to say, from mechanical to -physical astronomy—the plate can still replace the eye with advantage. - -The body of the telescope, with the object-glass or mirror at one end -and the plate at its focus in place of the eyepiece, forms the camera, -corresponding to those we find in photographic studies. The plate-holder -shown in section in the accompanying figure is therefore the only -addition required to make a telescope into a camera for ordinary work. -Fig. 208. - -[Illustration: - - FIG. 208.—Section of Plate-holder. -] - -A is a screw of such a size that it can be inserted into the eyepiece -end of the telescope; the sensitive plate is held between a lid at the -back, which opens for the plate to be inserted, and a slide in front, -which is drawn out so as to expose the face of the plate to the object. -A piece of ground glass of extreme fineness is inserted in the slide, on -which the object is focussed before the sensitive plate is put in. It is -easy then by the eyepiece focussing-screw to put this nearer or further -away from the object-glass, so that the image is thrown sharply on the -ground glass. When that is done the ground glass is taken away, and the -sensitive plate put there in its place, and then exposed as required, so -that the methods are similar to the ordinary photographic process. - -We have here an arrangement that enables us to photograph the moon, -stars, and planets. M. Faye has proposed that for the transit circle -also the photographic method should be applied, the chronograph -registering the time of the instantaneous opening of the slide, instead -of the time the star is seen to transit, so that the position of the -star with respect to the wires is registered at a certain known time; -therefore, not only for physical astronomy have we the means of making -observations without an observer at all, but also for position -observations. - -Every one knows sufficient of photography to be aware that, if we wish -to secure the image of a faint object, such as a faint star or a faint -part of the moon, we must expose the plate for some little time, as we -have to do in ordinary photography if the day is dull, and therefore the -larger the aperture of the telescope the more light passes; and the -shorter the focus is, and the more rapid the process, the shorter will -be the exposure; if the focus is short, the image will be small; but as -we can magnify the image afterwards, rapidity becomes of greater moment, -as the shorter the time of exposure is the less atmospheric and other -disturbances and errors in driving the telescope come into play. Still, -if we photograph the moon or other object, we do not wish to limit -ourselves to the size of the original negative obtained at the focus. If -the negative is well defined—that is, if it possesses the quality of -enlargeableness—there is no difficulty in getting enlarged prints. - -The method of enlarging photographs is very simple; all that is required -is a large camera, the negative to be copied being placed nearer the -lens than the prepared paper, so that the image is larger than the -original. Fig. 209 shows an enlarging camera: the body, A, can be made -of wood, or better still, of a soft material, bellows-fashion, so that -the length can be altered at pleasure. In the end, at B, is fixed a -lens—an ordinary portrait lens will do, but a proper copying lens is -preferable; and E is a piece of wood with a hole in its centre, over -which the negative is placed, the distance of E to B being also -adjustible; then, by altering the lengths of B E and B C, the image of -the negative can be made to appear of suitable size. At the end, C, a -piece of sensitive paper is placed, and the light of the sun being -allowed to fall through the negative and lens, the paper soon becomes -printed, and can be toned and fixed as an ordinary paper positive. The -camera may be carried on a rough equatorial mounting, consisting of an -axis pointing to the pole, and pulled round with the sun by attaching a -string to an equatorial telescope, moved by clockwork; or a heliostat -can be used with more advantage, thereby allowing the camera to be -stationary; a good enlarging lens is a very desirable thing, for most -lenses seem to distort the image considerably. - -[Illustration: - - FIG. 209.—Enlarging Camera. F, heliostat for throwing beam of sunlight - on the reflector, which throws it into the camera; E, negative; B, - focussing-lens; C, plate- or paper-holder; D, focussing-screw. -] - -If we wish to obtain a large direct image of the moon, we must, as said -before, employ a telescope of as long a focal length as possible; for -reasons just mentioned, this is not always desirable. If, however, large -images can be obtained as good as small ones, they can of course be -enlarged to a much greater size. The primary image of the moon taken by -Mr. De La Rue’s exquisite reflector is not quite an inch in diameter. In -one of Mr. Rutherfurd’s telescopes of fifteen feet focus, the image of -the moon is somewhat larger—about one and a half inch in diameter. In -Mr. Newall’s magnificent refractor, the focal length of which is thirty -feet, the diameter is over three inches. In the Melbourne reflector the -image obtained is larger still. - -In celestial photography we have not only to deal with faint objects. -With the sun the difficulty is of no ordinary character in the opposite -direction, because the light is so powerful that we have to get rid of -it. Now there are two methods of doing this, and as in a faint object we -get more light by increasing the aperture, so with a bright light like -that of the sun we can get rid of a large amount of it by reducing the -aperture of our telescope; but it is found better to reduce -infinitesimally the time of exposure, and methods have been adopted by -which that has been brought down to the one-hundredth part of a second. - -Let us show the simple way in which this can be done by the means of an -addition to an ordinary plate-holder. - -Fig. 208 shows the ordinary plate-holder, like those used generally for -photography. What is termed the instantaneous slide, B, Fig. 210, -consists of a plate with an adjustible slit in it inserted between the -object itself and the focus. This can be drawn rapidly across the path -of the rays by means of a spring, D; we can bring it to one side, and -fix it by a piece of cotton, E, and then we can release it by burning -the cotton, when the spring draws it rapidly across. The velocity of the -rush of the aperture across the plate, and the time of exposure, can be -determined by the strength of the spring and the aperture of the slit. -If the velocity is too great, we can alter the size of the slit, C. If -we absorb some of the superabundant light by means of yellow glass, or -some similar material, we can keep the opening wide enough to prevent -any bad effects of diffraction coming into play. - -[Illustration: - - FIG. 210.—Instantaneous Shutter. -] - -The light of the sun is so intense that another method may be employed. -Instead of having the plate at the focus of the object-glass we may -introduce a secondary magnifier in the telescope itself, and thus obtain -an enlarged image, the time necessary for its production being still so -short (1/50th of a second) that nothing is lost from the disturbances of -the air. - -A telescope with this addition is called a photoheliograph. The first -instrument of this kind was devised by Mr. De La Rue, and for many years -was regularly employed in taking photographs of the sun at Kew. - -[Illustration: - - FIG. 211.—Photoheliograph as erected in a Temporary Observatory for - Photographing the Transit of Venus in 1874. -] - -Some astronomers object to this secondary magnifier, and to obtain large -images use very long focal lengths, and of course a siderostat is -employed. In this way Professor Winlock obtained photographs of the sun -which have surpassed the limits of Mr. Newall’s refractor; the negatives -have a good definition, and show a considerable amount of detail about -the spots; they were taken by a lens, inserted at the end of a gas-pipe -forty feet long. The pipe was fixed in a horizontal position, facing the -north, and at the extreme north part of it was the lens, a single one of -crown glass, with no attempt to correct it. In front of it was a -siderostat, moved by a clock, reflecting the light down the tube, so -that the image of the sun could be focussed on the ground glass at the -opposite end. - -One will see the importance of shortening the time for even the -brightest object. Those who are favoured with many opportunities of -looking through large telescopes know that the great difficulty we have -to deal with is the atmosphere; because we have to wait for definition, -and the sum total of the photograph of any one particular thing depends -upon these atmospheric fits. If we require to photograph an object, it -will be obvious that the more fits we have, the worse it will be, -because we get a number of images partially superposed which would -otherwise give as good an effect as we could get by an ordinary eye -observation. It is therefore most important to reduce the interval as -much as possible. - - - - - CHAPTER XXXII. - CELESTIAL PHOTOGRAPHY (CONTINUED).—SOME RESULTS. - - -The process used should therefore be the most rapid attainable; any work -on photography will give a number of processes of different degrees of -rapidity, but a process that suits one person’s manipulation may prove a -failure in another’s, and the general principles are the only rules -suitable for all. First, the glass plate should be carefully cleaned, -the collodion lightly coloured, the bath strong and neutral, certainly -not acid, and the developer fairly strong. Pyrogallic acid and silver -should not be used for intensifying; a good intensifier is made by -adding to a solution of iodide of potassium, strength one grain to the -ounce of water, a saturated solution of bichloride of mercury, drop by -drop, until the precipitate at first formed ceases to be re-dissolved; -use this after fixing. - -Now let us inquire what has been done by this important adjunct to -ordinary means of observing. We may say that celestial photography was -founded in the year 1850 by Professor Bond, who obtained a daguerreotype -of the moon about that date. An immense advance has been made, but not -so great as there might have been if the true importance of the method -had been recognized as it ought to have been; and if we study the -history of the subject we find that till within the last few years we -have to limit ourselves to the works of two men who, after Bond, set the -work rolling. Several observers took it up for a time; but the work -requires much both of time and money, and different men dropped off from -time to time. There remained always steadfast one Englishman and one -American—Mr. De La Rue and Mr. Rutherfurd. The magnificent work Mr. De -La Rue has done was begun in 1852. He was so anxious to see whether -England could not do something similar to what had been done in America, -that, without waiting for a driving clock, he thought he would see -whether photographs of the moon could be taken by moving the telescope -by hand. He soon found that he was working against nature—that nature -refused to be wooed in this way; the moon in quite a decided manner -declined to be photographed, and we waited five years till Mr. De La Rue -was armed with a perfect driving clock. Mr. Rutherfurd was waiting for -the same thing in America. - -At last, in 1857, Mr. De La Rue got a driving clock to his reflector of -thirteen inches aperture, and began those admirable photographs of the -moon which are now so well known. Since the above date the moon has been -photographed times without number, and Mr. De La Rue has made a series -which shows the moon in all her different phases. They are remarkable -for the beautiful way in which the details come out in all parts of the -surface. We must recollect that these pictures of which we have spoken, -some of them a yard in diameter, were first taken on glass about three -inches across, the image covering the central inch. At the same time the -British Association granted funds for the photographic registration of -sun-spots at the Kew Observatory, where the sun was photographed every -day for many years. - -Encouraged by success, Mr. De La Rue, in 1858, attacked the planets -Jupiter and Saturn, and some of the stars. He discovered that -photographs of the moon can be combined in the stereoscope so that the -moon shows itself perfectly globular. - -To accomplish this result it was necessary to photograph her at -different epochs, so that the libration, which gives it the appearance -of being turned round slightly and looking as it would do to a person -several thousand miles to the right or left of the telescope, should be -utilized. These two views when combined give the appearance of solidity -just as the image of a near object combined by the two eyes gives that -appearance. The reason of this appearance of solidity is easily seen by -looking at an orange or ball first with one eye and then with the other, -when it is noticed that each eye sees a little more of one side than the -other; and it is the combination of these slightly dissimilar images -that gives the solid appearance. - -If we examine two of these photographs combined for the stereoscope, we -see that they have the appearance of being taken from two stations a -long distance apart. One shows a little more of the surface on one side -than the other. They are obtained in different lunations, when the moon, -in the same phase, has turned herself slightly round, showing more of -one side. In this way we have a distinct effect due to libration. In the -year 1859 Mr. De La Rue found that sun-pictures could be combined -stereoscopically in the same manner. - -When we turn to the labours of Mr. Rutherfurd, we find him in 1857 armed -with a refractor of 11¼ inches aperture; the actinic focus, or rather -the nearest approach to a focus, was 7/10ths of an inch from the visual -focus. With this telescope, without any correction whatever, he, in 1857 -and 1858, obtained photographs of the moon which, when enlarged to five -inches in diameter, were well defined. He also obtained impressions of -stars down to as far as the fifth magnitude, and also of double stars -some 3˝ apart—for instance, γ Virginis was photographed double. The ring -of Saturn and belts of Jupiter were also plainly visible, but -ill-defined. The satellites of Jupiter failed to give an image with any -exposure, while their primary did so in five or ten seconds. The actinic -rays, instead of coming to a point and producing an image of a -satellite, were spread over a certain area and thereby rendered too weak -to impress the plate. - -In the summer of 1858 Mr. Rutherfurd combined his first stereograph of -the moon independently of Mr. De La Rue’s success in England. - -Mr. Rutherfurd then commenced an inquiry of the greatest importance, -which will in time bring about a revolution in the processes employed. - -In 1859 he attempted, by placing lenses of different curvatures between -the object-glass and the focus, to bring the chemical rays together, -leaving the visual rays out of the question; this had the effect of -shortening the focus considerably and improving the photographs; but he -found that, except for the middle of the field, this method would not -answer. He therefore in 1860 attempted another arrangement, and one -which he found answered extremely well for short telescopes. - -Between the lenses of the object-glass of a 4½-inch refractor he put a -ring which separated the lenses by three-quarters of an inch, and -reduced the power of the flint-glass lens, which corrects the -crown-glass for colour, so that the combination became achromatic for -the violet rays instead of for the yellow. With this lens he was -successful to a certain extent: he obtained even better results than -with the 11¼ inch; but eventually he rejected this method, which we may -add has recently been tested by M. Cornu, who thinks very highly of it. - -He next attempted a silver-on-glass mirror in 1861; in the atmosphere of -New York it only lasted ten days; he gave it up; and he then very -bravely, in 1864, attacked the project _de novo_, and began an -object-glass of a telescope which should be constructed so as to give -best definition with the actinic rays, just as ordinary object-glasses -are made to act best with the visual rays. - -He found that in order to bring the actinic portion of the rays to a -perfect focus, it was necessary that a given crown-glass lens should be -combined with a flint, which will produce a combined focal length of -about ⅒ shorter than would be required to satisfy the conditions of -achromatism for the eye. This combination was of course absolutely -worthless for ordinary visual observation; his new lens when finished -was 11¼ inches aperture and a little less than 14 feet focal length. -With this he obtained impressions of ninth magnitude stars, and within -the area of a square degree in the Prœsepe in Cancer twenty-three stars -were photographed in three minutes’ exposure. Castor gave a strong -impression in one second, and stars of 2˝ distance showed as double. But -even with this method Mr. Rutherfurd was not satisfied. Coming back to -the 11¼-inch object-glass which he had used at first, he determined to -see whether or not the addition of a meniscus lens outside the front -lens would not give him the requisite shortness of the focus and bring -the actinic rays absolutely together. By this arrangement he got a -telescope which can be used for all purposes of astronomical research, -and he has also eclipsed all his former photographic efforts. - - - - - CHAPTER XXXIII. - CELESTIAL PHOTOGRAPHY (CONTINUED)—RECENT RESULTS. - - -Having in the previous chapter dealt with some of the pioneer work, we -come finally to consider some of the applications which in the last -years have occupied most attention. - -With regard to the sun, we need scarcely say that Messrs. De La Rue and -Stewart have been enabled, by the photographic method, to give us data -of a most remarkable character, showing the periodicity of the changes -on the sun’s surface, and so establishing their correlation with -magnetic and other physical phenomena. - -These photographic researches, following upon the eye observations of -Schwabe, Spörer, Carrington and others, have opened up to us a new field -of inquiry in connection with the meteorology of the globe; and it is -satisfactory to learn that photoheliographs are now daily at work at -Greenwich, Paris, Potsdam, and the Mauritius, and that shortly India -will be included in the list. - -Quite recently, the importance of these permanent records of the solar -surface has been demonstrated by Dr. Janssen, the distinguished director -of the Physical Observatory at Meudon, in a very remarkable manner. - -It seems a paradox that discoveries can be made depending on the -appearance of the sun’s surface by observations in which the eye applied -to the telescope is powerless; but this is the statement made by Dr. -Janssen himself, and there is little doubt that he has proved his point. - -Before we come to the discovery itself let us say a little concerning -Dr. Janssen’s recent endeavours. Among the six large telescopes which -now form a part of the equipment of the new Physical Observatory -recently established by the French government at Meudon, in the grounds -of the princely Chateau there, is one to which Dr. Janssen has recently -almost exclusively confined his attention. It is a photoheliograph -giving images of the sun on an enormous scale—compared with which the -pictures obtained by the Kew photoheliograph are, so to speak, pigmies, -while the perfection of the image and the photographic processes -employed are so exquisite, that the finest mottling on the sun’s surface -cannot be overlooked by those even who are profoundly ignorant of the -interest which attaches to it. - -This perfection of size and image have been obtained by Dr. Janssen by -combining all that is best in the principles utilised in one direction -by Mr. De La Rue, and in the other by Mr. Rutherfurd, to which we have -before referred. In the Kew photoheliograph, which has done such noble -work in its day that it will be regarded with the utmost veneration in -the future, we have first a small object-glass corrected after the -manner of photographic lenses, so as to make the so-called actinic and -the visual rays coincide, and then the image formed by this lens is -enlarged by a secondary magnifier constructed, though perhaps not too -accurately, so as to make the actinic and visual rays unite in a second -image on a prepared plate. Mr. Rutherfurd’s beautiful photographs of the -sun were obtained in a somewhat different manner. In his object-glass, -as we have seen, he discarded the visual rays altogether and brought -only the blue rays to a focus, but when enlargements were made, an -ordinary photographic lens—that is, one in which the blue and yellow -rays are made to coincide—was used. - -Dr. Janssen uses a secondary magnifier, but with the assistance of M. -Pragmowski he has taken care that both it and the object-glass are -effective only for those rays which are most strongly photographic. Nor -is this all; he has not feared largely to increase the aperture and -focal length, so that the total length of the Kew instrument is less -than one-third of that in operation in Paris. - -The largely-increased aperture which Dr. Janssen has given to his -instrument is a point of great importance. In the early days of solar -photography the aperture used was small, in order to prevent -over-exposure. It was soon found that this small aperture, as was to be -expected, produced poor images in consequence of the diffraction effects -brought about by it. It then became a question of increasing the -aperture while the exposure was reduced, and many forms of instantaneous -shutters have been suggested with this end in view. With these, if a -spring be used, the narrow slit which flashes across the beam to pay the -light out into the plate changes its velocity during its passage as the -tension of the spring changes. Of this again Dr. Janssen has not been -unmindful, and he has invented a contrivance in which the velocity is -constant during the whole length of run of the shutter. - -By these various arrangements the plates have now been produced at -Meudon of fifteen inches diameter, showing details on the sun’s surface -subtending an angle of less than one second of arc. - -So much for the _modus operandi_. Now for the branch of solar work which -has been advanced. - -It is more than fifteen years ago since the question of the minute -structure of the solar photosphere was one of the questions of the day. -The so-called “mottling” had long been observed. The keen-eyed Dawes had -pointed out the thatch-like formation of the penumbra of spots, when one -day Mr. Nasmyth announced the discovery that the whole sun was covered -with objects resembling willow-leaves, most strangely and effectively -interlaced. We may sum up the work of many careful observers since that -time by stating that the mottling on the sun’s surface is due to -dome-like masses, and that the “thatch” of the penumbra is due to these -dome-like masses being drawn, either directly or in the manner of a -cyclone, towards the centre of the spot. In fact the “pores” in the -interval between the domes are so many small spots, while the faculæ are -the higher levels of the cloudy surface. The fact that faculæ are so -much better seen near the limb proves that the absorption of the solar -atmosphere rapidly changes between the levels reached by the upper -faculæ and the pores. - -Thus much premised, we now come to Dr. Janssen’s discovery. - -An attentive examination of his photographs shows that the surface of -the photosphere has not a constitution uniform in all its parts, _but -that it is divided into a series of figures more or less distant from -each other, and presenting a peculiar constitution_. These figures have -contours more or less rounded, often very rectilinear, and generally -resembling polygons. The dimensions of these figures are very variable; -they attain sometimes a minute and more in diameter. - -While in the interior of the figures of which we speak the grains are -clear, distinctly terminated, although of very variable size, in the -boundary the grains are as if half effaced, stretched, stained; for the -most part, indeed, they have disappeared to make way for trains of -matter which have replaced the granulation. Everything indicates that in -these spaces, as in the penumbræ of spots, the photospheric matter is -submitted to violent movements which have confused the granular -elements. - -We have already referred to the paradox that the sun’s appearance can -now be best studied without the eye applied to the telescope. This is -what Dr. Janssen says on that point. - - “The photospheric network cannot be discovered by optical methods - applied directly to the sun. In fact, to ascertain it from the - plate, it is necessary to employ glasses which enabled us to embrace - a certain extent of the photographic image. Then if the magnifying - power is quite suitable, if the proof is quite pure, and especially - if it has received rigorously the proper exposure, it will be seen - that the granulation has not everywhere the same distinctness; that - the parts consisting of well-formed grains appear as currents which - circulate so as to circumscribe spaces where the phenomena present - the aspect we have described. But to establish this fact, it is - necessary to embrace a considerable portion of the solar disc, and - it is this which it is impossible to realise when we look at the sun - in a very powerful instrument, the field of which is, by the very - fact of its power, very small. In these conditions we may very - easily conclude that there exist portions where the granulation - ceases to be distinct or even visible; but it is impossible to - suppose that this fact is connected with a general system.” - -But it is not alone with the uneclipsed sun that the new method enables -us to make discoveries. The extreme importance of photography in -reference to eclipse observations cannot be over estimated. Most of our -best observations of eclipses have been wrought by means of photography. -The time of an eclipse is an exciting time to astronomers; and it is -important that we should have some mechanical operation which should not -fail to record it. - -[Illustration: - - FIG. 212.—Copy of Photograph taken during the Eclipse of 1869. -] - -The first eclipse photograph was taken in 1851. In 1860, chiefly owing -to the labours of Mr. De La Rue, our knowledge was enormously increased. -The Kew photoheliograph was the instrument used, and the series of -pictures obtained showed conclusively that the prominences belonged to -the sun. In 1868 the prominences were again photographed. In 1869 the -Americans attacked the corona, and their suggestion that the base of it -was truly solar has been confirmed by other photographs taken in 1870, -1871, and 1875. Although to the eye the phenomena changed from place to -place, to the camera it was everywhere the same with the same duration -of exposure. - - * * * * * - -It is not to be wondered at, then, that on the occasion of the last -transit of Venus, which may be regarded as a partial eclipse of the sun, -photography was suggested as a means of recording the phenomena. - -Science is largely indebted to Dr. Janssen, Mr. De La Rue, and others -for bringing celestial photography to aid us in this branch of work -also. While on the one hand astronomers have to deal with precious -moments, to do very much in very little time, in circumstances of great -excitement; the photographer on the other goes on quietly preparing and -exposing his plates, and noting the time of the exposure, and thus can -make the whole time taken by the planet in its transit over the sun’s -disc one enormous base line. His micrometrical measures of the position -of the planet on the sun’s disc can be made after all is over. It was -suggested by Dr. Janssen that a circular plate of sufficient size to -contain sixty photographs of the limb of the sun, at the points at which -Venus entered and left it could be moved on step by step round its -centre, and so expose a fresh surface to the sun’s image focussed on it, -say every second. In this way the phenomena of the transit were actually -recorded at several stations. - - * * * * * - -[Illustration: - - FIG. 213.—Part of Beer and Mädler’s Map of the Moon. -] - -With reference to the moon, we have said enough to show that if we wish -to map her correctly, it is now no longer necessary to depend on -ordinary eye observations alone; it is perfectly clear that by means of -an image of the moon, taken by photography, we are able to fix many -points on the lunar surface. Still, although we can thus fix these and -use them as so many points of the first order, as one might say, in a -triangulation, there is much that photography cannot do; the work of the -eye observer would be essential in filling in the details and giving the -contour lines required to make a map of the moon. - -The accompanying drawings on the same scale show that up to the present, -for minute work, the eye beats the camera. - -[Illustration: - - FIG. 214.—The same Region copied from a Photograph by De La Rue. -] - -The light of the moon is so feeble in blue rays that a long exposure is -necessary for a large image, and during the exposure all the errors in -the rate of the clock are magnified. - -We need not enlarge on the extreme importance of what Mr. Rutherfurd has -been doing in photographing star clusters and star groups. It is doubly -important to astronomy, and starts a new mode of using the equatorial -and the clock; in fact, it gives us a method by which observations may -be photographically made of the proper motion of stars, and even the -parallax of stars may be thus determined independently of any errors of -observers. Mr. Rutherfurd shows that the places of stars can be measured -by a micrometer on a plate in the same way as by ordinary observation; -hence photography can be made use of in the measurement of position and -distance of double stars. - -As an instance of the extreme beauty of the photographs of stars -produced by a proper instrument, it may be stated that with the full -aperture of the 11¼-inch object-glass corrected only for the ordinary -rays, Mr. Rutherfurd found that he required an exposure of more than ten -seconds to get an image of the bright star Castor; but now, instead of -requiring ten seconds, he can get a better image in one. The reason of -this is, that, with the object-glass corrected only for the visual rays, -the chemical ones are spread over a certain small area instead of coming -to a point, and so, of course, the intensity is reduced; but when the -chemical rays all come to one point the intensity is greater, since the -image of the star is smaller and the action more intense. - -Let us follow Mr. Rutherfurd a little in his actual work. First, a wet -plate is exposed for four minutes. This gives stars down to the tenth -magnitude. But there may be points on the plate which are not stars, -hence a second impression is taken on the same plate after it has been -slightly moved. All points now doubled are true stars. Now for measures -of arc. Another photograph is taken, and the driving clock is stopped; -the now moving stars down to the fourth magnitude are bright enough to -leave a continuous line, the length of this in a very accurately known -interval, say two minutes, enables the arc to be calculated. - -Next comes the mapping. The negative is fixed on a horizontal divided -circle on glass illuminated from below. Above it is a system of two -rails, along which travels a carrier with two microscopes, magnifying -fifty diameters. By the one in the centre, with two cross wires in the -field of view, the photograph is observed; by the other, armed with a -wire micrometer, a divided scale on glass which is fixed alongside the -rail is read. Suppose we wish to measure the distance between two stars -on the plate. The plate is rotated, so that the line which joins them -coincides with that which is described by the optical axis of the -central microscope marked by the cross wires when the carrier runs along -the rails. This microscope is then brought successively over the two -stars, and the other microscope over the scale reads the nearest -division, while the fractions are measured by the micrometer. Hence, -then, the fixed scale, and not a micrometer screw, is depended upon for -the complete distance. In this way the distance between the stars on the -plate can be measured to the 1/500 part of a millimetre. - - * * * * * - -So far then we have shown how photography has been called in to the aid -of the astronomer, and how, by means of photography, pictures of the -different celestial bodies have been obtained of surpassing excellence. -Now, photography is also the handmaiden to the spectroscope in the same -way as it is the handmaiden to the telescope. Not only are we able to -determine and register the appearance of the moon and planets, but, day -by day, or hour by hour, we can photograph a large portion of the solar -spectrum; and not only so, but the spectrum of different portions of the -sun: nay, even the prominences have been photographed in the same -manner; while more recently still, Drs. Huggins and Draper have -succeeded in photographing the spectrum of some of the stars. We owe the -first spectrum of the sun, showing the various lines, to Becquerel and -Draper; the finest hitherto published we owe to Mr. Rutherfurd. - -[Illustration: - - FIG. 215.—Comparison between Kirchhoff’s Map and Rutherfurd’s - Photograph. -] - -This magnificent spectrum extends from the green part of the spectrum -right into that part of the spectrum called the ultra-violet. Of course -it had to be put together from different pictures, because there is a -different length of exposure required for the different parts; the -exposure of any particular part of the spectrum must be varied according -to the amount of chemical intensity in that part. If the line G was -exposed, say for fifteen seconds, the spectrum near the line F would -require to be exposed for eight minutes, and at the line H, which is -further away from the luminous part of the spectrum than G, there the -exposure requisite would be two or three minutes. - -[Illustration: - - FIG. 216.—Arrangement for Photographically Determining the Coincidence - of Solar and Metallic Lines. -] - -[Illustration: - - FIG. 217.—Telespectroscope with Camera for obtaining Photographs of - the Solar Prominences. -] - -In order to obtain a photograph of the average solar spectrum, the -camera replaces the observing telescope, and a heliostat is used, as in -the ordinary way. The beam, however, should be sent through an -opera-glass in order to condense it, and thereby to render the exposure -as short as possible. - -Further, if an electric lamp be mounted as shown in Fig. 216, -observations, similar to those originally made by Kirchhoff, of the -coincidence on the various metallic lines with the Fraunhofer ones, can -be permanently recorded on the photographic plate. The lens between the -lamp and the heliostat is for the purpose of throwing an image of the -sun between the carbon poles. The lens between the lamp and spectroscope -then focuses both the poles and the image of the sun on to the slit. The -spectrum of the sun is first obtained by uncovering a small part of the -slit and allowing the image of the sun to fall on this uncovered -portion, the lamp not being in action. When this has been done the light -of the sun is shut off. The metal to be studied is placed in the lower -pole; the adjacent portion of the slit is uncovered, that at first used -being closed in the process. The current is then passed to render the -metal incandescent. After the proper exposure the plate is developed and -the spectra are seen side by side. Fig. 187 is a woodcut of a plate so -obtained. - -If the spectrum of any special part of the sun, or the prominences, has -to be photographed, then either a siderostat must be employed, or a -camera is adjusted to the telespectroscope, as shown in Fig. 217. - -For the stars, of course, much smaller dispersion must be used, but the -method is the same; and what has already been said by way of precaution -about the observation of stellar spectra applies equally to the attempt -to obtain spectrum photographs of these distant suns. - - - - - INDEX. - - - A. - - Aberration (_see_ Chromatic Aberration, Spherical Aberration) - - Absorption, general and selective, 403, 408; - spectroscope arranged for showing, 409 - - Adjustment of the transit instrument, 238 - - ADJUSTMENTS OF THE EQUATORIAL (Chap. XXI.), 328 - - Achromaticity of Huyghen’s eyepiece, 110 - - Achromatic lenses, 84, 86 - - Achromatism, 126 - - Airy’s transit circle, 284 - - Alexandrian Museum, astronomical observations, 19 - - Alt-azimuth, 287, 289 - - Altitudes, instrument used by Ptolemy for measuring, 35 - - Aluminium, line spectrum of, 406; - the sun, 417 - - Analyser for polarization of light, 443, 450 - - Anaximander, his theory of the form of the earth, 6; - invention of the gnomon ascribed to him, 16, 17; - meridian observations by, 25 - - Anchor escapement, 197 - - Angles of position, measurement of, 358-366, 372 - - Ångström, spectrum analysis, 402, 412; - wave-lengths, 406 - - Annealing of lenses and specula, 121 - - Archimedes, clocks used by, 176 - - Arcturus, heat of, 385 - - Argelander, magnitudes of stars, 382 - - Aries, its position in the zodiac, 34 - - Aristillus, his observations in the Alexandrian Museum, 19 - - _Armillæ Æquatoriæ_ of Tycho Brahe, 26, 41, 45; - his _Armillæ Zodiacales_, 28 - - Ascension, Right (_see_ Right Ascension) - - Arctic circle, Euclid’s observations of stars in the, 10 - - Astrolabe, invented by Hipparchus, 25; - engraving of Tycho Brahe’s, 26, 41; - his ecliptic astrolabe, 28 - - Astronomical clock, 240 (_see_ Clock) - - ASTRONOMICAL PHYSICS (Book VI.), 371 - - ASTRONOMY OF PRECISION, INSTRUMENTS USED IN (Chap. XIX.), 284-290 - - Astrophotometer, Zöllner’s, 379 - - Autolycus, first map of the stars by, 8, 9 - - Automatic spectroscope, 397 - - Auzout, invention of micrometer ascribed to, 219, 221 - - Axis of collimation, 218, 220 - - - B. - - Barium, in the sun, 419 - - Barlow, correction of aberration in lenses, 88; - “Barlow lenses,” 89, 229 - - Barometrical pressure, its effect on the pendulum, 193 - - Berthon’s dynameter, 116 - - Bessel’s transit instrument, 284 - - Binary stars, 351, 359, 360 - - Blair (Dr.), object-glasses, 88 - - Bloxam’s improved gravity escapement, 201 - - Bond (Prof.), spring governor, 320, 321; - celestial photography, 463 - - Bouguer’s photometer, 379 - - Brahe, Tycho (_see_ Tycho Brahe) - - Brewster (Sir David), his list of Tycho Brahe’s instruments, 38; - spectrum analysis, 410 - - British Horological Institute, time signals, 280 - - Browning’s method of silvering glass specula, 137; - of mounting specula, 144; - automatic spectroscope, 397; - solar spectroscope, 428 - - Bunsen (Ernest de), on ancient astronomical observations, 6 - - Bunsen (Prof.) spectroscope, 396; - his burner, flame of, 407; - his work in spectrum analysis, 402, 412, 423 - - - C. - - Calcium, line spectra of, 406, 418 - - Cambridge Observatory (U.S.), equatorial at, 339; - star spectroscope, 430; - transit circle, 247, 248, 251 - - Camera, enlarging, for celestial photography, 458 - - Canada balsam, its power of refracting light, 447 - - Candles used to measure time, 176 - - Canopus, observations of, by Posidonius, 8 - - Cassegrain’s reflecting telescope, 103, 149, 169; - with Mr. Grubb’s mounting, 301 - - Casting lenses and specula, 121 - - Castor, photograph of, 478 - - Catalogues of stars (_see_ Stars) - - Celestial globe, 23 - - CELESTIAL PHOTOGRAPHY (Chap. XXXI., XXXII.), 454 - - Chair, observing, for equatorial telescopes, 339 - - Chaldeans, their observations of the motions of the moon, 4; - early use of the gnomon, 16 - - Chance and Feil, manufacture of glass discs, 119, 305 - - CHEMISTRY OF THE STARS (Chap. XXVII.-XXX.), 386-453 - - Chinese, observations of conjunctions of planets, 4, 5; - early use of the gnomon, 16, 17 - - Chromatic aberration of object-glasses and eyepieces, 87, 109, 123 - - CHRONOGRAPH, THE (Chap. XVII.), 253-270 - - “Chronographic method” of transit observation, 259 - - Chronograph at Greenwich Observatory, 260-264 - - CHRONOMETER, THE (Chap. XIII.), rise and progress of time-keeping, - 206-210; - compensating balance, 207; - detached lever escapement, 208; - chronometer escapement fusee, 209 - - Chronometers used for determining “local time,” 281 - - Chronophers, for distributing “Greenwich time,” 275, 276 - - Cincinnati Observatory, 338 - - Circle, the; its first application as an astronomical instrument, 6, 7, - 8, 10; - division into degrees, 8, 17, 21 - - Circles, great, defined by Euclid, 12 - - CIRCLE READING (Chap. XIV.), 211-217; - Digges’ diagonal scale, 213; - the vernier, 214 - - CIRCLE, TRANSIT (_see_ Transit Circle) - - Circle, meridian, at Cambridge (U.S.), 248; - mural, 241, 242 - - Circumpolar stars, 239 - - Clarke (Alvan), improvement in telescope lenses, 305; - great equatorial at Washington, 309, 319 - - Clement, inventor of the anchor escapement, 197 - - Clepsydras, 36 - - CLOCK, THE (Chap. XIII.), 175-205; - ancient escapement, 177; - crown wheel, 178; - clock train, 180; - winding arrangements, 181; - pendulum, 183; - cycloidal pendulum, 185; - compensating pendulums, 187; - Graham’s, Harrison’s, and Greenwich pendulums, 188; - clock at Royal Observatory, Greenwich, 194; - escapements, 196; - anchor escapement, 197; - Graham’s dead-beat, 199; - Mudge’s gravity escapement, 200; - escapement of clock at Greenwich, 203; - arrangements at Edinburgh Observatory, 269; - astronomical, 240, 244, 245, 346; - sidereal, 254, 256, 266; - solar, 254; - standard, at Greenwich, 194, 203, 204, 271, 274 - - Clock, driving, for large telescopes, 318 - - Clocks driven and controlled by electricity, 272 - - Clock stars, 267 - - Clock tower at Westminster, 277 - - Coggia’s comet, its light polarized, 450 - - Collimation and collimation-error in the transit instrument and - equatorial, 238, 247, 328 - - Colour, amount produced by a lens, 81, 84, 86; - spectrum analysis, 407, 408, 414, 416; - of stars, 165, 351, 433; - of waves of light, 420; - refrangibility of, 387 - - Comet of 1677, discovered by Tycho Brahe, 47 - - Comet, measurement of the angle of position of its axis, 359 - - Comparison prism of the spectroscope, 423 - - Compensating balance, 207 - - Compensating pendulums, 187-193 - - Composite mounting of large telescopes, 310 - - Concave lenses (_see_ Lenses) - - Concave mirrors (_see_ Mirrors) - - Conjugate images, 64 - - Conjunctions of planets, first observations, 4 - - Constellations, first observations, 5, 9; - Orion and its neighbourhood, 156 - - Convex lenses (_see_ Lenses) - - Convex mirrors (_see_ Mirrors) - - Cooke, adjustment of object-glasses, 141; - improvement in telescope lenses, 305; - equatorial refractor, 300; - driving clock for large telescopes, 321; - illuminating lamp for equatorial telescopes, 326 - - Copernicus, parallactic rules of, 41 - - Copernicus (lunar crater), 354 - - Cross wires for circle reading, 212, 216, 218; - in transit eyepiece, 234, 257 - - Crown-glass prisms, 83, 84; - lenses, 86, 88 - - Crystals of Iceland spar, double refraction by (_see_ Iceland Spar) - - Culmination of stars, first observations of, 5 - - Cycloidal pendulum, 185 - - - D. - - Dawes, solar eyepiece, 114, 115, 349; - photometry, 378 - - Day, solar and sidereal, 253, 254, 256 - - Day eyepiece, 113 - - Days, first reckoning of, 19; - measurement of, 176 - - Dead-beat escapement, 198 - - Deal time-ball, 275, 279 - - Declination, 24, 234, 241, 243, 251; - measured by Tycho Brahe, 45 - - Declination axis of the equatorial, 299, 308, 327, 328 - - Defining power of the modern telescope, 160, 164; - stars in Orion a test of, 165 - - Degrees, division of the circle into, 8, 17, 21 - - De La Rue (Warren, F.R.S.), his reflecting telescope, 108; - improvements in polishing specula, 134; - celestial photography, 454, 459, 460, 464, 465, 475 - - Denderah, the zodiac of, 7 - - Dent (E. & Co.), clock at Royal Observatory, Greenwich, 194, 203, 204, - 271, 274 - - Detached lever escapement, 208 - - Deviation of light, 79, 82 - - Deviation error in the transit instrument, 240, 248 - - Dials of ancient clocks, 257 - - Diagonal scale, Digges’, 213 - - Differential observations made with the equatorial, 367 - - Digges’ diagonal scale, 213 - - Diogenes Laertes, on the invention of the gnomon, 16 - - Dioptrics, Kepler’s treatise on, 386 - - Direct vision spectroscope, 431 - - Dispersion of light by prism, 79, 80, 82 - - Dividing power of telescopes, 165 - - Dollond, experiments with lenses, 85; - correction of chromatic aberration, 89; - on manufacture of flint-glass discs, 118; - pancratic eyepiece, 113 - - Dome form of observatory, 338, 339 - - Double stars, 351, 359; - measurement of, 360 - - Double-image micrometer, 225, 229 - - Double refraction by crystals of Iceland spar (_see_ Iceland Spar) - - Driving clock, for large telescopes, 318, 346 - - Drum form of observatory, 338 - - Dundee time signal, 278 - - - E. - - Earth, The, its position in Ptolemy’s system, 3; - early theories of its form, 6; - circumference measured by Posidonius, 8; - Euclid’s theory of its position, 12; - inclination of its axis, 14, 17; - size measured by Eratosthenes, 19; - position in Tycho Brahe’s system, 46 - - Eclipses, first observations of, 4; - eclipses of Jupiter’s moons; - eclipses, solar, photograph of, 474 - - Ecliptic, plane of the, 13, 14; - discovery of its inclination, 17; - inclination measured by Eratosthenes, 19 - - Ecliptic astrolabe of Tycho Brahe, 28 - - Edinburgh Observatory, clock arrangements at, 269; - standard clock, 272; - time signals, 278 - - Egyptians, their record of eclipses, 4; - zodiac of Denderah, 7 - - Eichens, his equatorial telescope at Paris, 314, 315; - siderostat constructed by him, 344 - - Electricity, its application to the chronograph, 265; - to driving and controlling clocks, 272 - - Electric lamp, 404; - arranged for spectrum analysis, 405 - - Emery used in grinding lenses and specula, 127 - - English mounting of large telescopes, 310 - - Equation of time, 254 - - EQUATORIAL, THE (Book V.), 293-368 (_see_ Telescopes) - - EQUATORIAL OBSERVATORY, THE (Chap. XXII.), 337-342 (_see_ - Observatories) - - EQUATORIAL, THE; its ordinary work, (Chap. XXIV.), 349-368 - - Equinoctial circle, observations of, by Euclid, 11 - - Equinoxes, first observations of, 15, 16, 17, 22; - precession of the, 33 - - Eratosthenes, observations of, 17; - his measurement of the earth, and inclination of the ecliptic, 19; - meridian circle invented by, 20 - - Erecting eyepiece, 113 - - Errors, collimation and deviation, in the transit instrument, 238, 240, - 247, 328 - - Errors; personal equation, 259; - adjustments of the equatorial, 329 - - Ertel, vertical circle designed by, 290 - - Escapements of clocks, 196-205; - ancient, 177; - anchor, 197; - Graham’s, 199; - Mudge’s, 200; - Greenwich clock, 203; - detached lever, 208; - chronometer escapement, 209 - - Ethereal vibrations, 373, 401, 410, 420, 449, 450 - - Euclid, his observations of the stars, 8, 9, 10; - of great circles, horizon, meridian and tropics, 11, 12; - theory of the earth’s position, 12; - pole star, 14 - - Extra-meridional observations, first employment of, 23, 25 - - “Eye and ear” method in transit observations, 259 - - Eyeball, section of the, 66 - - Eyepieces, Huyghen’s, 110; - Ramsden’s, Dollond’s, 112; - erecting or “day eyepiece,” 112; - Dawes’s solar eyepiece, 114; - magnifying power of, 116 - - Eyepiece of Greenwich transit circle, 246; - of transit instrument, 257 - - - F. - - Faye, M., celestial photography, 456 - - Feil and Chance, manufacture of flint glass discs, 119, 305 - - Fixed stars (_see_ Stars) - - Flame of salts in a Bunsen’s burner, 407 - - Flint-glass prisms, 83, 84; - lenses, 86, 170 - - Flint-glass, improvements in the manufacture of discs of, 118, 119, 305 - - Focal length of telescopes, 82, 458; - of lenses, 62, 63; - of convex mirrors, 94 - - Foucault; his reflecting telescope, 108; - improvement of specula, 117; - mode of polishing specula, 134, 136; - mounting of his telescope, 311; - governor of driving clock for large telescopes, 323; - siderostat, 343; - spectrum analysis, 410; - heliostat, 424 - - Fraunhofer; manufacture of flint-glass discs, 118; - large telescopes, 303; - lines in the solar spectrum, 392; - spectrum analysis, 402, 410, 422, 425, 432, 438 - - Frederick II. of Denmark, his patronage of Tycho Brahe, 38 - - Fusee for chronometers, 209 - - - G. - - Galileo; his telescopes, 73, 78; - their magnifying power, 77; - the pendulum, 183, 184 - - Gascoigne, eyepieces and circle reading, 212; - cross wires for “telescopic sight,” 219 - - Gateshead, Mr. Newall’s refractor, 302 - - Geissler’s tubes, 413 - - German mounting of large telescopes, 299 - - Gizeh, great pyramid of, an astronomical instrument, 6 - - Glasgow, electric time-gun, 278 - - Glass, injurious effects of the duty on, 305 - - Glass specula, methods of silvering, 137 - - Globe, celestial, 23; - terrestrial, 23 - - Gnomon; its invention and early use, 16; - improvements in, 18, 175 - - Graham; dead-beat escapement, 192, 199; - mercurial pendulum, 188 - - Gravity escapement, 200, 202 - - Greeks, their early use of the gnomon, 16 - - Greenwich, Royal Observatory; perspective view and plan of transit - circle, 243, 245, 251; - transit room, 251, 257; - meridian of, 252; - chronograph, 260-264; - computing room, 267; - standard sidereal clock, 267; - mean solar time clock, 268; - standard clock, 274; - pendulum, 188; - reflex zenith tube, 286; - alt-azimuth, 290; - equatorial, 310; - thermopile, 384; - photoheliograph, 469 - - “GREENWICH TIME” AND THE USE MADE OF IT (Chap. XVIII.), 271-283 - - Gregorian telescope, 149 - - Gridiron pendulum, 188, 189, 192 - - Grinding of lenses and specula, 127 - - Grubb; production and polishing of metallic specula, 121, 134; - adjustment of object-glasses, 141; - Cassegrainian and Newtonian reflectors, 102, 108, 301, 303; - great Melbourne equatorial telescope, 108, 314, 315, 317, 324, 327; - mode of mounting its speculum, 145-149; - automatic spectroscope, 397; - solar spectroscope, 428 - - Guinand, manufacture of flint-glass discs, 118 - - Guns fired as time-signals, 278 - - - H. - - Haliburton, on ancient astronomical observations, 6 - - Hall; experiments with lenses, 85; - manufacture of flint-glass discs, 118 - - Harcourt, Vernon, experiments with phosphatic glass, 123 - - Harrison’s gridiron pendulum, 188 - - HEAT OF STARS, DETERMINATION OF (Chap. XXVI.), 377-385 - - Heliometer, 224 - - Heliostat, 423, 458 - - Henry (Prof.), radiation of heat from sun-spots, 385 - - Herschel (Sir John), lenses corrected for aberration, 88; - table of reflective powers, 169; - star magnitudes, 381 - - Herschel, Sir William, his reflecting telescopes, 103, 108; - his mode of polishing specula, 129; - great telescope at Slough, 169, 294 - - Herschel-Browning direct-vision prism, 400 - - Hipparchus, trigonometrical tables constructed by, 17; - discoveries of, 25-35; - his measurement of space, 213 - - Hittorf, spectrum analysis, 413 - - Holmes (N. J.), his proposal of the electric time-gun, 278 - - Hooke, improvement in clock escapements, 196; - micrometer, 221, 222; - zenith sector invented by, 285; - siderostat suggested by, 343 - - Horizon, the first astronomical instrument, 4, 7, 8; - defined by Euclid, 12 - - Horological Institute, time-signals, 280 - - Hours, first reckoning of, 19; - measurement of, 176 - - Hour circle of the equatorial telescope, 328, 335 - - Huen, island of, granted to Tycho Brahe, 38 - - Huggins (Dr.), telespectroscope, 429, 432 - - Huyghens; telescopes used by, 81; - eyepiece, 110, 116, 212; - application of the pendulum to clocks, 183; - his measurements of space, 219, 223, 343; - polarized light, 442 - - Hydrogen in the sun, 435 - - - I. - - Iceland spar crystals; double refraction by, 226, 228; - polarization of light, 442, 445, 447, 449, 450 - - Illuminating power of the telescope, 158, 166, 168, 169; - stars in Orion, a test of, 164 - - Images, double, seen through Iceland spar, 227 - - Inclination of the earth’s axis, 14, 17 - - Inclination of the ecliptic, 17; - measured by Eratosthenes, 19 - - Index error, adjustments of the equatorial, 330 - - Iron, line spectrum of, 406, 418 - - Irrationality of the spectrum, 87 - - - J. - - Janssen (Dr.), solar photography, 471; - discoveries in solar physics, 472 - - Jupiter, in Ptolemy’s system, 3; - in Tycho Brahe’s, 46; - as a telescopic object, 351; - photographs of, 465, 466 - - Jupiter’s moons, observation of their eclipses to determine “local - time,” 282 - - - K. - - Kepler’s treatise on dioptrics, 386 - - Kew Observatory, photographs of the sun and sun-spots, 460, 465, 470, - 475 - - Kirchhoff; spectroscope, 396; - spectrum analysis, 402, 403, 412, 422, 428 - - Kitchener (Dr.), improved eyepiece, 113; - stars in Orion, 164 - - Knobel’s photometer, 378 - - Knott, star magnitudes, 381 - - - L. - - Lamp for equatorial telescope, 325 - - Lamp, electric (_see_ Electric Lamp) - - Lassell; his Newtonian telescope, 108, 311; - production, polishing, and mounting metallic specula, 121, 132, 144 - - Latitude; observations of Posidonius, 8; - parallels of, 23 - - Lattice-work for tubes of telescopes, 172 - - Lenses; action of, 55, 58, 85; - concave and convex, 61, 71, 75; - amount of colour produced by, 81; - achromatic, 84; - Hall and Dollond’s experiments, 85; - correction for colour, 87; - correction for aberration in eyepieces, 109, 116; - production of, 117 - - Lens, crystalline, of the eye, 67 - - Lewis (Sir G. C.), his “Astronomy of the Ancients,” 9 - - Liebig, improvement in specula, 117 - - Light; refraction, 55-72; - deviation and dispersion, 79, 80, 82, 83; - decomposition and recomposition, 83; - reflection, 90-99; - action of a reflecting surface, 91; - angles of incidence and reflection, 92; - concave and convex mirrors, 94-98; - velocity of, 159; - loss due to reflection, 168; - effective, in reflectors, 169; - vibration of particles, 373, 401; - polarization, 441-453 - - LIGHT OF STARS, DETERMINATION OF (Chap. XXVI.), 377-385 - - Lindsay (Lord), siderostat at his observatory, 347 - - Local time, 281 - - Longitude, meridians of, 23; - as determined by Hipparchus and Tycho Brahe, 44; - determined by clock and transit instrument, 280; - expressed in degrees and time, 280 - - - M. - - Magnesium vapour; colour of, 416; - in the sun, 435 - - Magnifying power of large telescopes, 154, 155; - stars in Orion, a test of, 163 - - Magnitude of stars, 377 - - Malus, discovery of polarization by reflection, 442, 448 - - Malvasia (Marquis), his micrometer, 219, 221 - - Manlius, gnomon erected by him at Rome, 18 - - Maps of the stars (_see_ Stars) - - Mars, in Ptolemy’s system, 3; - in Tycho Brahe’s, 46; - as a telescopic object, 350 - - Martin’s method of silvering glass specula, 138 - - Mauritius, photoheliograph at, 469 - - Mean time, 254 - - Mean solar time clock at Greenwich, 268 - - Melbourne Observatory, great reflecting telescope, 312, 313, 337; - composition and production of specula, 120, 121, 129; - view of optical part, 143; - mode of mounting speculum, 144-149; - photographs of the moon, 459 - - Mercurial pendulum, 187, 188, 192 - - Mercury, in Ptolemy’s system, 3; - in Tycho Brahe’s, 46; - as a telescopic object, 350 - - Meridian, defined by Euclid, 12 - - Meridional observations, first employment of, 20 - - Meridian of Greenwich, 252 - - Meridian circle, the first, 20; - at Cambridge (U.S.), 248 - - Meridians of longitude (_see_ Longitude) - - MERIDIONAL OBSERVATIONS, MODERN (Book IV.), 233-290 - - Merz (M.), manufacture of flint-glass discs, 119; - cost of large object-glasses, 172; - large telescopes, 303 - - Metallic specula, 120, 171 - - Meton, meridian observations by, 25 - - Meudon Observatory, solar photography at, 470 - - MICROMETER, THE (Chap. XV.), 218-232; - wire micrometer, 221, 352; - heliometer, 224; - double image, 229; - position, 353; - measurements made by, 355, 359-366, 368 - - Microscopes, for reading transit circles, 247; - for Newall’s telescope, 307 - - Middlesborough, time signal, 278 - - Milky Way, observations of Euclid, 11 - - Miller, spectrum analysis, 410 - - Mirrors, concave and convex, 94-98 - - Mirrors for reflecting telescopes (_see_ Specula) - - MODERN MERIDIONAL OBSERVATIONS (Book IV.), 233-290 - - Molecular vibration, 373, 401, 410, 429, 449, 450 - - Months, first observations of, 5 - - Moon, The, in Ptolemy’s system, 3; - motions observed by the Chaldeans, 4; - parallax observed by Ptolemy, 35; - used by Hipparchus to determine longitude, 44; - as a telescopic object, 350; - the lunar crater, Copernicus, 354; - measurement of shadow thrown by a lunar hill, 355; - photographs and stereographs, 459, 464, 465, 466; - part of Beer and Mädler’s map, 476; - of De La Rue’s photograph, 477 - - MOUNTING OF LARGE TELESCOPES (Chap. XX.), 293-327 - - Mounting of specula for reflecting telescopes, 144, 149, 169 - - Mudge, grinding and polishing specula, 129; - gravity escapement, 200 - - Mural circle, 241, 242 - - Mural quadrant, Tycho Brahe’s, 233, 235 - - Multiple stars, 351 - - - N. - - Nebulæ, 351 - - Nebula of Orion, 157, 158 - - Neptune, as a telescopic object, 351 - - Newall’s equatorial refractor, 302; - with spectroscope, 427; - flint-glass discs for, 119; - production of discs for object-glass, 128; - photographs of the moon, 459 - - Newcastle, time signals, 278 - - Newton (Sir Isaac), on refracting telescopes, 82; - his reflecting telescope, 101, 102; - use of pitch in polishing specula, 128; - refrangibility of light, 387; - polarized light, 442 - - Newtonian reflector, 149; - view of optical part, 143; - effective light, 169; - Grubb’s form, 303; - Browning’s form, 304; - mounting of, 310 - - Nicols’ prism, 115; - measurement of the light of stars, 380; - polarization of light, 443, 447, 448, 449, 450 - - North pole, diagram illustrating how it is found, 249, 251 - - - O. - - Object-glasses, production of, 118, 119; - correction of colour, 88; - correction for spherical aberration, 126; - mode of polishing, 128; - mode of centring, 140; - illustrations of defective adjustment, 141; - adjustment of, 163; - its perfection in modern telescopes, 166, 305; - cost of production, 172; - divided, for duplication of image, 225 - - Object-glass prism, 426 - - Observatories [_see_ Alexandrian Museum, Cambridge (U.S.), Cincinnati, - Edinburgh, Greenwich, Huen (Tycho Brahe’s), Kew, Lord Lindsay’s, - Mauritius, Melbourne, Meudon, Paris, Potsdam, Vienna, Washington] - - Observing chair for equatorial telescopes, 339 - - Optical action of the eye, 67; - long and short sight, 69, 71 - - Optical qualities of telescopes, permanence of, 170 - - Optic axis in crystals of Iceland spar, 228 - - “Optick tube,” telescope so first called, 55, 139-151 - - Orion, first observations of, 5; - Orion and the neighbouring constellations, 156; - nebula of, 157, 158; - stars in, a test for power of telescopes, 164-166; - facilities for observing, 164 - - - P. - - Parallactic rules, 51; - used by Ptolemy, 35; - by Tycho Brahe, 38, 41 - - Parallax of the moon, observed by Ptolemy, 35 - - Paris Observatory, reflecting equatorial telescope, 314, 315, 337; - siderostat, 344; - photoheliograph, 469 - - Pendulum, 183, 185, 187, 188 - - Personal equation, 259 - - Phosphatic glass for lenses, 123 - - PHOTOGRAPHY, CELESTIAL (Chap. XXXI., XXXII.), 454-483 - - Photography, stellar, 172 - - Photoheliograph, for photographs of the sun, 460, 470; - for transit of Venus (1874), 461 - - Photometry, 373, 377 - - PHYSICS, ASTRONOMICAL (Book VI.), 371 - - PHYSICAL INQUIRY, GENERAL FIELD OF (Chap. XXV.), 371-376 - - Picard, transit circle, 284 - - Pisces, its position in the zodiac, 34 - - Pitch employed in polishing lenses and specula, 128, 132 - - Plane of the ecliptic, 13, 14 - - Planets, in Ptolemy’s system, 3; - first observations of conjunction, 4, 5; - motions observed by Autolycus, 9; - in Tycho Brahe’s system, 46; - Saturn seen with object-glasses of 3¾ and 26 inches, 160, 161; - as telescopic objects, 350; - photographs of, 465 - - Pleiades, the first observations of, 5 - - Plücker, spectrum analysis, 413 - - Pogson, star magnitudes, 381, 382 - - Pointers of pre-telescopic instruments, 35, 49, 214, 216 - - Polar axis of the equatorial, 299, 302, 308, 311, 312, 324, 328, 329, - 346 - - Polariscope, 441-453 - - Polarization of light, 441-453 - - Pole, North, 238; - diagram illustrating how it is found, 249 - - Pole star, first observations of, 6; - observations of Euclid, 10, 14; - its position, 238 - - Polishing lenses and specula, 128, 171; - Lord Rosse’s polishing machine, 131; - Mr. Lassell’s, 132 - - Posidonius, measurement of the earth’s circumference, 8 - - Position circle, 353 - - Position micrometer, 353, 358 - - Post Office Telegraphs, for distribution of Greenwich time, 275 - - Potsdam, photoheliograph at, 469 - - Precession of the equinoxes, 33 - - Prime-vertical, 285 - - Prime-vertical instrument, 287 - - Primum mobile of Ptolemy, 3 - - Prisms, action of, 55; - crown and flint-glass, 83, 84; - water, 85; - doubly refracting, for the micrometer, 226; - direct vision, 400; - in the spectroscope, 393-400; - object-glass prism, 426 - - Ptolemy, the Heavens according to, 3; - trigonometrical tables, 17; - sun’s altitude, 21; - his discoveries, 35; - parallax of the moon, 35; - his measurement of time, 36; - parallactic rules, 38, 51 - - Purbach, observation of altitudes by, 36 - - Pyramids, the first constructed astronomical instruments, 5, 6 - - - Q. - - Quadrants used by Tycho Brahe, 38; - his _quadrans maximus_, 48 - - Quadrant, mural, 233, 235 - - Quartz crystals for polarizing light, 450, 452 - - - R. - - Radiation of stars, visual, 383; - thermal, 385 - - Radiation, general and selective, 403, 408 - - Ramsden’s eyepiece, 112, 212 - - Reading microscopes, for Greenwich and Cambridge (U.S.) transit - circles, 247; - for Newall’s telescope, 307 - - Red stars (_see_ Colour of Stars) - - Reflection of light (_see_ Light) - - Reflecting telescopes (_see_ Telescope) - - Reflective powers, Sir John Herschel’s table of, 168 - - Reflector, diagonal, for solar observations, 114 - - Reflecting and refracting telescopes compared, 170 - - Reflex zenith-tube at Greenwich, 286 - - Refracting telescopes (_see_ Telescopes) - - Refracting and reflecting telescopes compared, 170 - - Refraction of light (_see_ Light) - - Refraction, double, by crystals of Iceland spar (_see_ Iceland Spar) - - Refrangibility of colours, 387; - of light, 420 - - Regiomontanus, altitudes measured by, 36 - - Regulation of clocks by electricity, 272 - - Rising of stars (_see_ Stars) - - Right ascension, 24, 234, 241, 249, 257; - measured by Hipparchus, 44; - by Tycho Brahe, 45 - - Ring micrometer, 368 - - Robinson (Dr.), - specula of Melbourne telescope, 129; - apertures of object-glasses, 168 - - Rockets fired as time signals, 281 - - Römer, wires in a transit eyepiece, 220; - transit circle and transit instrument, 284 - - Rosse (Lord), his reflecting telescope, 108, 294, 311, 312; - composition of reflector, 120; - production of metallic specula, 121, 131; - nebula of Orion as seen by his reflector, 157, 158; - illuminating power of his telescope, 159; - effective light, 169; - thermopile observations, 384 - - Royal Observatory, Greenwich (_see_ Greenwich) - - Rudolph II. (Emperor), his patronage of Tycho Brahe, 42 - - Rumford’s photometer, 377 - - Rutherfurd, his work in celestial photography, 455, 464, 466, 471, 477, - 480 - - - S. - - Salts, flame of, in a Bunsen’s burner, 407 - - Sand clocks and sand glasses, 176 - - Saturn, in Ptolemy’s system, 3; - in Tycho Brahe’s, 46; - as seen with a 3¾ inch and 26 inch object-glass, 160, 161; - as a telescopic object, 351; - mode of measuring its rings, 357; - photographs of, 465, 466 - - Savart’s analyser for polarization of light, 452 - - Scarphie, employed by Eratosthenes, 19 - - Scheiner’s telescope, 78 - - Seasons, The, 15, 16 - - Secchi (Father), direct-vision star spectroscope, 431; - stellar spectra, 433 - - Setting of stars (_see_ Stars) - - Sextants used by Tycho Brahe, 38, 50 - - Sidereal clock, 254, 266 (_see_ Clock) - - Sidereal day, 256 - - Sidereal time, 240, 254, 324 - - SIDEROSTAT, THE (Chap. XXIII.), 343-348, 461; - at Lord Lindsay’s Observatory, 347 - - Signals for distributing “Greenwich time,” 278 - - Signals, time, 281, 283 - - Signs of the zodiac (_see_ Zodiac) - - Silver-on-glass reflector at the Paris Observatory, 316 - - Silvering glass specula, modes of, 137; - silvered glass reflectors, 171 - - Simms, his introduction of the collimator in the spectroscope, 393, 425 - - Sirius, first observations of, 5; - spectrum of, 432 - - Slough, Sir Wm. Herschel’s telescope at, 294 - - Smyth (Admiral), stars in Orion, 165; - colours of stars, 351; - star magnitudes, 381 - - Smyth (Prof. Piazzi), on the pyramids as astronomical instruments, 6; - position of the vernal equinox, 34; - clock arrangements at Edinburgh Observatory, 269 - - Sodium, discovery of its presence in the sun, 412 - - Solar photography, 459, 465 - - Solar spectroscope, 435; - Browning’s and Grubb’s forms, 428 - - Solar spectrum, 390, 391, 392, 423, 433, 436, 438, 439; - photographs of, 479, 480 - - Solar time, 253, 255 - - Solstices, first observations of the, 15, 16, 17, 22 - - Southing of stars, 234 - - SPACE MEASURERS (Book III.), 135-232; - circle reading, 211; - Digges’ diagonal scale, 213; - the vernier, 214; - micrometers, 218 - - Space-penetrating power of the telescope, 154; - stars in Orion, a test of, 165 - - Spectroscope, construction of the, 393-400; - automatic, 397; - arranged for showing absorption, 409; - attached to Newall’s refractor, 427; - solar, Browning’s and Grubb’s forms, 428 - - Spectrum produced by prisms, irrationality of the, 86, 87 - - Spectrum, solar, 390, 391, 392 - - Spectrum analysis, principles of, 401-421 - - Specula, production of, 117, 120; - casting, annealing, 121; - curvature, 122; - grinding, 127; - polishing, 128; - silvering, 137; - mounting, 142, 169, 172; - effective light, 169; - repolishing, 171; - cost as compared with object-glasses, 172 - - Spherical aberration, 87; - diagram illustrating, 104, 105; - its correction in eyepieces, 109, 111; - of specula, 123, 124 - - Sprengel pump, 413 - - Spring governor of driving-clock for large telescopes, 319, 320 - - “Spurious disc” of fixed stars, 163 - - Standard clock at Edinburgh Observatory, 272 - - Standard sidereal clock of Greenwich Observatory, 267 - - Standard solar time clock of Greenwich Observatory, 267 - - STARS, CHEMISTRY OF THE (Chap. XXVII.-XXX.), 386-453 - - STARS, LIGHT AND HEAT OF (Chap. XXVI.), 377; - variable, 377-385 - - Stars, first observations of the, 4, 5, 6, 7; - first maps of, 8; - observations of Autolycus, Euclid, and Posidonius, 8, 10; - first catalogues of, 19; - latitude and longitude of, 24, 30; - positions tabulated by Hipparchus, 30; - Tycho Brahe’s catalogue and map of, 42, 44; - stars in Gemini seen through a large telescope, 155; - nebula of Orion, 157; - Orion and its neighbourhood, 156; - double, as defined by telescopes of different power, 162, 164, 167, - 167; - distance of stars from the earth, 159; - facilities for observing Orion, its stars, a test for power of - telescopes, 164; - stellar photography, 172, 465, 466, 467, 478; - their rising and setting as measurers of time, 176; - double, measurement of, 359, 361, 362; - spectrum of red star, 433 - - Star-clusters, double and multiple stars, 351 - - Star-spectra, from Father Secchi’s observations, 433; - photographs of, 479 - - Star spectroscopes, at Cambridge (U.S.), 430; - direct vision, 431 - - Star-time (_see_ Sidereal Time) - - Steinheil, improvement of specula, 117 - - Stellar day, 256 - - Stereographs of the moon, 465, 466 - - Sternberg, Tycho Brahe’s Observatory, 38 - - Stewart (Prof. Balfour), spectrum analysis, 402; - solar photography, 471 - - Stokes (Prof.), experiments with phosphatic glass, 123; - spectrum analysis, 402, 410 - - Stone, thermopile at Greenwich, 384 - - Strontium in the sun, 419 - - Struve, transit instrument, 285; - double stars, 362; - star magnitudes, 381 - - Sun, The; in Ptolemy’s system, 3; - first determination of its yearly course, 8, 15; - course in the zodiac, described by Autolycus, 9; - altitude determined by the gnomon, 16, 18; - and the Scarphie, 19, 20; - telescopes for observing, 114; - “mean sun,” 256; - as a telescopic object, 349; - presence of sodium in, 412, 415; - vapour of other metals, 417; - absorption spectrum, 418; - telespectroscopic observations, 436; - of the chromosphere, 437; - sun-storms, 438, 439; - photographs, 459, 469, 470 - - Sun-dials, 18 - - Sun-spots observed by Galileo and Scheiner, 78; - examined by the position micrometer, 358; - spectra of, 415, 435 - - Sunderland time signals, 278 - - - T. - - Talcott, zenith telescope designed by, 285 - - Taurus, its position in the zodiac, 34 - - Telegraph wires, their application in determining “local time,” 281 - - TELEPOLARISCOPE, THE (Chap. XXX.), 441-453 - - Telespectroscope, 426 - - TELESCOPE, THE (Book II.), 55-172 - - TELESCOPE, THE EQUATORIAL (Book V.), 293-368 - - TELESCOPE:—VARIOUS METHODS OF MOUNTING LARGE TELESCOPES (Chap. XX.), - 293-327; - refracting, 73-89; - Galilean, 73; - magnifying power of the telescope, 76, 79; - Scheiner’s telescope, 78; - focal length of early telescopes, 79; - achromatic, 86; - reflecting, 100-108; - Gregory’s telescope, 101; - Newton’s, 102; - Cassegrain’s, 103; - Sir W. Herschel’s 103, 108; - Lord Rosse’s, De La Rue’s, Lassell’s, Foucault’s, Grubb’s, 108; - eyepieces, 109-116; - Huyghen’s eyepiece, 110; - Ramsden’s eyepiece, 112; - magnifying power of eyepieces, 116; - lenses and specula, 117-138; - flint glass for lenses, 119; - the “optick tube,” 139-151; - the modern telescope, 152-172; - magnifying and space penetrating power, 154, 155; - illuminating power, 158; - defining power, 160; - reflecting and refracting compared, 170; - permanence of optical qualities, 170; - “telescopic sight,” 219; - Sir Wm. Herschel’s at Slough, 294; - Lord Rosse’s reflector, 294, 311, 312; - refractor on alt-azimuth tripod, 296; - simple equatorial mounting, 298; - the German mounting, 299; - Washington great equatorial, 309; - English mounting, 310; - forked mounting, 310; - Greenwich equatorial, 310; - Melbourne reflector, 312, 313; - Paris reflector, 314; - driving clock, 318; - Newall’s refractor with spectroscope, 427; - De La Rue’s, 459; - Rutherfurd’s, 466; - Newall’s, 459; - Melbourne, 459 - - Telescope, zenith (_see_ Zenith Telescope) - - Temperature, its effect on the pendulum, 187, 193 - - Terrestrial globe, 23 - - Thales, his employment of the gnomon, 17 - - Theodolite, 288 - - Theodolite, astronomical, 287 - - Thermometry, 374, 384 - - Thermopile, 374 - - Time; first reckoning of, 19; - early measurements, 36, 44, 175; - modern measurement of, 253; - sidereal, solar, and mean, 254, 256 - - TIME AND SPACE MEASURERS (Book III.), 175-232 - - Time, Greenwich (_see_ Greenwich Time) - - Time, local, 281 - - Time balls for distributing Greenwich time, 275 - - Time signals, 278, 281, 283 - - Timocharis, his observations in the Alexandrian museum, 19 - - Tourmaline, in polarization of light, 443 - - TRANSIT CIRCLE, THE (Chap. XVI.), 233-252; - system of wires in eyepiece, 220; - at Greenwich and Cambridge (U.S.), 247, 248, 251; - mode of using, 253, 284 - - TRANSIT CLOCK, THE (Chap. XVII.), 253-270 - - Transit instrument, 171, 234, 236, 237; - mode of using, 253; - Römer’s, 284; - Struve’s, 285 - - Transit of Venus, photographic observations, 475 - - Trigonometrical tables, first construction of, 17 - - Tropics, defined by Euclid, 12 - - Trouvelot, ring of Saturn observed with the Washington refractor, 161 - - Tube of the telescope, 139-151 - - Tycho Brahe; astrolabe, 26; - ecliptic astrolabe, 28; - discoveries of, 37-52; - biography of, 37; - list of his instruments, 38; - portrait, 39; - catalogue of stars, 42; - observatory (engraving), 43, 287; - his solar system, 46; - discovery of comet of 1677, 47; - instruments for measuring distances and altitudes of stars, 51; - clocks, 179, 184, 196; - diagonal scale for measuring space, 213; - mural quadrant, 233; - transit circle, 284 - - - U. - - United States Naval Observatory, 341 - - Uranus, as a telescopic object, 351 - - Uraniberg, Tycho Brahe’s Observatory, 38 - - - V. - - Variable stars, 377 - - Velocity of gases in sun-storms, 440 - - Venice, ancient clock dials, 257 - - Venus, in Ptolemy’s system, 3; - in Tycho Brahe’s, 46; - employed by Tycho Brahe in determining longitude, 44; - as a telescopic object, 350; - transit of, instrument used in the expedition of 1874, 236; - photographic observations, 475 - - Vibrations, ethereal, 373, 401, 410, 449, 450 - - Vienna, refracting telescope, 141 - - Villarceau, Yvon, driving clocks, 324 - - Vega, heat of, 385 - - Vernal equinox, its position in the constellations, 34 - - Vernier, the, 214 - - Vertical circle, Ertel’s, 290 - - - W. - - Walther, altitudes measured by, 36 - - Washington Observatory; great refracting telescope, 302, 309; - flint glass discs, 119; - ring of Saturn seen through it, 161 - - Watches, detached lever escapement for, 207 - - Water clocks, 176 - - Wave-lengths of light of solar gases, 440 - - Westminster clock-tower, 277 - - Wheatstone (Sir C.); “chronographic method” of transit observation, - 259; - apparatus for controlling clocks, 271 - - Winlock (Prof.), photographs of the sun, 461 - - Wires, cross, for circle reading, 212, 216; - system of wires in a transit eyepiece, 220, 234, 257; - in eyepiece of Greenwich transit circle, 246; - wires of the transit instrument, 234 - - Wire micrometer, 221, 352 - - Wolfius, correction of chromatic aberration in lenses, 89 - - Wollaston (Dr.), lines in the solar spectrum, 391; - spectrum analysis, 402, 422 - - Wyck (Henry de), clock made in 1364 by, 178 - - - Y. - - Ys of the transit instrument, 238, 284 - - Years, first observation of, 5; - determination of their length, 22 - - - Z. - - Zenith, zenith sector, zenith telescope, reflex zenith tube, at - Greenwich, 285 - - Zenith distances, measurement of, 51 - - Zodiac, first defined, 8, 9; - observations of Euclid, 11, 12; - of Denderah, 7 - - Zöllner’s astrophotometer, 379 - - Zero of right ascension, 249 - - Zinc in the sun, 419 - - - THE END. - - - LONDON: R. CLAY, SONS, AND TAYLOR, BREAD STREET HILL, E.C. - - - - - TRANSCRIBER'S NOTES - - - 1. Silently corrected typographical errors. - 2. Retained anachronistic and non-standard spellings as printed. - 3. Enclosed italics font in _underscores_. - 4. Enclosed bold font in =equals=. - 5. Superscripts are denoted by a carat before a single superscript - character or a series of superscripted characters enclosed in - curly braces, e.g. M^r. or M^{ister}. - 6. Subscripts are denoted by an underscore before a series of - subscripted characters enclosed in curly braces, e.g. H_{2}O. - - - - - -End of Project Gutenberg's Stargazing: Past and Present, by J. 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