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diff --git a/40370-h/40370-h.htm b/40370-h/40370-h.htm index c06e743..c8b1bb9 100644 --- a/40370-h/40370-h.htm +++ b/40370-h/40370-h.htm @@ -3,7 +3,7 @@ <head> <meta http-equiv="Content-Type" content= - "text/html; charset=iso-8859-1" /> + "text/html; charset=UTF-8" /> <title> The Project Gutenberg eBook of Encyclopædia Britannica, Volume XIV Slice II − Hydromechanics to Ichnography. @@ -147,46 +147,7 @@ </style> </head> <body> - - -<pre> - -The Project Gutenberg EBook of Encyclopaedia Britannica, 11th Edition, -Volume 14, Slice 2, by Various - -This eBook is for the use of anyone anywhere 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 - - -Title: Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 2 - "Hydromechanics" to "Ichnography" - -Author: Various - -Release Date: July 29, 2012 [EBook #40370] - -Language: English - -Character set encoding: ISO-8859-1 - -*** START OF THIS PROJECT GUTENBERG EBOOK ENCYCLOPAEDIA BRITANNICA *** - - - - -Produced by Marius Masi, Don Kretz and the Online -Distributed Proofreading Team at http://www.pgdp.net - - - - - - -</pre> - - +<div>*** START OF THE PROJECT GUTENBERG EBOOK 40370 ***</div> <table border="0" cellpadding="10" style="background-color: #dcdcdc; color: #696969; " summary="Transcriber's note"> <tr> @@ -234,8 +195,8 @@ Hydromechanics to Ichnography</h3> <tr><td class="tcl"><a href="#ar8">HYDROXYLAMINE</a></td> <td class="tcl"><a href="#ar62">IAPYDES</a></td></tr> <tr><td class="tcl"><a href="#ar9">HYDROZOA</a></td> <td class="tcl"><a href="#ar63">IATROCHEMISTRY</a></td></tr> <tr><td class="tcl"><a href="#ar10">HYENA</a></td> <td class="tcl"><a href="#ar64">IAZYGES</a></td></tr> -<tr><td class="tcl"><a href="#ar11">HYRES</a></td> <td class="tcl"><a href="#ar65">IBADAN</a></td></tr> -<tr><td class="tcl"><a href="#ar12">HYGIEIA</a></td> <td class="tcl"><a href="#ar66">IBAGU</a></td></tr> +<tr><td class="tcl"><a href="#ar11">HYÈRES</a></td> <td class="tcl"><a href="#ar65">IBADAN</a></td></tr> +<tr><td class="tcl"><a href="#ar12">HYGIEIA</a></td> <td class="tcl"><a href="#ar66">IBAGUÉ</a></td></tr> <tr><td class="tcl"><a href="#ar13">HYGIENE</a></td> <td class="tcl"><a href="#ar67">IBARRA</a></td></tr> <tr><td class="tcl"><a href="#ar14">HYGINUS</a> (eighth pope)</td> <td class="tcl"><a href="#ar68">IBERIANS</a></td></tr> <tr><td class="tcl"><a href="#ar15">HYGINUS</a> (Latin writer)</td> <td class="tcl"><a href="#ar69">IBEX</a></td></tr> @@ -282,7 +243,7 @@ Hydromechanics to Ichnography</h3> <hr class="art" /> <p><span class="pagenum"><a name="page115" id="page115"></a>115</span></p> -<p><span class="bold">HYDROMECHANICS<a name="ar1" id="ar1"></a></span> (<span class="grk" title="hydromchanika">ὑδρομηχανικά</span>), the science of the +<p><span class="bold">HYDROMECHANICS<a name="ar1" id="ar1"></a></span> (<span class="grk" title="hydromêchanika">ὑδρομηχανικά</span>), the science of the mechanics of water and fluids in general, including <i>hydrostatics</i> or the mathematical theory of fluids in equilibrium, and <i>hydromechanics</i>, the theory of fluids in motion. The practical application @@ -290,7 +251,7 @@ of hydromechanics forms the province of hydraulics (<i>q.v.</i>).</p> <div class="condensed"> <p><i>Historical.</i>—The fundamental principles of hydrostatics were first -given by Archimedes in his work <span class="grk" title="Peri tn ochoumenn">Περὶ τῶν ὀχουμένων</span>, or <i>De iis quae +given by Archimedes in his work <span class="grk" title="Peri tôn ochoumenôn">Περὶ τῶν ὀχουμένων</span>, or <i>De iis quae vehuntur in humido</i>, about 250 <span class="scs">B.C.</span>, and were afterwards applied to experiments by Marino Ghetaldi (1566-1627) in his <i>Promotus Archimedes</i> (1603). Archimedes maintained that each particle of @@ -356,14 +317,14 @@ of water discharged from different ajutages under different pressures <p>In the hands of Blaise Pascal (1623-1662) hydrostatics assumed the dignity of a science, and in a treatise on the equilibrium of -liquids (<i>Sur l’quilibre des liqueurs</i>), found among his manuscripts +liquids (<i>Sur l’équilibre des liqueurs</i>), found among his manuscripts after his death and published in 1663, the laws of the equilibrium of liquids were demonstrated in the most simple manner, and amply confirmed by experiments.</p> <p>The theorem of Torricelli was employed by many succeeding -writers, but particularly by Edm Mariotte (1620-1684), whose -<i>Trait du mouvement des eaux</i>, published after his death in the year +writers, but particularly by Edmé Mariotte (1620-1684), whose +<i>Traité du mouvement des eaux</i>, published after his death in the year 1686, is founded on a great variety of well-conducted experiments on the motion of fluids, performed at Versailles and Chantilly. In the discussion of some points he committed considerable mistakes. @@ -473,7 +434,7 @@ motions of bodies to that of their equilibrium. He applied this <span class="pagenum"><a name="page116" id="page116"></a>116</span> principle to the motion of fluids, and gave a specimen of its application at the end of his <i>Dynamics</i> in 1743. It was more fully developed -in his <i>Trait des fluides</i>, published in 1744, in which he gave simple +in his <i>Traité des fluides</i>, published in 1744, in which he gave simple and elegant solutions of problems relating to the equilibrium and motion of fluids. He made use of the same suppositions as Daniel Bernoulli, though his calculus was established in a very different @@ -489,8 +450,8 @@ equilibrium, is itself in equilibrium, and that a portion of the fluid, in passing from one place to another, preserves the same volume when the fluid is incompressible, or dilates itself according to a given law when the fluid is elastic. His ingenious method, published -in 1752, in his <i>Essai sur la rsistance des fluides</i>, was brought to perfection -in his <i>Opuscules mathmatiques</i>, and was adopted by Leonhard +in 1752, in his <i>Essai sur la résistance des fluides</i>, was brought to perfection +in his <i>Opuscules mathématiques</i>, and was adopted by Leonhard Euler.</p> <p>The resolution of the questions concerning the motion of fluids @@ -501,8 +462,8 @@ in formulae restricted by no particular hypothesis.</p> <p>One of the most successful labourers in the science of hydrodynamics at this period was Pierre Louis Georges Dubuat (1734-1809). -Following in the steps of the Abb Charles Bossut (<i>Nouvelles -Experiences sur la rsistance des fluides</i>, 1777), he published, in 1786, +Following in the steps of the Abbé Charles Bossut (<i>Nouvelles +Experiences sur la résistance des fluides</i>, 1777), he published, in 1786, a revised edition of his <i>Principes d’hydraulique</i>, which contains a satisfactory theory of the motion of fluids, founded solely upon experiments. Dubuat considered that if water were a perfect @@ -549,14 +510,14 @@ discharge of vessels. His object was to measure the contracted part of a fluid vein, to examine the phenomena attendant on additional tubes, and to investigate the form of the fluid vein and the results obtained when different forms of orifices are employed. Extensive -experiments on the discharge of water from orifices (<i>Expriences +experiments on the discharge of water from orifices (<i>Expériences hydrauliques</i>, Paris, 1832) were conducted under the direction of the French government by J. V. Poncelet (1788-1867) and J. A. Lesbros (1790-1860). P. P. Boileau (1811-1891) discussed their results and -added experiments of his own (<i>Trait de la msure des eaux courantes</i>, +added experiments of his own (<i>Traité de la mésure des eaux courantes</i>, Paris, 1854). K. R. Bornemann re-examined all these results with great care, and gave formulae expressing the variation of the coefficients -of discharge in different conditions (<i>Civil Ingnieur</i>, 1880). +of discharge in different conditions (<i>Civil Ingénieur</i>, 1880). Julius Weisbach (1806-1871) also made many experimental investigations on the discharge of fluids. The experiments of J. B. Francis (<i>Lowell Hydraulic Experiments</i>, Boston, Mass., 1855) led him @@ -567,8 +528,8 @@ flow of water in pipes and channels was conducted by H. G. P. Darcy (1803-1858) and continued by H. Bazin, at the expense of the French government (<i>Recherches hydrauliques</i>, Paris, 1866). German engineers have also devoted special attention to the measurement -of the flow in rivers; the <i>Beitrge zur Hydrographie des Knigreiches -Bhmen</i> (Prague, 1872-1875) of A. R. Harlacher (1842-1890) +of the flow in rivers; the <i>Beiträge zur Hydrographie des Königreiches +Böhmen</i> (Prague, 1872-1875) of A. R. Harlacher (1842-1890) contained valuable measurements of this kind, together with a comparison of the experimental results with the formulae of flow that had been proposed up to the date of its publication, and important data @@ -716,7 +677,7 @@ area ΔA ft.<span class="sp">2</span> enclosing a point B, the pressure p a <p>6. <i>The Equality of Fluid Pressure in all Directions.</i>—This fundamental principle of hydrostatics follows at once from the principle of the normality of fluid pressure implied in the definition of a fluid in - 4. Take any two arbitrary directions in the plane of the paper, and +§ 4. Take any two arbitrary directions in the plane of the paper, and draw a small isosceles triangle abc, whose sides are perpendicular to the two directions, and consider the equilibrium of a small triangular prism of fluid, of which the triangle is the cross section. Let P, Q @@ -806,14 +767,14 @@ prism of liquid; so that, denoting the cross section of the prism by α ft.<span class="sp">2</span>, the pressure at A and By by p<span class="su">0</span> and p ℔/ft.<span class="sp">2</span>, and by w the density of the liquid estimated in ℔/ft.<span class="sp">3</span>,</p> -<p class="center">pα − p<span class="su">0</span>α = wαAB,</p> +<p class="center">pα − p<span class="su">0</span>α = wα·AB,</p> <div class="author">(1)</div> -<p class="center">p = wAB + p<span class="su">0</span>.</p> +<p class="center">p = w·AB + p<span class="su">0</span>.</p> <div class="author">(2)</div> <p>Thus in water, where w = 62.4℔/ft.<span class="sp">3</span>, the pressure increases -62.4 ℔/ft.<span class="sp">2</span>, or 62.4 144 = 0.433 ℔/in.<span class="sp">2</span> for every additional foot of +62.4 ℔/ft.<span class="sp">2</span>, or 62.4 ÷ 144 = 0.433 ℔/in.<span class="sp">2</span> for every additional foot of depth.</p> <p>10. <i>Theorem.</i>—If two liquids of different density are resting in @@ -836,7 +797,7 @@ called the height of the homogeneous atmosphere. Thus water being about 800 times denser than air and mercury 13.6 times denser than water,</p> -<p class="center">k/h = σ/ρ = 800 13.6 = 10,880;</p> +<p class="center">k/h = σ/ρ = 800 × 13.6 = 10,880;</p> <div class="author">(2)</div> <p class="noind">and with an average barometer height of 30 in. this makes k 27,200 @@ -845,7 +806,7 @@ ft., about 8300 metres.</p> <p>11. <i>The Head of Water or a Liquid.</i>—The pressure σh at a depth h ft. in liquid of density σ is called the pressure due to a <i>head</i> of h ft. of the liquid. The atmospheric pressure is thus due to an average -head of 30 in. of mercury, or 30 13.6 12 = 34 ft. of water, or +head of 30 in. of mercury, or 30 × 13.6 ÷ 12 = 34 ft. of water, or 27,200 ft. of air. The pressure of the air is a convenient unit to employ in practical work, where it is called an “atmosphere”; it is made the equivalent of a pressure of one kg/cm<span class="sp">2</span>; and one ton/inch<span class="sp">2</span>, @@ -1041,7 +1002,7 @@ employing the gravitation unit of force,</p> <p class="center">P = <span class="f150">∫</span> dp/ρ = z + a constant.</p> <div class="author">(2)</div> -<p>When the density ρ is uniform, this becomes, as before in (2) 9</p> +<p>When the density ρ is uniform, this becomes, as before in (2) § 9</p> <p class="center">p = ρz + p<span class="su">0</span>.</p> <div class="author">(3)</div> @@ -1172,7 +1133,7 @@ atmosphere at the surface, θ is given by</p> <table class="math0" summary="math"> <tr><td>θ</td> <td rowspan="2">=</td> <td>a</td> -<td rowspan="2"></td> <td>c − r</td> +<td rowspan="2">·</td> <td>c − r</td> <td rowspan="2">.</td></tr> <tr><td class="denom">θ<span class="su">0</span></td> <td class="denom">r</td> <td class="denom">c − a</td></tr></table> @@ -1194,7 +1155,7 @@ on this law to double the density. Then</p> <p class="noind">and if the liquid was incompressible, the depth at pressure p would be (p − p<span class="su">0</span>)/p<span class="su">0</span>, so that the lowering of the surface due to compression is</p> -<p class="center">ke<span class="sp">z/k</span> − k − z = z<span class="sp">2</span>/k, when k is large.</p> +<p class="center">ke<span class="sp">z/k</span> − k − z = ½z<span class="sp">2</span>/k, when k is large.</p> <div class="author">(17)</div> <p>For sea water, λ is about 25,000 atmospheres, and k is then 25,000 @@ -1256,10 +1217,10 @@ the centre of pressure (C.P.) of the area.</p> <p class="center"><span class="ov">x</span>R = <span class="f150">∫ ∫</span> xp dx dy,   <span class="ov">y</span>R = <span class="f150">∫ ∫</span> yp dx dy.</p> <div class="author">(2)</div> -<p>The CP. is thus the CG. of a plane lamina bounded by the area, +<p>The C·P. is thus the C·G. of a plane lamina bounded by the area, in which the surface density is p.</p> -<p>If p is uniform, the CP. and CG. of the area coincide.</p> +<p>If p is uniform, the C·P. and C·G. of the area coincide.</p> <p>For a homogeneous liquid at rest under gravity, p is proportional to the depth below the surface, <i>i.e.</i> to the perpendicular distance @@ -1313,13 +1274,13 @@ the C.G. of the area.</p> <p>Thus the C.P. of a rectangle or parallelogram with a side in the surface is at <span class="spp">2</span>⁄<span class="suu">3</span> of the depth of the lower side; of a triangle with a -vertex in the surface and base horizontal is of the depth of the base; -but if the base is in the surface, the CP. is at half the depth of the +vertex in the surface and base horizontal is ¾ of the depth of the base; +but if the base is in the surface, the C·P. is at half the depth of the vertex; as on the faces of a tetrahedron, with one edge in the surface.</p> <p>The <i>core</i> of an area is the name given to the limited area round -its C.G. within which the CP. must lie when the area is immersed +its C.G. within which the C·P. must lie when the area is immersed completely; the boundary of the core is therefore the locus of the antipodes with respect to the momental ellipse of water lines which touch the boundary of the area. Thus the core of a circle or an @@ -1342,7 +1303,7 @@ of tension anywhere and so liable to open and admit the water.</p> <tr><td class="caption"><span class="sc">Fig. 3.</span></td></tr></table> <p>17. <i>Equilibrium and Stability of a Ship or Floating Body.</i> -<i>The Metacentre.</i>—The principle of Archimedes in 12 leads +<i>The Metacentre.</i>—The principle of Archimedes in § 12 leads immediately to the conditions of equilibrium of a body supported @@ -1409,14 +1370,14 @@ of a pendulum 20 ft. long to move through 10 in., so that</p> <table class="math0" summary="math"> <tr><td rowspan="2">GM =</td> <td>240</td> -<td rowspan="2"> 42 </td> <td>20</td> +<td rowspan="2">× 42 ×</td> <td>20</td> <td rowspan="2">2.24 ft.</td></tr> <tr><td class="denom">10</td> <td class="denom">9000</td></tr></table> <div class="author">(2)</div> <p class="noind">also</p> -<p class="center">cot θ = 24, θ = 224′.</p> +<p class="center">cot θ = 24, θ = 2°24′.</p> <div class="author">(3)</div> <p>In a diagram it is conducive to clearness to draw the ship in one @@ -1434,7 +1395,7 @@ and call the centre of flotation.</p> <p>The righting couple of the wedges of immersion and emersion will be</p> -<p class="center">Σwy dA tan θy = w tan θ Σ y<span class="sp">2</span> dA = w tan θAk<span class="sp">2</span> ft. tons,</p> +<p class="center">Σwy dA tan θ·y = w tan θ Σ y<span class="sp">2</span> dA = w tan θ·Ak<span class="sp">2</span> ft. tons,</p> <div class="author">(4)</div> <p class="noind">w denoting the density of water in tons/ft.<span class="sp">3</span>, and W = wV, for a @@ -1458,8 +1419,8 @@ of displacement.</p> the ship about an axis perpendicular to the plane of the couple, only when this axis is a principal axis at F of the momental ellipse of the water-line area A. For if the ship turns through a small angle θ -about the line FF′, then b<span class="su">1</span>, b<span class="su">2</span>, the CG. of the wedge of immersion -and emersion, will be the CP. with respect to FF′ of the two parts of +about the line FF′, then b<span class="su">1</span>, b<span class="su">2</span>, the C·G. of the wedge of immersion +and emersion, will be the C·P. with respect to FF′ of the two parts of the water-line area, so that b<span class="su">1</span>b<span class="su">2</span> will be conjugate to FF′ with respect to the momental ellipse at F.</p> @@ -1468,13 +1429,13 @@ represented by the righting couple W.BM, and the <i>stability of ballasting</i>, represented by W.BG. Ballasted with G at B, the righting couple when the ship is heeled through θ is given by W.BM. tanθ; but if weights inside the ship are raised to bring G above B, the righting -couple is diminished by WBG.tanθ, so that the resultant righting -couple is WGMtanθ. Provided the ship is designed to float +couple is diminished by W·BG.tanθ, so that the resultant righting +couple is W·GM·tanθ. Provided the ship is designed to float upright at the smallest draft with no load on board, the stability at any other draft of water can be arranged by the stowage of the weight, high or low.</p> -<p>19. Proceeding as in 16 for the determination of the C.P. of an +<p>19. Proceeding as in § 16 for the determination of the C.P. of an area, the same argument will show that an inclining couple due to <span class="pagenum"><a name="page120" id="page120"></a>120</span> the movement of a weight P through a distance c will cause the ship @@ -1505,9 +1466,9 @@ from F</p> <tr><td rowspan="2">sin θ =</td> <td>1</td> <td rowspan="2">=</td> <td>P</td> <td rowspan="2">=</td> <td>P</td> -<td rowspan="2"></td> <td>V</td> +<td rowspan="2">·</td> <td>V</td> <td rowspan="2">FQ sin QFF′</td></tr> -<tr><td class="denom">m</td> <td class="denom">wAFK</td> +<tr><td class="denom">m</td> <td class="denom">wA·FK</td> <td class="denom">W</td> <td class="denom">Ak<span class="sp">2</span> − hV</td></tr></table> <div class="author">(3)</div> @@ -1705,7 +1666,7 @@ unit of hydrostatics; in a numerical application it is assumed that C.G.S. units are intended.</p> <p>These equations may be simplified slightly, using the equation of -continuity (5) 21; for</p> +continuity (5) § 21; for</p> <table class="math0" summary="math"> <tr><td>dρu</td> @@ -1796,7 +1757,7 @@ for a moving particle; denoting the change by DF/dt,</p> <table class="math0" summary="math"> <tr><td>DF</td> -<td rowspan="2">= lt</td> <td> F(x + uδt, y + vδt, z + wδt, t + δt) − F(x, y, z, t)</td> +<td rowspan="2">= lt·</td> <td> F(x + uδt, y + vδt, z + wδt, t + δt) − F(x, y, z, t)</td> </tr> <tr><td class="denom">dt</td> <td class="denom">δt</td></tr></table> @@ -1942,7 +1903,7 @@ rate of diminution of V, or its downward gradient; and then</p> <p class="noind">where</p> -<p class="center">H = ∫ dp/ρ + V + q<span class="sp">2</span>,</p> +<p class="center">H = ∫ dp/ρ + V + ½q<span class="sp">2</span>,</p> <div class="author">(7)</div> <p class="center">q<span class="sp">2</span> = u<span class="sp">2</span> + v<span class="sp">2</span> + w<span class="sp">2</span>,</p> @@ -1950,7 +1911,7 @@ rate of diminution of V, or its downward gradient; and then</p> <p class="noind">and the three terms in H may be called the pressure head, potential head, and head of velocity, when the gravitation unit is employed -and q<span class="sp">2</span> is replaced by q<span class="sp">2</span>/g.</p> +and ½q<span class="sp">2</span> is replaced by ½q<span class="sp">2</span>/g.</p> <p>Eliminating H between (5) and (6)</p> @@ -2034,9 +1995,9 @@ functions φ, ψ, m of x, y, z, such that</p> (<i>Crelle</i>, lvi.); and then</p> <table class="math0" summary="math"> -<tr><td rowspan="2">ξ = </td> <td>d(ψ, m)</td> -<td rowspan="2">,   η = </td> <td>d(ψ, m)</td> -<td rowspan="2">,   ζ = </td> <td>d(ψ, m)</td> +<tr><td rowspan="2">ξ = ½</td> <td>d(ψ, m)</td> +<td rowspan="2">,   η = ½</td> <td>d(ψ, m)</td> +<td rowspan="2">,   ζ = ½</td> <td>d(ψ, m)</td> <td rowspan="2">,</td></tr> <tr><td class="denom">d(y, z)</td> <td class="denom">d(z, x)</td> <td class="denom">d(x, y)</td></tr></table> @@ -2069,7 +2030,7 @@ intersect in the vortex lines.</p> <tr><td class="denom">dt</td> <td class="denom">dt</td></tr></table> <div class="author">(4)</div> -<p class="noind">the equations of motion (4), (5), (6) 24 can be written</p> +<p class="noind">the equations of motion (4), (5), (6) § 24 can be written</p> <table class="math0" summary="math"> <tr><td>dK</td> @@ -2127,9 +2088,9 @@ intersect in the vortex lines.</p> <td class="denom">dt</td></tr></table> <div class="author">(8)</div> -<p class="noind">and as we prove subsequently ( 37) that the vortex lines are composed +<p class="noind">and as we prove subsequently (§ 37) that the vortex lines are composed of the same fluid particles throughout the motion, the surface m and -ψ satisfies the condition of (6) 23; so that K is uniform throughout +ψ satisfies the condition of (6) § 23; so that K is uniform throughout the fluid at any instant, and changes with the time only, and so may be replaced by F(t).</p> @@ -2157,7 +2118,7 @@ point of space does not change with the time,</p> <p class="noind">and</p> -<p class="center">K = ∫ dp/ρ + V + q<span class="sp">2</span> = H</p> +<p class="center">K = ∫ dp/ρ + V + ½q<span class="sp">2</span> = H</p> <div class="author">(3)</div> <p class="noind">is constant along a vortex line, and a <i>stream line</i>, the path of a fluid @@ -2194,7 +2155,7 @@ perpendicular.</p> <td rowspan="2"> </td> <td>dp</td> <td rowspan="2">+</td> <td>dV</td> <td rowspan="2">=</td> <td>dH</td> -<td rowspan="2">−</td> <td>d q<span class="sp">2</span></td> +<td rowspan="2">−</td> <td>d ½q<span class="sp">2</span></td> <td rowspan="2">=</td> <td>q<span class="sp">2</span></td> <td rowspan="2">,</td></tr> <tr><td class="denom">ρ</td> <td class="denom">dν</td> @@ -2211,8 +2172,8 @@ the resultant acceleration, the direction ratios of which are</p> <tr><td rowspan="2">u</td> <td>du</td> <td rowspan="2">+ v</td> <td>du</td> <td rowspan="2">+ w</td> <td>du</td> -<td rowspan="2">=</td> <td>d q<span class="sp">2</span></td> -<td rowspan="2">− 2vζ + 2wη =</td> <td>d q<span class="sp">2</span></td> +<td rowspan="2">=</td> <td>d ½q<span class="sp">2</span></td> +<td rowspan="2">− 2vζ + 2wη =</td> <td>d ½q<span class="sp">2</span></td> <td rowspan="2">−</td> <td>dH</td> <td rowspan="2">, ...,</td></tr> <tr><td class="denom">dx</td> <td class="denom">dy</td> @@ -2278,7 +2239,7 @@ accordance with the continuity.</p> <p>Thus if dψ is the increase of ψ due to a displacement from P to P′, and k is the component of velocity normal to PP′, the flow across -PP′ is dψ = kPP′; and taking PP′ parallel to Ox, dψ = v dx; and +PP′ is dψ = k·PP′; and taking PP′ parallel to Ox, dψ = v dx; and similarly dψ= −u dy with PP′ parallel to Oy; and generally dψ/ds is the velocity across ds, in a direction turned through a right angle forward, against the clock.</p> @@ -2414,7 +2375,7 @@ and longitude λ can be written</p> <p class="noind">and then</p> -<p class="center">φ + ψi = F (tan θe<span class="sp">λi</span>).</p> +<p class="center">φ + ψi = F (tan ½θ·e<span class="sp">λi</span>).</p> <div class="author">(14)</div> <p>28. <i>Uniplanar Motion of a Liquid due to the Passage of a Cylinder @@ -2453,7 +2414,7 @@ moving with components U and V of velocity.</p> <tr><td class="denom">ds</td> <td class="denom">ds</td></tr></table> <div class="author">(5)</div> -<p class="center">ψ + R (x<span class="sp">2</span> + y<span class="sp">2</span>) = ψ′,</p> +<p class="center">ψ + ½R (x<span class="sp">2</span> + y<span class="sp">2</span>) = ψ′,</p> <div class="author">(6)</div> <p class="noind">a constant over the boundary; and ψ′ is the current-function of @@ -2471,7 +2432,7 @@ the relative motion past the cylinder, but now</p> <p class="noind">where α, β, γ are the perpendiculars on the sides of the triangle.</p> -<p>In the general case ψ′ = ψ + Uy − Vx + R (x<span class="sp">2</span> + y<span class="sp">2</span>) is the relative +<p>In the general case ψ′ = ψ + Uy − Vx + ½R (x<span class="sp">2</span> + y<span class="sp">2</span>) is the relative stream function for velocity components, U, V, R.</p> <p>29. <i>Example 1.</i>—Liquid motion past a circular cylinder.</p> @@ -2551,7 +2512,7 @@ velocity U through the origin O in the direction Ox.</p> <tr><td rowspan="2">tan θ′ =</td> <td>dφ</td> <td rowspan="2"><span class="f150">/</span></td> <td>dφ</td> <td rowspan="2">=</td> <td>2xy</td> -<td rowspan="2">= tan 2θ,   θ = θ′,</td></tr> +<td rowspan="2">= tan 2θ,   θ = ½θ′,</td></tr> <tr><td class="denom">dy</td> <td class="denom">dx</td> <td class="denom">x<span class="sp">2</span> − y<span class="sp">2</span></td></tr></table> <div class="author">(9)</div> @@ -2561,14 +2522,14 @@ velocity U through the origin O in the direction Ox.</p> <p>Along the path of a particle, defined by the C<span class="su">3</span> of (3),</p> <table class="math0" summary="math"> -<tr><td rowspan="2">sin<span class="sp">2</span> θ′ =</td> <td>y<span class="sp">2</span></td> +<tr><td rowspan="2">sin<span class="sp">2</span> ½θ′ =</td> <td>y<span class="sp">2</span></td> <td rowspan="2">=</td> <td>y (y − c)</td> <td rowspan="2">,</td></tr> <tr><td class="denom">x<span class="sp">2</span> + y<span class="sp">2</span></td> <td class="denom">a<span class="sp">2</span></td></tr></table> <div class="author">(10)</div> <table class="math0" summary="math"> -<tr><td rowspan="2"> sin θ′</td> <td>dθ′</td> +<tr><td rowspan="2">½ sin θ′</td> <td>dθ′</td> <td rowspan="2">=</td> <td>2y − c</td> <td rowspan="2"> </td> <td>dy</td> <td rowspan="2">,</td></tr> @@ -2576,7 +2537,7 @@ velocity U through the origin O in the direction Ox.</p> <td class="denom">ds</td></tr></table> <div class="author">(11)</div> -<p class="noind">on the radius of curvature is a<span class="sp">2</span>/(y − c), which shows that the curve +<p class="noind">on the radius of curvature is ¼a<span class="sp">2</span>/(y − ½c), which shows that the curve is an Elastica or Lintearia. (J. C. Maxwell, <i>Collected Works</i>, ii. 208.)</p> <p>If φ<span class="su">1</span> denotes the velocity function of the liquid filling the cylinder @@ -2597,7 +2558,7 @@ r = b, and moving bodily with it with velocity U<span class="su">1</span>,</p> <td class="denom">b<span class="sp">2</span></td> <td class="denom">a<span class="sp">2</span> − b<span class="sp">2</span></td></tr></table> <div class="author">(13)</div> -<p class="noind">and this, by 36, is also the ratio of the kinetic energy in the annular +<p class="noind">and this, by § 36, is also the ratio of the kinetic energy in the annular interspace between the two cylinders to the kinetic energy of the liquid moving bodily inside r = b.</p> @@ -2692,10 +2653,10 @@ velocity U<span class="su">1</span> along Ox,</p> <div class="author">(19)</div> <p>The resultant impulse of the liquid on the cylinder is given by the -component, over r = a ( 36),</p> +component, over r = a (§ 36),</p> <table class="math0" summary="math"> -<tr><td rowspan="2">X = ∫ ρφ cos θa dθ = πρa<span class="sp">2</span> <span class="f150">(</span> U</td> <td>b<span class="sp">2</span> + a<span class="sp">2</span></td> +<tr><td rowspan="2">X = ∫ ρφ cos θ·a dθ = πρa<span class="sp">2</span> <span class="f150">(</span> U</td> <td>b<span class="sp">2</span> + a<span class="sp">2</span></td> <td rowspan="2">− U<span class="su">1</span></td> <td>2b<span class="sp">2</span></td> <td rowspan="2"><span class="f150">)</span>;</td></tr> <tr><td class="denom">b<span class="sp">2</span> − a<span class="sp">2</span></td> <td class="denom">b<span class="sp">2</span> − a<span class="sp">2</span></td></tr></table> @@ -2704,7 +2665,7 @@ component, over r = a ( 36),</p> <p class="noind">and over r = b</p> <table class="math0" summary="math"> -<tr><td rowspan="2">X<span class="su">1</span> = ∫ ρφ cos θb dθ = πρb<span class="sp">2</span> <span class="f150">(</span> U</td> <td>2a<span class="sp">2</span></td> +<tr><td rowspan="2">X<span class="su">1</span> = ∫ ρφ cos θ·b dθ = πρb<span class="sp">2</span> <span class="f150">(</span> U</td> <td>2a<span class="sp">2</span></td> <td rowspan="2">− U<span class="su">1</span></td> <td>b<span class="sp">2</span> + a<span class="sp">2</span></td> <td rowspan="2"><span class="f150">)</span>,</td></tr> <tr><td class="denom">b<span class="sp">2</span> − a<span class="sp">2</span></td> <td class="denom">b<span class="sp">2</span> − a<span class="sp">2</span></td></tr></table> @@ -2743,7 +2704,7 @@ inside cylinder is solid or filled with liquid of density σ,</p> <p class="noind">and the inside cylinder starts forward or backward with respect to the outside cylinder, according as ρ > or < σ.</p> -<p>30. The expression for ω in (1) 29 may be increased by the +<p>30. The expression for ω in (1) § 29 may be increased by the addition of the term</p> <p class="center">im log z = −mθ + im log r,</p> @@ -2840,7 +2801,7 @@ or golf.</p> <p>Another explanation may be given of the sidelong force, arising from the velocity of liquid past a cylinder, which is encircled by a -vortex. Taking two planes x = b, and considering the increase of +vortex. Taking two planes x = ± b, and considering the increase of momentum in the liquid between them, due to the entry and exit of liquid momentum, the increase across dy in the direction Oy, due to elements at P and P′ at opposite ends of the diameter PP′, is</p> @@ -2859,7 +2820,7 @@ due to elements at P and P′ at opposite ends of the diameter PP′, is <p class="center">2ρmU dθ (1 − a<span class="sp">2</span>b<span class="sp">−2</span> cos 3θ cos θ),</p> <div class="author">(9)</div> -<p class="noind">and integrating between the limits θ = π, the resultant, as before, +<p class="noind">and integrating between the limits θ = ±½π, the resultant, as before, is 2πρmU.</p> <p>31. <i>Example 2.—Confocal Elliptic Cylinders.</i>—Employ the elliptic @@ -2882,12 +2843,12 @@ and hyperbolas, and</p> <p class="noind">if OD is the semi-diameter conjugate to OP, and r<span class="su">1</span>, r<span class="su">2</span> the focal distances,</p> -<p class="center">r<span class="su">1</span>, r<span class="su">2</span> = c (ch η cos ξ);</p> +<p class="center">r<span class="su">1</span>, r<span class="su">2</span> = c (ch η ± cos ξ);</p> <div class="author">(3)</div> <p class="center">r<span class="sp">2</span> = x<span class="sp">2</span> + y<span class="sp">2</span> = c<span class="sp">2</span> (ch<span class="sp">2</span> η − sin<span class="sp">2</span> ξ)</p> -<p class="center">= c<span class="sp">2</span> (ch 2η + cos 2ξ).</p> +<p class="center">= ½c<span class="sp">2</span> (ch 2η + cos 2ξ).</p> <div class="author">(4)</div> <p>Consider the streaming motion given by</p> @@ -2977,7 +2938,7 @@ when the tangent has turned through a right angle, and then</p> = −Uc ch (η − α) sh η cos ξ/sh (η − α)</p> <div class="author">(12)</div> -<p class="noind">over the cylinder η, and as in (12) 29,</p> +<p class="noind">over the cylinder η, and as in (12) § 29,</p> <p class="center">φ<span class="su">1</span> = −Ux = −Uc ch η cos ξ,</p> <div class="author">(13)</div> @@ -3006,13 +2967,13 @@ the liquid extends to infinity.</p> <p class="noind">in which ψ = 0 over the ellipse α, and</p> -<p class="center">ψ′ = ψ + R (x<span class="sp">2</span> + y<span class="sp">2</span>) -= [ −m sh 2 (η − α) + Rc<span class="sp">2</span> ] cos 2ξ + Rc<span class="sp">2</span> ch 2η,</p> +<p class="center">ψ′ = ψ + ½R (x<span class="sp">2</span> + y<span class="sp">2</span>) += [ −m sh 2 (η − α) + ¼Rc<span class="sp">2</span> ] cos 2ξ + ¼Rc<span class="sp">2</span> ch 2η,</p> <div class="author">(2)</div> <p class="noind">which is constant over the ellipse η if</p> -<p class="center"> Rc<span class="sp">2</span> = m sh 2 (η − α);</p> +<p class="center">¼ Rc<span class="sp">2</span> = m sh 2 (η − α);</p> <div class="author">(3)</div> <p class="noind">so that this ellipse can be rotating with this angular velocity R for @@ -3031,13 +2992,13 @@ cross section</p> <p class="center">∇<span class="sp">2</span>ψ<span class="su">1</span>′ = −2R = −2m<span class="su">1</span> (1/a<span class="sp">2</span> + 1/b<span class="sp">2</span>),</p> -<p class="center">ψ<span class="su">1</span> = m<span class="su">1</span> (x<span class="sp">2</span>/a<span class="sp">2</span> + y<span class="sp">2</span>/b<span class="sp">2</span>) − R (x<span class="sp">2</span> + y<span class="sp">2</span>)<br /> -= −R (x<span class="sp">2</span> − y<span class="sp">2</span>) (a<span class="sp">2</span> − b<span class="sp">2</span>) / (a<span class="sp">2</span> + b<span class="sp">2</span>),</p> +<p class="center">ψ<span class="su">1</span> = m<span class="su">1</span> (x<span class="sp">2</span>/a<span class="sp">2</span> + y<span class="sp">2</span>/b<span class="sp">2</span>) − ½R (x<span class="sp">2</span> + y<span class="sp">2</span>)<br /> += −½R (x<span class="sp">2</span> − y<span class="sp">2</span>) (a<span class="sp">2</span> − b<span class="sp">2</span>) / (a<span class="sp">2</span> + b<span class="sp">2</span>),</p> <div class="author">(6)</div> <p class="center">φ<span class="su">1</span> = Rxy (a<span class="sp">2</span> − b<span class="sp">2</span>) / (a<span class="sp">2</span> + b<span class="sp">2</span>),</p> -<p class="center">w<span class="su">1</span> = φ<span class="su">1</span> + ψ<span class="su">1</span>i = −iR (x + yi)<span class="sp">2</span> (a<span class="sp">2</span> − b<span class="sp">2</span>) / (a<span class="sp">2</span> + b<span class="sp">2</span>).</p> +<p class="center">w<span class="su">1</span> = φ<span class="su">1</span> + ψ<span class="su">1</span>i = −½iR (x + yi)<span class="sp">2</span> (a<span class="sp">2</span> − b<span class="sp">2</span>) / (a<span class="sp">2</span> + b<span class="sp">2</span>).</p> <p>The velocity of a liquid particle is thus (a<span class="sp">2</span> − b<span class="sp">2</span>)/(a<span class="sp">2</span> + b<span class="sp">2</span>) of what it would be if the liquid was frozen and rotating bodily with @@ -3045,7 +3006,7 @@ the ellipse; and so the effective angular inertia of the liquid is (a<span class="sp">2</span> − b<span class="sp">2</span>)<span class="sp">2</span>/(a<span class="sp">2</span> + b<span class="sp">2</span>)<span class="sp">2</span> of the solid; and the effective radius of gyration, solid and liquid, is given by</p> -<p class="center">k<span class="sp">2</span> = (a<span class="sp">2</span> + b<span class="sp">2</span>), and (a<span class="sp">2</span> − b<span class="sp">2</span>)<span class="sp">2</span> / (a<span class="sp">2</span> + b<span class="sp">2</span>).</p> +<p class="center">k<span class="sp">2</span> = ¼(a<span class="sp">2</span> + b<span class="sp">2</span>), and ¼(a<span class="sp">2</span> − b<span class="sp">2</span>)<span class="sp">2</span> / (a<span class="sp">2</span> + b<span class="sp">2</span>).</p> <div class="author">(7)</div> <p>For the liquid in the interspace between α and η,</p> @@ -3054,31 +3015,31 @@ solid and liquid, is given by</p> <tr><td>φ</td> <td rowspan="2">=</td> <td>m ch 2 (η − α) sin 2ξ</td> </tr> -<tr><td class="denom">φ<span class="su">1</span></td> <td class="denom"> Rc<span class="sp">2</span> sh 2η sin 2ξ (a<span class="sp">2</span> − b<span class="sp">2</span>) / (a<span class="sp">2</span> + b<span class="sp">2</span>)</td></tr></table> +<tr><td class="denom">φ<span class="su">1</span></td> <td class="denom">¼ Rc<span class="sp">2</span> sh 2η sin 2ξ (a<span class="sp">2</span> − b<span class="sp">2</span>) / (a<span class="sp">2</span> + b<span class="sp">2</span>)</td></tr></table> <p class="center">= 1/th 2 (η − α) th 2η;</p> <div class="author">(8)</div> <p class="noind">and the effective k<span class="sp">2</span> of the liquid is reduced to</p> -<p class="center"> c<span class="sp">2</span>/th 2 (η − α) sh 2η,</p> +<p class="center">¼ c<span class="sp">2</span>/th 2 (η − α) sh 2η,</p> <div class="author">(9)</div> -<p class="noind">which becomes c<span class="sp">2</span>/sh 2η = <span class="spp">1</span>⁄<span class="suu">8</span> (a<span class="sp">2</span> − b<span class="sp">2</span>)/ab, when α = ∞, and the liquid +<p class="noind">which becomes ¼ c<span class="sp">2</span>/sh 2η = <span class="spp">1</span>⁄<span class="suu">8</span> (a<span class="sp">2</span> − b<span class="sp">2</span>)/ab, when α = ∞, and the liquid surrounds the ellipse η to infinity.</p> <p>An angular velocity R, which gives components −Ry, Rx of velocity to a body, can be resolved into two shearing velocities, −R parallel to Ox, and R parallel to Oy; and then ψ is resolved into -ψ<span class="su">1</span> + ψ<span class="su">2</span>, such that ψ<span class="su">1</span> + Rx<span class="sp">2</span> and ψ<span class="su">2</span> + Ry<span class="sp">2</span> is constant over the +ψ<span class="su">1</span> + ψ<span class="su">2</span>, such that ψ<span class="su">1</span> + ½Rx<span class="sp">2</span> and ψ<span class="su">2</span> + ½Ry<span class="sp">2</span> is constant over the boundary.</p> <p>Inside a cylinder</p> -<p class="center">φ<span class="su">1</span> + ψ<span class="su">1</span>i = − iR (x + yi)<span class="sp">2</span> a<span class="sp">2</span> / (a<span class="sp">2</span> + b<span class="sp">2</span>),</p> +<p class="center">φ<span class="su">1</span> + ψ<span class="su">1</span>i = −½ iR (x + yi)<span class="sp">2</span> a<span class="sp">2</span> / (a<span class="sp">2</span> + b<span class="sp">2</span>),</p> <div class="author">(10)</div> -<p class="center">φ<span class="su">2</span> + ψ<span class="su">2</span>i = iR (x + yi)<span class="sp">2</span> b<span class="sp">2</span> / (a<span class="sp">2</span> + b<span class="sp">2</span>),</p> +<p class="center">φ<span class="su">2</span> + ψ<span class="su">2</span>i = ½ iR (x + yi)<span class="sp">2</span> b<span class="sp">2</span> / (a<span class="sp">2</span> + b<span class="sp">2</span>),</p> <div class="author">(11)</div> <p class="noind">and for the interspace, the ellipse α being fixed, and α<span class="su">1</span> revolving @@ -3093,10 +3054,10 @@ with angular velocity R</p> <p class="noind">satisfying the condition that ψ<span class="su">1</span> and ψ<span class="su">2</span> are zero over η = α, and over η = α<span class="su">1</span></p> -<p class="center">ψ<span class="su">1</span> + Rx<span class="sp">2</span> = <span class="spp">1</span>⁄<span class="suu">8</span> Rc<span class="sp">2</span> (ch 2α<span class="su">1</span> + 1),</p> +<p class="center">ψ<span class="su">1</span> + ½ Rx<span class="sp">2</span> = <span class="spp">1</span>⁄<span class="suu">8</span> Rc<span class="sp">2</span> (ch 2α<span class="su">1</span> + 1),</p> <div class="author">(14)</div> -<p class="center">ψ<span class="su">2</span> + Ry<span class="sp">2</span> = <span class="spp">1</span>⁄<span class="suu">8</span> Rc<span class="sp">2</span> (ch 2α<span class="su">1</span> − 1),</p> +<p class="center">ψ<span class="su">2</span> + ½ Ry<span class="sp">2</span> = <span class="spp">1</span>⁄<span class="suu">8</span> Rc<span class="sp">2</span> (ch 2α<span class="su">1</span> − 1),</p> <div class="author">(15)</div> <p class="noind">constant values.</p> @@ -3118,7 +3079,7 @@ term mζ in w.</p> <p class="noind">the function</p> -<p class="center">ψ = Qc sh (η − α) sin (ξ − β)</p> +<p class="center">ψ = Qc sh ½ (η − α) sin ½ (ξ − β)</p> <div class="author">(18)</div> <p class="noind">will give motion streaming past the fixed cylinder η = α, and dividing @@ -3132,7 +3093,7 @@ along ξ = β; and then</p> <p class="center">x<span class="sp">4</span> + 6x<span class="sp">2</span>y<span class="sp">2</span> + y<span class="sp">4</span> = 2c<span class="sp">4</span>, or x<span class="sp">4</span> + y<span class="sp">4</span> = c<span class="sp">4</span></p> <div class="author">(20)</div> -<p class="noind">when the axes are turned through 45.</p> +<p class="noind">when the axes are turned through 45°.</p> <p>33. <i>Example 3.</i>—Analysing in this way the rotation of a rectangle filled with liquid into the two components of shear, the stream @@ -3141,16 +3102,16 @@ function ψ<span class="su">1</span> is to be made to satisfy the conditions< <table class="reg" summary="poem"><tr><td> <div class="poemr"> <p>(i.) ∇<span class="sp">2</span>ψ<span class="su">1</span> = 0,</p> -<p>(ii.) ψ<span class="su">1</span> + Rx<span class="sp">2</span> = Ra<span class="sp">2</span>, or ψ<span class="su">1</span> = 0 when x = a,</p> +<p>(ii.) ψ<span class="su">1</span> + ½Rx<span class="sp">2</span> = ½Ra<span class="sp">2</span>, or ψ<span class="su">1</span> = 0 when x = ±a,</p> -<p>(iii.) ψ<span class="su">1</span> + Rx<span class="sp">2</span> = Ra<span class="sp">2</span>, ψ<span class="su">1</span> = R (a<span class="sp">2</span> − x<span class="sp">2</span>), when y = b.</p> +<p>(iii.) ψ<span class="su">1</span> + ½Rx<span class="sp">2</span> = ½Ra<span class="sp">2</span>, ψ<span class="su">1</span> = ½R (a<span class="sp">2</span> − x<span class="sp">2</span>), when y = ± b.</p> </div> </td></tr></table> <p>Expanded in a Fourier series,</p> <table class="math0" summary="math"> <tr><td rowspan="2">a<span class="sp">2</span> − x<span class="sp">2</span> =</td> <td>32</td> -<td rowspan="2">a<span class="sp">2</span> <span class="f150">Σ</span></td> <td>cos (2n + 1) πx/a</td> +<td rowspan="2">a<span class="sp">2</span> <span class="f150">Σ</span></td> <td>cos (2n + 1) ½ πx/a</td> <td rowspan="2">,</td></tr> <tr><td class="denom">π<span class="sp">3</span></td> <td class="denom">(2n + 1)<span class="sp">3</span></td></tr></table> <div class="author">(1)</div> @@ -3159,15 +3120,15 @@ function ψ<span class="su">1</span> is to be made to satisfy the conditions< <table class="math0" summary="math"> <tr><td rowspan="2">ψ<span class="su">1</span> = R</td> <td>16</td> -<td rowspan="2">a<span class="sp">2</span> <span class="f150">Σ</span></td> <td>cos (2n + 1) πx/a ch (2n + 1) πy/a)</td> +<td rowspan="2">a<span class="sp">2</span> <span class="f150">Σ</span></td> <td>cos (2n + 1) ½πx/a · ch (2n + 1) ½πy/a)</td> <td rowspan="2">,</td></tr> -<tr><td class="denom">π<span class="sp">3</span></td> <td class="denom">(2n + 1)<span class="sp">3</span> ch (2n + 1) πb/a</td></tr></table> +<tr><td class="denom">π<span class="sp">3</span></td> <td class="denom">(2n + 1)<span class="sp">3</span> · ch (2n + 1) ½πb/a</td></tr></table> <table class="math0" summary="math"> <tr><td rowspan="2">w<span class="su">1</span> = φ<span class="su">1</span> + ψ<span class="su">1</span>i = iR</td> <td>16</td> -<td rowspan="2">a<span class="sp">2</span> <span class="f150">Σ</span></td> <td>cos (2n + 1) πz/a</td> +<td rowspan="2">a<span class="sp">2</span> <span class="f150">Σ</span></td> <td>cos (2n + 1) ½πz/a</td> <td rowspan="2">,</td></tr> -<tr><td class="denom">π<span class="sp">3</span></td> <td class="denom">(2n + 1)<span class="sp">3</span> ch (2n + 1) πb/a</td></tr></table> +<tr><td class="denom">π<span class="sp">3</span></td> <td class="denom">(2n + 1)<span class="sp">3</span> ch (2n + 1) ½πb/a</td></tr></table> <div class="author">(2)</div> <p class="noind">an elliptic-function Fourier series; with a similar expression for ψ<span class="su">2</span> @@ -3178,15 +3139,15 @@ past.</p> <p>The polar equation of the cross-section being</p> -<p class="center">r<span class="sp">1/2</span> cos θ = a<span class="sp">1/2</span>, or r + x = 2a,</p> +<p class="center">r<span class="sp">1/2</span> cos ½θ = a<span class="sp">1/2</span>, or r + x = 2a,</p> <div class="author">(3)</div> <p class="noind">the conditions are satisfied by</p> -<p class="center">ψ′ = Ur sin θ − 2Ua<span class="sp">1/2</span>r<span class="sp">1/2</span> sin θ = 2Ur<span class="sp">1/2</span> sin θ (r<span class="sp">1/2</span> cos θ − a<span class="sp">1/2</span>),</p> +<p class="center">ψ′ = Ur sin θ − 2Ua<span class="sp">1/2</span>r<span class="sp">1/2</span> sin ½θ = 2Ur<span class="sp">1/2</span> sin ½θ (r<span class="sp">1/2</span> cos ½θ − a<span class="sp">1/2</span>),</p> <div class="author">(4)</div> -<p class="center">ψ = 2Ua<span class="sp">1/2</span>r<span class="sp">1/2</span> sin θ = −U √ [ 2a (r − x) ],</p> +<p class="center">ψ = 2Ua<span class="sp">1/2</span>r<span class="sp">1/2</span> sin ½θ = −U √ [ 2a (r − x) ],</p> <div class="author">(5)</div> <p class="center">w = −2Ua<span class="sp">1/2</span>z<span class="sp">1/2</span>,</p> @@ -3221,7 +3182,7 @@ plane motion, such that the flux across the surface generated by the revolution of any curve AP from A to P is the same, and represented by 2π (ψ − ψ<span class="su">0</span>); and, as before, if dψ is the increase in ψ due to a displacement of P to P′, then k the component of velocity normal -to the surface swept out by PP′ is such that 2πdψ = 2πykPP′; and +to the surface swept out by PP′ is such that 2πdψ = 2πyk·PP′; and taking PP′ parallel to Oy and Ox,</p> <p class="center">u = −dψ/ydy,   v = dψ/ydx,</p> @@ -3345,8 +3306,8 @@ exceptional case of</p> <table class="reg" summary="poem"><tr><td> <div class="poemr"> <p>ψ = A<span class="su">0</span> cos θ, φ = A<span class="su">0</span>/r;</p> -<p>ψ = B<span class="su">0</span>r, φ = −B<span class="su">0</span> log tan θ - = −B<span class="su">0</span> sh<span class="sp">−1</span> x/y.</p> +<p>ψ = B<span class="su">0</span>r, φ = −B<span class="su">0</span> log tan ½θ + = −½B<span class="su">0</span> sh<span class="sp">−1</span> x/y.</p> </div> </td></tr></table> <div class="author">(11)</div> @@ -3360,31 +3321,31 @@ of a solid of revolution, moving with axial velocity U, is such that</p> <tr><td>1</td> <td rowspan="2"> </td> <td>dψ</td> <td rowspan="2">= −U</td> <td>dy</td> -<td rowspan="2">, ψ + Uy<span class="sp">2</span> = constant,</td></tr> +<td rowspan="2">, ψ + ½Uy<span class="sp">2</span> = constant,</td></tr> <tr><td class="denom">y</td> <td class="denom">ds</td> <td class="denom">ds</td></tr></table> <div class="author">(12)</div> -<p class="noind">over the surface of the solid; and ψ must be replaced by ψ′ = ψ + Uy<span class="sp">2</span> +<p class="noind">over the surface of the solid; and ψ must be replaced by ψ′ = ψ + ½Uy<span class="sp">2</span> in the general equations of steady motion above to obtain the steady relative motion of the liquid past the solid.</p> <p>For instance, with n = 1 in equation (9), the relative stream function is obtained for a sphere of radius a, by making it</p> -<p class="center">ψ′ = ψ + Uy<span class="sp">2</span> = U (r<span class="sp">2</span> − a<span class="sp">3</span>/r) sin<span class="sp">2</span> θ, ψ = −Ua<span class="sp">3</span> sin<span class="sp">2</span> θ/r;</p> +<p class="center">ψ′ = ψ + ½Uy<span class="sp">2</span> = ½U (r<span class="sp">2</span> − a<span class="sp">3</span>/r) sin<span class="sp">2</span> θ, ψ = −½Ua<span class="sp">3</span> sin<span class="sp">2</span> θ/r;</p> <div class="author">(13)</div> <p class="noind">and then</p> -<p class="center">φ′ = Ux (1 + a<span class="sp">3</span>/r<span class="sp">2</span>), φ = Ua<span class="sp">3</span> cos θ/r<span class="sp">2</span>,</p> +<p class="center">φ′ = Ux (1 + ½a<span class="sp">3</span>/r<span class="sp">2</span>), φ = ½Ua<span class="sp">3</span> cos θ/r<span class="sp">2</span>,</p> <div class="author">(14)</div> <table class="math0" summary="math"> <tr><td rowspan="2">−</td> <td>dφ</td> <td rowspan="2">= U</td> <td>a<span class="sp">3</span></td> <td rowspan="2">cos θ,   −</td> <td>dφ</td> -<td rowspan="2">= U</td> <td>a<span class="sp">3</span></td> +<td rowspan="2">= ½U</td> <td>a<span class="sp">3</span></td> <td rowspan="2">sin θ,</td></tr> <tr><td class="denom">dr</td> <td class="denom">r<span class="sp">3</span></td> <td class="denom">r dθ</td> <td class="denom">r<span class="sp">3</span></td></tr></table> @@ -3392,11 +3353,11 @@ function is obtained for a sphere of radius a, by making it</p> <p class="noind">so that, if the direction of motion makes an angle ψ with Ox,</p> -<p class="center">tan (ψ − θ) = tan θ, tan ψ = 3 tan θ/(2 − tan<span class="sp">2</span> θ),</p> +<p class="center">tan (ψ − θ) = ½ tan θ, tan ψ = 3 tan θ/(2 − tan<span class="sp">2</span> θ),</p> <div class="author">(16)</div> <p>Along the path of a liquid particle ψ′ is constant, and putting it -equal to Uc<span class="sp">2</span>,</p> +equal to ½Uc<span class="sp">2</span>,</p> <p class="center">(r<span class="sp">2</span> − a<span class="sp">3</span>/r) sin<span class="sp">2</span> θ = c<span class="sp">2</span>, sin<span class="sp">2</span> θ = c<span class="sp">2</span>r / (r<span class="sp">3</span> − a<span class="sp">3</span>),</p> <div class="author">(17)</div> @@ -3420,7 +3381,7 @@ equal to Uc<span class="sp">2</span>,</p> <table class="math0" summary="math"> <tr><td>1</td> <td rowspan="2"> </td> <td>dψ′</td> -<td rowspan="2">= U <span class="f150">(</span> 2r +</td> <td>a<span class="sp">3</span></td> +<td rowspan="2">= ½U <span class="f150">(</span> 2r +</td> <td>a<span class="sp">3</span></td> <td rowspan="2"><span class="f150">)</span></td> <td>sin<span class="sp">2</span> θ</td> <td rowspan="2">= <span class="spp">3</span>⁄<span class="suu">2</span> U sin θ, when r = a;</td></tr> <tr><td class="denom">r sin θ</td> <td class="denom">dr</td> @@ -3437,10 +3398,10 @@ cavitation at the surface of the sphere.</p> <p>With n = 2, a state of motion is given by</p> -<p class="center">ψ = − Uy<span class="sp">2</span>a<span class="sp">4</span> μ/r<span class="sp">4</span>,   ψ′ = Uy<span class="sp">2</span> (1 − a<span class="sp">4</span> μ/r<span class="sp">4</span>),</p> +<p class="center">ψ = −½ Uy<span class="sp">2</span>a<span class="sp">4</span> μ/r<span class="sp">4</span>,   ψ′ = ½ Uy<span class="sp">2</span> (1 − a<span class="sp">4</span> μ/r<span class="sp">4</span>),</p> <div class="author">(22)</div> -<p class="center">φ′ = Ux + φ,   φ = −<span class="spp">1</span>⁄<span class="suu">3</span> U (a<span class="sp">4</span> / r<span class="sp">3</span>) P<span class="su">2</span>,   P<span class="su">2</span> = <span class="spp">3</span>⁄<span class="suu">2</span> μ<span class="sp">2</span> − ,</p> +<p class="center">φ′ = Ux + φ,   φ = −<span class="spp">1</span>⁄<span class="suu">3</span> U (a<span class="sp">4</span> / r<span class="sp">3</span>) P<span class="su">2</span>,   P<span class="su">2</span> = <span class="spp">3</span>⁄<span class="suu">2</span> μ<span class="sp">2</span> − ½,</p> <div class="author">(23)</div> <p class="noind">representing a stream past the surface r<span class="sp">4</span> = a<span class="sp">4</span>μ.</p> @@ -3478,7 +3439,7 @@ any rotation.</p> velocity function φ is given by</p> <table class="math0" summary="math"> -<tr><td rowspan="2">T = ρ <span class="f150">∫ ∫ ∫ [ (</span></td> <td>dφ</td> +<tr><td rowspan="2">T = ½ρ <span class="f150">∫ ∫ ∫ [ (</span></td> <td>dφ</td> <td rowspan="2"><span class="f150">)</span></td> <td><span class="sp">2</span></td> <td rowspan="2">+ <span class="f150">(</span></td> <td>dφ</td> <td rowspan="2"><span class="f150">)</span></td> <td><span class="sp">2</span></td> @@ -3490,7 +3451,7 @@ velocity function φ is given by</p> <td class="denom">dz</td> <td> </td></tr></table> <table class="math0" summary="math"> -<tr><td rowspan="2">= ρ <span class="f150">∫ ∫</span> φ</td> <td>dφ</td> +<tr><td rowspan="2">= ½ρ <span class="f150">∫ ∫</span> φ</td> <td>dφ</td> <td rowspan="2">dS</td></tr> <tr><td class="denom">dν</td></tr></table> <div class="author">(1)</div> @@ -3577,11 +3538,11 @@ its position. Thus, in (5), the cyclic constant k = 2πm.</p> <p>In plane motion the kinetic energy per unit length parallel to Oz</p> <table class="math0" summary="math"> -<tr><td rowspan="2">T = ρ <span class="f150">∫ ∫ [ (</span></td> <td>dφ</td> +<tr><td rowspan="2">T = ½ρ <span class="f150">∫ ∫ [ (</span></td> <td>dφ</td> <td rowspan="2"><span class="f150">)</span></td> <td><span class="sp">2</span></td> <td rowspan="2">+ <span class="f150">(</span></td> <td>dφ</td> <td rowspan="2"><span class="f150">)</span></td> <td><span class="sp">2</span></td> -<td rowspan="2"><span class="f150">]</span> dx dy = ρ <span class="f150">∫ ∫ [ (</span></td> <td>dψ</td> +<td rowspan="2"><span class="f150">]</span> dx dy = ½ρ <span class="f150">∫ ∫ [ (</span></td> <td>dψ</td> <td rowspan="2"><span class="f150">)</span></td> <td><span class="sp">2</span></td> <td rowspan="2">+ <span class="f150">(</span></td> <td>dψ</td> <td rowspan="2"><span class="f150">)</span></td> <td><span class="sp">2</span></td> @@ -3592,43 +3553,43 @@ its position. Thus, in (5), the cyclic constant k = 2πm.</p> <td class="denom">dy</td> <td> </td></tr></table> <table class="math0" summary="math"> -<tr><td rowspan="2">= ρ <span class="f150">∫</span> φ</td> <td>dφ</td> -<td rowspan="2">ds = ρ <span class="f150">∫</span> ψ</td> <td>dψ</td> +<tr><td rowspan="2">= ½ρ <span class="f150">∫</span> φ</td> <td>dφ</td> +<td rowspan="2">ds = ½ρ <span class="f150">∫</span> ψ</td> <td>dψ</td> <td rowspan="2">ds.</td></tr> <tr><td class="denom">dν</td> <td class="denom">dν</td></tr></table> <div class="author">(7)</div> -<p>For example, in the equilateral triangle of (8) 28, referred to coordinate +<p>For example, in the equilateral triangle of (8) § 28, referred to coordinate axes made by the base and height,</p> -<p class="center">ψ′ = −2Rαβγ/h = − Ry [ (h − y)<span class="sp">2</span> − 3x<span class="sp">2</span> ] /h</p> +<p class="center">ψ′ = −2Rαβγ/h = −½ Ry [ (h − y)<span class="sp">2</span> − 3x<span class="sp">2</span> ] /h</p> <div class="author">(8)</div> <table class="reg" summary="poem"><tr><td> <div class="poemr"> -<p>ψ = ψ′ − R [ ( <span class="spp">1</span>⁄<span class="suu">3</span> h − y)<span class="sp">2</span> + x<span class="sp">2</span> ]</p> +<p>ψ = ψ′ − ½R [ ( <span class="spp">1</span>⁄<span class="suu">3</span> h − y)<span class="sp">2</span> + x<span class="sp">2</span> ]</p> -<p class="i1">= −R [ h<span class="sp">3</span> + <span class="spp">1</span>⁄<span class="suu">3</span> h<span class="sp">2</span>y + h) (x<span class="sp">2</span> − y<span class="sp">2</span>) − 3x<span class="sp">2</span>y + y<span class="sp">3</span> ] /h</p> +<p class="i1">= −½R [ ½h<span class="sp">3</span> + <span class="spp">1</span>⁄<span class="suu">3</span> h<span class="sp">2</span>y + h) (x<span class="sp">2</span> − y<span class="sp">2</span>) − 3x<span class="sp">2</span>y + y<span class="sp">3</span> ] /h</p> </div> </td></tr></table> <div class="author">(9)</div> <p class="noind">and over the base y = 0,</p> -<p class="center">dx/dν = −dx/dy = + R ( <span class="spp">1</span>⁄<span class="suu">3</span> h<span class="sp">2</span> − 3x<span class="sp">2</span>) / h, ψ = −R ( <span class="spp">1</span>⁄<span class="suu">9</span> h<span class="sp">2</span> + x<span class="sp">2</span>).</p> +<p class="center">dx/dν = −dx/dy = + ½R ( <span class="spp">1</span>⁄<span class="suu">3</span> h<span class="sp">2</span> − 3x<span class="sp">2</span>) / h, ψ = −½R ( <span class="spp">1</span>⁄<span class="suu">9</span> h<span class="sp">2</span> + x<span class="sp">2</span>).</p> <div class="author">(10)</div> <p>Integrating over the base, to obtain one-third of the kinetic energy T,</p> <table class="math0" summary="math"> -<tr><td rowspan="2"><span class="spp">1</span>⁄<span class="suu">3</span>T = ρ <span class="f150">∫</span></td> <td>h / √3</td> -<td rowspan="2">R<span class="sp">2</span> (3x<span class="sp">4</span> − <span class="spp">1</span>⁄<span class="suu">27</span> h<span class="sp">4</span>) dx/h = ρR<span class="sp">2</span> h<span class="sp">4</span> / 135 √3</td></tr> +<tr><td rowspan="2"><span class="spp">1</span>⁄<span class="suu">3</span>T = ½ρ <span class="f150">∫</span></td> <td>h / √3</td> +<td rowspan="2">¼R<span class="sp">2</span> (3x<span class="sp">4</span> − <span class="spp">1</span>⁄<span class="suu">27</span> h<span class="sp">4</span>) dx/h = ρR<span class="sp">2</span> h<span class="sp">4</span> / 135 √3</td></tr> <tr><td>−h / √3</td></tr></table> <div class="author">(11)</div> <p class="noind">so that the effective k<span class="sp">2</span> of the liquid filling the triangle is given by</p> <table class="reg" summary="poem"><tr><td> <div class="poemr"> -<p>k<span class="sp">2</span> = T / ρR<span class="sp">2</span>A = 2h<span class="sp">2</span> / 45</p> +<p>k<span class="sp">2</span> = T / ½ρR<span class="sp">2</span>A = 2h<span class="sp">2</span> / 45</p> <p class="i1">= <span class="spp">2</span>⁄<span class="suu">5</span> (radius of the inscribed circle)<span class="sp">2</span>,</p> </div> </td></tr></table> @@ -3641,14 +3602,14 @@ energy T,</p> <p class="center">dφ/dν = dψ/ds,   dφ/ds = −dψ/dν,</p> <div class="author">(13)</div> -<p class="center">T = ρ ∫ φ dψ = −ρ ∫ ψ dφ.</p> +<p class="center">T = ½ρ ∫ φ dψ = −½ρ ∫ ψ dφ.</p> <div class="author">(14)</div> <p>With the Stokes’ function ψ for motion symmetrical about an axis.</p> <table class="math0" summary="math"> -<tr><td rowspan="2">T = ρ <span class="f150">∫</span> φ</td> <td>dψ</td> +<tr><td rowspan="2">T = ½ρ <span class="f150">∫</span> φ</td> <td>dψ</td> <td rowspan="2">2πy ds = πρ ∫ φ dψ.</td></tr> <tr><td class="denom">y ds</td></tr></table> <div class="author">(15)</div> @@ -3715,13 +3676,13 @@ equal to</p> <p class="noind">so that the component spin is</p> <table class="math0" summary="math"> -<tr><td rowspan="2"> <span class="f150">(</span></td> <td>dv</td> +<tr><td rowspan="2">½ <span class="f150">(</span></td> <td>dv</td> <td rowspan="2">−</td> <td>du</td> <td rowspan="2"><span class="f150">)</span> = ζ,</td></tr> <tr><td class="denom">dx</td> <td class="denom">dy</td></tr></table> <div class="author">(5)</div> -<p class="noind">in the previous notation of 24; so also for the other two components +<p class="noind">in the previous notation of § 24; so also for the other two components ξ and η.</p> <p>Since the circulation round any triangular area of given aspect @@ -3743,7 +3704,7 @@ constant where α is the cross-section of the filament and ω the resultant spin (W. K. Clifford, <i>Kinematic</i>, book iii.).</p> <p>So far these theorems on vortex motion are kinematical; but -introducing the equations of motion of 22,</p> +introducing the equations of motion of § 22,</p> <table class="math0" summary="math"> <tr><td>Du</td> @@ -3769,7 +3730,7 @@ introducing the equations of motion of 22,</p> <tr><td>D</td> <td rowspan="2"><span class="f150">(</span> u dx + v dy + w dz <span class="f150">)</span> =</td> <td>Du</td> <td rowspan="2">dx + u</td> <td>D dx</td> -<td rowspan="2">+ ... = −dQ + dq<span class="sp">2</span>,</td></tr> +<td rowspan="2">+ ... = −dQ + ½ dq<span class="sp">2</span>,</td></tr> <tr><td class="denom">dt</td> <td class="denom">dt</td> <td class="denom">dt</td></tr></table> <div class="author">(8)</div> @@ -3825,7 +3786,7 @@ while the aggregate vorticity of a mass M inside a surface S is</p> <p class="noind">which is expressed by</p> -<p class="center">∇<span class="sp">2</span> (u, v, w) = 2 curl (ξ, η, ζ), (ξ, η, ζ) = curl (u, v, w).</p> +<p class="center">∇<span class="sp">2</span> (u, v, w) = 2 curl (ξ, η, ζ), (ξ, η, ζ) = ½ curl (u, v, w).</p> <div class="author">(11)</div> <p>38. <i>Moving Axes in Hydrodynamics.</i>—In many problems, such as @@ -3946,11 +3907,11 @@ moving axes.</p> <td class="denom">dz</td> <td class="denom">dz</td></tr></table> <div class="author">(6)</div> -<p class="noind">as in 25 (1), a first integral of the equations in (5) may be written</p> +<p class="noind">as in § 25 (1), a first integral of the equations in (5) may be written</p> <table class="math0" summary="math"> <tr><td rowspan="2"><span class="f150">∫</span></td> <td>dp</td> -<td rowspan="2">+ V + q<span class="sp">2</span> −</td> <td>dφ</td> +<td rowspan="2">+ V + ½q<span class="sp">2</span> −</td> <td>dφ</td> <td rowspan="2">− m</td> <td>dψ</td> <td rowspan="2">+ (u − u′) <span class="f150">(</span></td> <td>dφ</td> <td rowspan="2">+ m</td> <td>dψ</td> @@ -3995,37 +3956,37 @@ left behind with velocity components u − u′, v − v′, w & <p>In the case of a steady motion of homogeneous liquid symmetrical about Ox, where O is advancing with velocity U, the equation (5) -of 34</p> +of § 34</p> -<p class="center">p/ρ + V + q′<span class="sp">2</span> − ƒ (ψ′) = constant</p> +<p class="center">p/ρ + V + ½q′<span class="sp">2</span> − ƒ (ψ′) = constant</p> <div class="author">(9)</div> <p class="noind">becomes transformed into</p> <table class="math0" summary="math"> <tr><td>p</td> -<td rowspan="2">+ V + q<span class="sp">2</span> −</td> <td>U</td> +<td rowspan="2">+ V + ½q<span class="sp">2</span> −</td> <td>U</td> <td rowspan="2"> </td> <td>dψ</td> -<td rowspan="2">+ U<span class="sp">2</span> − ƒ (ψ + Uy<span class="sp">2</span>) = constant,</td></tr> +<td rowspan="2">+ ½U<span class="sp">2</span> − ƒ (ψ + ½Uy<span class="sp">2</span>) = constant,</td></tr> <tr><td class="denom">ρ</td> <td class="denom">y</td> <td class="denom">dy</td></tr></table> <div class="author">(10)</div> -<p class="center">ψ′ = ψ + U y<span class="sp">2</span>,</p> +<p class="center">ψ′ = ψ + ¼U y<span class="sp">2</span>,</p> <div class="author">(11)</div> -<p class="noind">subject to the condition, from (4) 34,</p> +<p class="noind">subject to the condition, from (4) § 34,</p> -<p class="center">y<span class="sp">−2</span> ∇<span class="sp">2</span>ψ′ = −ƒ′(ψ′),   y<span class="sp">−2</span> ∇<span class="sp">2</span>ψ = −ƒ′ (ψ + Uy<span class="sp">2</span>).</p> +<p class="center">y<span class="sp">−2</span> ∇<span class="sp">2</span>ψ′ = −ƒ′(ψ′),   y<span class="sp">−2</span> ∇<span class="sp">2</span>ψ = −ƒ′ (ψ + ½Uy<span class="sp">2</span>).</p> <div class="author">(12)</div> <p>Thus, for example, with</p> -<p class="center">ψ′ = U y<span class="sp">2</span> (r<span class="sp">2</span>a<span class="sp">−2</span> − 1), r<span class="sp">2</span> = x<span class="sp">2</span> + y<span class="sp">2</span>,</p> +<p class="center">ψ′ = ¾U y<span class="sp">2</span> (r<span class="sp">2</span>a<span class="sp">−2</span> − 1), r<span class="sp">2</span> = x<span class="sp">2</span> + y<span class="sp">2</span>,</p> <div class="author">(13)</div> <p class="noind">for the space inside the sphere r = a, compared with the value of -ψ′ in 34 (13) for the space outside, there is no discontinuity of the +ψ′ in § 34 (13) for the space outside, there is no discontinuity of the velocity in crossing the surface.</p> <p>Inside the sphere</p> @@ -4046,7 +4007,7 @@ velocity in crossing the surface.</p> <td class="denom">2</td> <td class="denom">a<span class="sp">2</span></td></tr></table> <div class="author">(14)</div> -<p class="noind">so that 34 (4) is satisfied, with</p> +<p class="noind">so that § 34 (4) is satisfied, with</p> <table class="math0" summary="math"> <tr><td rowspan="2">ƒ′ (ψ′) =</td> <td>15</td> @@ -4063,7 +4024,7 @@ velocity in crossing the surface.</p> <td rowspan="2">U <span class="f150">{</span> <span class="f150">(</span></td> <td>x<span class="sp">2</span></td> <td rowspan="2">− 1 <span class="f150">)</span></td> <td><span class="sp">2</span></td> <td rowspan="2">− <span class="f150">(</span></td> <td>y<span class="sp">2</span></td> -<td rowspan="2">− <span class="f150">)</span></td> <td><span class="sp">2</span></td> +<td rowspan="2">− ½ <span class="f150">)</span></td> <td><span class="sp">2</span></td> <td rowspan="2"><span class="f150">}</span> = constant;</td></tr> <tr><td class="denom">ρ</td> <td class="denom">8</td> <td class="denom">a<span class="sp">2</span></td> <td> </td> @@ -4202,7 +4163,7 @@ of the form</p> <p class="noind">and integrating</p> <p class="center">pρ<span class="sp">−1</span> + 2πρ (Ax<span class="sp">2</span> + By<span class="sp">2</span> + Cz<span class="sp">2</span>)<br /> -+ (αx<span class="sp">2</span> + βy<span class="sp">2</span> + γz<span class="sp">2</span> + 2fyz + 2gzx + 2hxy) = const.,</p> ++ ½ (αx<span class="sp">2</span> + βy<span class="sp">2</span> + γz<span class="sp">2</span> + 2fyz + 2gzx + 2hxy) = const.,</p> <div class="author">(14)</div> <p class="noind">so that the surfaces of equal pressure are similar quadric surfaces, @@ -4344,7 +4305,7 @@ except when c = a, or 3a.</p> <table class="math0" summary="math"> <tr><td>dφ</td> <td rowspan="2">= ζ −</td> <td>(a<span class="sp">2</span> + c<span class="sp">2</span>)</td> -<td rowspan="2"></td> <td> +<td rowspan="2">·</td> <td> <table class="math0" summary="math"> <tr><td rowspan="2">N +</td> <td>a<span class="sp">2</span> + c<span class="sp">2</span></td> </tr> @@ -4364,7 +4325,7 @@ except when c = a, or 3a.</p> <tr><td rowspan="2">N +</td> <td>a<span class="sp">2</span> + c<span class="sp">2</span></td> </tr> <tr><td class="denom">4c<span class="sp">2</span></td></tr></table></td> -<td rowspan="2"></td> <td>ζ dζ</td> +<td rowspan="2">·</td> <td>ζ dζ</td> <td rowspan="2">,</td></tr> <tr><td class="denom">√Z</td> <td class="denom">a<span class="sp">2</span> − c<span class="sp">2</span></td> <td class="denom"><table class="math0" summary="math"> @@ -4423,7 +4384,7 @@ so also for ψ, where ξ = ω cos ψ, η = −ω sin &p <table class="math0" summary="math"> <tr><td rowspan="2"><span class="f150">(</span></td> <td>ω</td> -<td rowspan="2">− </td> <td>a<span class="sp">2</span> + c<span class="sp">2</span></td> +<td rowspan="2">− ½</td> <td>a<span class="sp">2</span> + c<span class="sp">2</span></td> <td rowspan="2"><span class="f150">)</span></td> <td><span class="sp">2</span></td> <td rowspan="2">=</td> <td>(a<span class="sp">2</span> − c<span class="sp">2</span>) (9a<span class="sp">2</span> − c<span class="sp">2</span>)</td> <td rowspan="2">,</td></tr> @@ -4521,16 +4482,16 @@ liquid is coming from an infinite distance between two parallel walls at a distance xx′ (fig. 4), and issues in a jet between two edges A and A′; the wall xA being bent -at a corner B, with the external angle β = π/n.</p> +at a corner B, with the external angle β = ½π/n.</p> <p>The theory of conformal representation shows that the motion is given by</p> <table class="math0" summary="math"> -<tr><td rowspan="2">ζ = <span class="f150">[</span></td> <td> √ (b − a′u − a) + √(b − au − a′)</td> +<tr><td rowspan="2">ζ = <span class="f150">[</span></td> <td> √ (b − a′·u − a) + √(b − a·u − a′)</td> <td rowspan="2"><span class="f150">]</span></td> <td><span class="sp">1/n</span></td> <td rowspan="2">, u = ae<span class="sp">−πw/m</span>;</td></tr> -<tr><td class="denom">√ (a − a′u − b)</td> <td> </td></tr></table> +<tr><td class="denom">√ (a − a′·u − b)</td> <td> </td></tr></table> <div class="author">(5)</div> <p class="noind">where u = a, a′ at the edge A, A′; u = b at a corner B; u = 0 across @@ -4550,10 +4511,10 @@ expression for ζ is the product of corresponding factors, such as in (5).</ <table class="math0" summary="math"> <tr><td rowspan="2">ζ<span class="sp">n</span> = <span class="f150">(</span></td> <td>Q</td> <td rowspan="2"><span class="f150">)</span></td> <td><span class="sp">n</span></td> -<td rowspan="2">(cos nθ + i sin nθ) =</td> <td>√ (b − a′u − a) + √ (b − au − a′)</td> +<td rowspan="2">(cos nθ + i sin nθ) =</td> <td>√ (b − a′·u − a) + √ (b − a·u − a′)</td> <td rowspan="2">,</td></tr> <tr><td class="denom">q</td> <td> </td> -<td class="denom">√ (a − a′u − b)</td></tr></table> +<td class="denom">√ (a − a′·u − b)</td></tr></table> <div class="author">(6)</div> <table class="math0" summary="math"> @@ -4566,7 +4527,7 @@ expression for ζ is the product of corresponding factors, such as in (5).</ <td class="denom">q</td> <td> </td></tr></table> <table class="math0" summary="math"> -<tr><td rowspan="2">= (ζ<span class="sp">n</span> + ζ<span class="sp">−n</span>) = <span class="f150">√</span></td> <td>b − a′</td> +<tr><td rowspan="2">= ½(ζ<span class="sp">n</span> + ζ<span class="sp">−n</span>) = <span class="f150">√</span></td> <td>b − a′</td> <td rowspan="2"><span class="f150">√</span></td> <td>u − a</td> <td rowspan="2">,</td></tr> <tr><td class="denom">a − a′</td> <td class="denom">u − b</td></tr></table> @@ -4581,7 +4542,7 @@ expression for ζ is the product of corresponding factors, such as in (5).</ <td> </td></tr></table> <table class="math0" summary="math"> -<tr><td rowspan="2">= (ζ<span class="sp">n</span> + ζ<span class="sp">−n</span>) = <span class="f150">√</span></td> <td>b − a</td> +<tr><td rowspan="2">= ½(ζ<span class="sp">n</span> + ζ<span class="sp">−n</span>) = <span class="f150">√</span></td> <td>b − a</td> <td rowspan="2"><span class="f150">√</span></td> <td>u − a′</td> <td rowspan="2">,</td></tr> <tr><td class="denom">a − a′</td> <td class="denom">u − b</td></tr></table> @@ -4595,27 +4556,27 @@ expression for ζ is the product of corresponding factors, such as in (5).</ <table class="math0" summary="math"> <tr><td>dΩ</td> <td rowspan="2">= −</td> <td>1</td> -<td rowspan="2"> </td> <td>√ (b − a′b − a′)</td> +<td rowspan="2"> </td> <td>√ (b − a′·b − a′)</td> <td rowspan="2">,</td> <td>dw</td> <td rowspan="2">= −</td> <td>m</td> <td rowspan="2">,</td></tr> <tr><td class="denom">du</td> <td class="denom">2n</td> -<td class="denom">(u − b) √ (a − au − a′)</td> <td class="denom">du</td> +<td class="denom">(u − b) √ (a − a·u − a′)</td> <td class="denom">du</td> <td class="denom">πu</td></tr></table> <div class="author">(10)</div> <p class="noind">the formulas by which the conformal representation is obtained.</p> <p>For the Ω polygon has a right angle at u = a, a′, and a zero angle at -u = b, where θ changes from 0 to π/n and Ω increases by iπ/n; so +u = b, where θ changes from 0 to ½π/n and Ω increases by ½iπ/n; so that</p> <table class="math0" summary="math"> <tr><td>dΩ</td> <td rowspan="2">=</td> <td>A</td> -<td rowspan="2">, where A =</td> <td>√ (b − ab − a′)</td> +<td rowspan="2">, where A =</td> <td>√ (b − a·b − a′)</td> <td rowspan="2">.</td></tr> -<tr><td class="denom">du</td> <td class="denom">(u − b) √ (u − au − a′)</td> +<tr><td class="denom">du</td> <td class="denom">(u − b) √ (u − a·u − a′)</td> <td class="denom">2n</td></tr></table> <div class="author">(11)</div> @@ -4683,11 +4644,11 @@ of curvature</p> <table class="math0" summary="math"> <tr><td rowspan="2">=</td> <td>c</td> -<td rowspan="2"></td> <td>u − b</td> -<td rowspan="2"> </td> <td>√ (u − au − a′)</td> +<td rowspan="2">·</td> <td>u − b</td> +<td rowspan="2"> </td> <td>√ (u − a·u − a′)</td> <td rowspan="2">,</td></tr> <tr><td class="denom">π</td> <td class="denom">u</td> -<td class="denom">√ (a − bb − a′)</td></tr></table> +<td class="denom">√ (a − b·b − a′)</td></tr></table> <div class="author">(18)</div> <p class="noind">not requiring the integration of (11) and (12)</p> @@ -4704,19 +4665,19 @@ of curvature</p> <p class="noind">Then</p> <table class="math0" summary="math"> -<tr><td rowspan="2">cos 2nα − cos 2nθ = 2</td> <td>a − bb − a′</td> -<td rowspan="2">= sin<span class="sp">2</span> 2nα</td> <td>a − a′</td> +<tr><td rowspan="2">cos 2nα − cos 2nθ = 2</td> <td>a − b·b − a′</td> +<td rowspan="2">= ½sin<span class="sp">2</span> 2nα</td> <td>a − a′</td> </tr> -<tr><td class="denom">a − a′u − b</td> <td class="denom">u − b</td></tr></table> +<tr><td class="denom">a − a′·u − b</td> <td class="denom">u − b</td></tr></table> <table class="math0" summary="math"> -<tr><td rowspan="2">sin 2nθ = 2</td> <td>√ (a − b.b − a′) √ (u − au − b′)</td> +<tr><td rowspan="2">sin 2nθ = 2</td> <td>√ (a − b.b − a′) √ (u − a·u − b′)</td> </tr> -<tr><td class="denom">a − a′u − b</td></tr></table> +<tr><td class="denom">a − a′·u − b</td></tr></table> <div class="author">(20)</div> <table class="math0" summary="math"> -<tr><td rowspan="2">= sin 2nα</td> <td>√ (a − ab − a′)</td> +<tr><td rowspan="2">= sin 2nα</td> <td>√ (a − a·b − a′)</td> <td rowspan="2">;</td></tr> <tr><td class="denom">u − b</td></tr></table> @@ -4724,15 +4685,15 @@ of curvature</p> <tr><td>2n</td> <td rowspan="2"> </td> <td>c</td> <td rowspan="2"><span class="f150">(</span> 1 +</td> <td>b</td> -<td rowspan="2"><span class="f150">)</span></td> <td>√ (a − bb − a′)</td> +<td rowspan="2"><span class="f150">)</span></td> <td>√ (a − b·b − a′)</td> </tr> <tr><td class="denom">φ</td> <td class="denom">ρ</td> -<td class="denom">u − b</td> <td class="denom">√ (u − au − a′)</td></tr></table> +<td class="denom">u − b</td> <td class="denom">√ (u − a·u − a′)</td></tr></table> <div class="author">(21)</div> <table class="math0" summary="math"> <tr><td rowspan="2">=</td> <td>a − a′ + (a + a′) cos 2nα − [ a + a′ + (a − a′) cos 2nα ] cos 2nθ</td> -<td rowspan="2"></td> <td>cos 2nα − cos 2nθ</td> +<td rowspan="2">×</td> <td>cos 2nα − cos 2nθ</td> <td rowspan="2">.</td></tr> <tr><td class="denom">(a − a′) sin<span class="sp">2</span> 2nα</td> <td class="denom">sin 2nθ</td></tr></table> @@ -4830,7 +4791,7 @@ of curvature</p> <p>In crossing to the line of flow x′A′P′J′, ψ changes from 0 to m, so that with q = Q across JJ′, while across xx′ the velocity is q<span class="su">0</span>, so that</p> -<p class="center">m = q<span class="su">0</span>xx′ = QJJ′</p> +<p class="center">m = q<span class="su">0</span>·xx′ = Q·JJ′</p> <div class="author">(31)</div> <table class="math0" summary="math"> @@ -4919,15 +4880,15 @@ n = 1, b = 0, a′ = −∞, as in fig. 5,</p> <div class="author">(2)</div> <table class="math0" summary="math"> -<tr><td rowspan="2">PM = <span class="f150">∫</span><span class="sp1">∞</span><span class="su1">s</span> sinθ ds = <span class="f150">∫</span> e<span class="sp">−πs/c</span> ds =</td> <td>c</td> +<tr><td rowspan="2">PM = <span class="f150">∫</span><span class="sp1">∞</span><span class="su1">s</span> sinθ ds = <span class="f150">∫</span> e<span class="sp">−½πs/c</span> ds =</td> <td>c</td> <td rowspan="2">e<span class="sp">−1/2 πs/c</span> =</td> <td>c</td> <td rowspan="2">sin θ,</td></tr> -<tr><td class="denom">π</td> <td class="denom">π</td></tr></table> +<tr><td class="denom">½π</td> <td class="denom">½π</td></tr></table> <div class="author">(3)</div> <p><span class="pagenum"><a name="page129" id="page129"></a>129</span></p> -<p class="noind">so that PT = c/π, and the curve AP is the tractrix; and the coefficient +<p class="noind">so that PT = c/½π, and the curve AP is the tractrix; and the coefficient of contraction, or</p> <table class="math0" summary="math"> @@ -4939,8 +4900,8 @@ of contraction, or</p> <p>A change of Ω and θ into nΩ and nθ will give the solution for two walls converging symmetrically to the orifice AA<span class="su">1</span> at an angle π/n. -With n = , the reentrant walls are given of Borda’s mouthpiece, -and the coefficient of contraction becomes . Generally, by making +With n = ½, the reentrant walls are given of Borda’s mouthpiece, +and the coefficient of contraction becomes ½. Generally, by making a′ = −∞, the line x′A′ may be taken as a straight stream line of infinite length, forming an axis of symmetry; and then by duplication the result can be obtained, @@ -4983,7 +4944,7 @@ wedge extends to infinity; then</p> <div class="author">(2)</div> <table class="math0" summary="math"> -<tr><td rowspan="2">e<span class="sp">π<span class="sp">2</span>/c</span> = tan nθ,</td> <td>π</td> +<tr><td rowspan="2">e<span class="sp">½π<span class="sp">2</span>/c</span> = tan nθ,</td> <td>½π</td> <td rowspan="2"> </td> <td>ds</td> <td rowspan="2">=</td> <td>2n</td> <td rowspan="2">.</td></tr> @@ -4993,15 +4954,15 @@ wedge extends to infinity; then</p> <p class="noind">For a jet impinging normally on an infinite plane, as in fig. 6, n = 1,</p> -<p class="center">e<span class="sp">π<span class="sp">2</span>/c</span> = tan θ, ch (πs/c) sin 2θ = 1,</p> +<p class="center">e<span class="sp">½π<span class="sp">2</span>/c</span> = tan θ, ch (½πs/c) sin 2θ = 1,</p> <div class="author">(4)</div> -<p class="center">sh πx/c = cot θ, sh πy/c = tan θ,</p> +<p class="center">sh ½πx/c = cot θ, sh ½πy/c = tan θ,</p> -<p class="center">sh πx/c sh πy/c = 1, e<span class="sp">π(x + y)/c</span> = e<span class="sp">1/2 πx/c</span> + e<span class="sp">1/2 πy/c</span> + 1.</p> +<p class="center">sh ½πx/c sh ½πy/c = 1, e<span class="sp">½π(x + y)/c</span> = e<span class="sp">1/2 πx/c</span> + e<span class="sp">1/2 πy/c</span> + 1.</p> <div class="author">(5)</div> -<p>With n = , the jet is reversed in direction, and the profile is the +<p>With n = ½, the jet is reversed in direction, and the profile is the catenary of equal strength.</p> <p>In Bobyleff’s problem of the wedge of finite breadth,</p> @@ -5087,9 +5048,9 @@ is made now with</p> <table class="math0" summary="math"> <tr><td>dΩ</td> -<td rowspan="2">= −</td> <td>√ (b − ab − a′)</td> +<td rowspan="2">= −</td> <td>√ (b − a·b − a′)</td> <td rowspan="2"></td></tr> -<tr><td class="denom">du</td> <td class="denom">(u − b) √ (u − au − a′)</td></tr></table> +<tr><td class="denom">du</td> <td class="denom">(u − b) √ (u − a·u − a′)</td></tr></table> <div class="author">(1)</div> <table class="math0" summary="math"> @@ -5105,9 +5066,9 @@ is made now with</p> <table class="math0" summary="math"> <tr><td rowspan="2">= −</td> <td>m + m′</td> -<td rowspan="2"></td> <td>u − b</td> +<td rowspan="2">·</td> <td>u − b</td> <td rowspan="2">,</td></tr> -<tr><td class="denom">π</td> <td class="denom">u − ju − j′</td></tr></table> +<tr><td class="denom">π</td> <td class="denom">u − j·u − j′</td></tr></table> <table class="math0" summary="math"> <tr><td rowspan="2">b =</td> <td>mj′ + m′j</td> @@ -5124,9 +5085,9 @@ of the jets, and (m + m′)/Q is the initial breadth, c<span class="su">1</s stream. Then</p> <table class="math0" summary="math"> -<tr><td rowspan="2">ch Ω = <span class="f150">√</span></td> <td>b − a′</td> +<tr><td rowspan="2">ch ½Ω = <span class="f150">√</span></td> <td>b − a′</td> <td rowspan="2"><span class="f150">√</span></td> <td>u − b</td> -<td rowspan="2">, sh Ω = <span class="f150">√</span></td> <td>b − a</td> +<td rowspan="2">, sh ½Ω = <span class="f150">√</span></td> <td>b − a</td> <td rowspan="2"><span class="f150">√</span></td> <td>u − a′</td> <td rowspan="2">,</td></tr> <tr><td class="denom">a − a′</td> <td class="denom">u − b</td> @@ -5140,19 +5101,19 @@ stream. Then</p> <tr><td class="denom">a − a′</td> <td class="denom">u − b</td></tr></table> <table class="math0" summary="math"> -<tr><td rowspan="2">sh Ω = √ N</td> <td>√ (2a − uu − a′)</td> +<tr><td rowspan="2">sh Ω = √ N</td> <td>√ (2·a − u·u − a′)</td> <td rowspan="2">,</td></tr> <tr><td class="denom">u − b</td></tr></table> <table class="math0" summary="math"> -<tr><td rowspan="2">N = 2</td> <td>a − bb − a′</td> +<tr><td rowspan="2">N = 2</td> <td>a − b·b − a′</td> <td rowspan="2">.</td></tr> <tr><td class="denom">a − a′</td></tr></table> <div class="author">(4)</div> <p>Along a jet surface, q = Q, and</p> -<p class="center">chΩ = cos θ = cos α − sin<span class="sp">2</span> α(a − a′) / (u − b),</p> +<p class="center">chΩ = cos θ = cos α − ½sin<span class="sp">2</span> α(a − a′) / (u − b),</p> <div class="author">(5)</div> <p class="noind">if θ = α at the source x of the jet xB, where u = ∞; and supposing @@ -5160,16 +5121,16 @@ stream. Then</p> <table class="math0" summary="math"> <tr><td>u − b</td> -<td rowspan="2">=</td> <td>sin<span class="sp">2</span> α</td> +<td rowspan="2">=</td> <td>½sin<span class="sp">2</span> α</td> <td rowspan="2">,</td> <td>u − j</td> -<td rowspan="2">sin<span class="sp">2</span> α</td> <td>cosθ − cosβ</td> +<td rowspan="2">½sin<span class="sp">2</span> α</td> <td>cosθ − cosβ</td> <td rowspan="2">,</td></tr> <tr><td class="denom">a − a′</td> <td class="denom">cos α − cos θ</td> <td class="denom">a − a′</td> <td class="denom">(cos α − cos β) (cos α − cos θ)</td></tr></table> <table class="math0" summary="math"> <tr><td>u − j′</td> -<td rowspan="2">= sin<span class="sp">2</span> α</td> <td>cos θ − cos β′</td> +<td rowspan="2">= ½sin<span class="sp">2</span> α</td> <td>cos θ − cos β′</td> <td rowspan="2">;</td></tr> <tr><td class="denom">a − a′</td> <td class="denom">(cosα − cos β′) (cos α − cosθ)</td></tr></table> <div class="author">(6)</div> @@ -5202,14 +5163,14 @@ stream. Then</p> <table class="math0" summary="math"> <tr><td rowspan="2">=</td> <td>sin θ</td> <td rowspan="2">+</td> <td>cos α − cos β′</td> -<td rowspan="2"></td> <td>sin θ</td> +<td rowspan="2">·</td> <td>sin θ</td> </tr> <tr><td class="denom">cos α − cos θ</td> <td class="denom">cos β − cos β′</td> <td class="denom">cos θ − cos β</td></tr></table> <table class="math0" summary="math"> <tr><td>cos α − cos β</td> -<td rowspan="2"></td> <td>sin θ</td> +<td rowspan="2">·</td> <td>sin θ</td> <td rowspan="2">,</td></tr> <tr><td class="denom">cos β − cos β′</td> <td class="denom">cos θ − cos β′</td></tr></table> <div class="author">(7)</div> @@ -5221,19 +5182,19 @@ attention to the sign.</p> <table class="math0" summary="math"> <tr><td rowspan="2">ch Ω = ch log</td> <td>Q</td> -<td rowspan="2">= cos α − sin<span class="sp">2</span> α</td> <td>a − a′</td> +<td rowspan="2">= cos α − ½ sin<span class="sp">2</span> α</td> <td>a − a′</td> </tr> <tr><td class="denom">q</td> <td class="denom">a − b</td></tr></table> <table class="math0" summary="math"> <tr><td rowspan="2">sh Ω = sh log</td> <td>Q</td> -<td rowspan="2">=</td> <td>√ (a − uu − a′)</td> +<td rowspan="2">=</td> <td>√ (a − u·u − a′)</td> <td rowspan="2">sinα</td></tr> <tr><td class="denom">q</td> <td class="denom">u − b</td></tr></table> <table class="math0" summary="math"> <tr><td>Q</td> -<td rowspan="2">=</td> <td>(u − b) cos α − (a − a′) sin<span class="sp">2</span> α + √ (a − uu − a′) sin α</td> +<td rowspan="2">=</td> <td>(u − b) cos α − ½ (a − a′) sin<span class="sp">2</span> α + √ (a − u·u − a′) sin α</td> </tr> <tr><td class="denom">q</td> <td class="denom">u − b</td></tr></table> <div class="author">(8)</div> @@ -5251,15 +5212,15 @@ attention to the sign.</p> <table class="math0" summary="math"> <tr><td rowspan="2">=</td> <td>m + m′</td> -<td rowspan="2"></td> <td>(u − b) cos α − (a − a′) sin<span class="sp">2</span> α + √ (a − uu − a′) sin α</td> +<td rowspan="2">·</td> <td>(u − b) cos α − ½ (a − a′) sin<span class="sp">2</span> α + √ (a − u·u − a′) sin α</td> </tr> -<tr><td class="denom">π</td> <td class="denom">j − uu − j′</td></tr></table> +<tr><td class="denom">π</td> <td class="denom">j − u·u − j′</td></tr></table> <table class="math0" summary="math"> <tr><td rowspan="2">π</td> <td>AB</td> -<td rowspan="2">= <span class="f150">∫</span><span class="sp1">a</span><span class="su1">b</span></td> <td>(2b − a − a′) (u − b) − 2(a − b) (b − a′) + 2√ (a − bb − a′a − uu − a′)</td> +<td rowspan="2">= <span class="f150">∫</span><span class="sp1">a</span><span class="su1">b</span></td> <td>(2b − a − a′) (u − b) − 2(a − b) (b − a′) + 2√ (a − b·b − a′·a − u·u − a′)</td> <td rowspan="2">du,</td></tr> -<tr><td class="denom">c</td> <td class="denom">a − a′j − uu − j′</td></tr></table> +<tr><td class="denom">c</td> <td class="denom">a − a′·j − u·u − j′</td></tr></table> <div class="author">(10)</div> <p class="noind">with a similar expression for BA′.</p> @@ -5276,7 +5237,7 @@ will give the solution, by duplication, of a jet issuing by a reentrant mouthpiece placed symmetrically in the end wall of the channel; or else of the channel blocked partially by a diaphragm across the middle, with edges turned back symmetrically, problems discussed -by J. H. Michell, A. E. H. Love and M. Rthy.</p> +by J. H. Michell, A. E. H. Love and M. Réthy.</p> <p><span class="pagenum"><a name="page130" id="page130"></a>130</span></p> @@ -5294,13 +5255,13 @@ polygon (<i>Phil. Trans.</i>, 1890); the solution is given by</p> <p class="noind">so that, round the boundary of the polygon, ψ = K′, sin nθ = 0; and on the surface of the vortex ψ = 0, q = Q, and</p> -<p class="center">cos nθ = sn φ, nθ = π − am s/c,</p> +<p class="center">cos nθ = sn φ, nθ = ½π − am s/c,</p> <div class="author">(12)</div> <p class="noind">the intrinsic equation of the curve.</p> <p>This is a closed Sumner line for n = 1, when the boundary consists -of two parallel walls; and n = gives an Elastica.</p> +of two parallel walls; and n = ½ gives an Elastica.</p> <p>44. <i>The Motion of a Solid through a Liquid.</i>—An important problem in the motion of a liquid is the determination of the state @@ -5620,12 +5581,12 @@ pendulum.</p> <p class="noind">and</p> -<p class="center">A + B + C = abc / P,   A<span class="su">0</span> + B<span class="su">0</span> + C<span class="su">0</span> = 1.</p> +<p class="center">A + B + C = abc / ½P,   A<span class="su">0</span> + B<span class="su">0</span> + C<span class="su">0</span> = 1.</p> <div class="author">(28)</div> <p>For a sphere</p> -<p class="center">a = b = c,   A<span class="su">0</span> = B<span class="su">0</span> = C<span class="su">0</span> = <span class="spp">1</span>⁄<span class="suu">3</span>,   α = β = γ = ,</p> +<p class="center">a = b = c,   A<span class="su">0</span> = B<span class="su">0</span> = C<span class="su">0</span> = <span class="spp">1</span>⁄<span class="suu">3</span>,   α = β = γ = ½,</p> <div class="author">(29)</div> <p><span class="pagenum"><a name="page131" id="page131"></a>131</span></p> @@ -5637,7 +5598,7 @@ weight W, will describe a parabola with vertical acceleration</p> <table class="math0" summary="math"> <tr><td>W − W′</td> <td rowspan="2">g.</td></tr> -<tr><td class="denom">W + W′</td></tr></table> +<tr><td class="denom">W + ½W′</td></tr></table> <div class="author">(30)</div> <p class="noind">Thus a spherical air bubble, in which W/W′ is insensible, will begin @@ -5691,7 +5652,7 @@ liquid in the interspace is</p> <p>If the ellipsoid is of revolution, with b = c,</p> <table class="math0" summary="math"> -<tr><td rowspan="2">φ = Ux</td> <td>A + 2B<span class="su">1</span></td> +<tr><td rowspan="2">φ = ½Ux</td> <td>A + 2B<span class="su">1</span></td> <td rowspan="2">,</td></tr> <tr><td class="denom">B<span class="su">0</span> − B<span class="su">1</span></td></tr></table> <div class="author">(3)</div> @@ -5699,7 +5660,7 @@ liquid in the interspace is</p> <p class="noind">and the Stokes’ current function ψ can be written down</p> <table class="math0" summary="math"> -<tr><td rowspan="2">ψ = − Uy<span class="sp">2</span></td> <td>B − B<span class="su">1</span></td> +<tr><td rowspan="2">ψ = − ½ Uy<span class="sp">2</span></td> <td>B − B<span class="su">1</span></td> <td rowspan="2">;</td></tr> <tr><td class="denom">B<span class="su">0</span> − B<span class="su">1</span></td></tr></table> <div class="author">(4)</div> @@ -5707,8 +5668,8 @@ liquid in the interspace is</p> <p class="noind">reducing, when the liquid extends to infinity and B<span class="su">1</span> = 0, to</p> <table class="math0" summary="math"> -<tr><td rowspan="2">φ = Ux</td> <td>A</td> -<td rowspan="2">,   ψ = − Uy<span class="sp">2</span></td> <td>B</td> +<tr><td rowspan="2">φ = ½ Ux</td> <td>A</td> +<td rowspan="2">,   ψ = − ½ Uy<span class="sp">2</span></td> <td>B</td> <td rowspan="2">;</td></tr> <tr><td class="denom">B<span class="su">0</span></td> <td class="denom">B<span class="su">0</span></td></tr></table> <div class="author">(5)</div> @@ -5717,8 +5678,8 @@ liquid in the interspace is</p> current U parallel to xO,</p> <table class="math0" summary="math"> -<tr><td rowspan="2">φ′ = Ux <span class="f150">(</span> 1 +</td> <td>A</td> -<td rowspan="2"><span class="f150">)</span>,   ψ′ = Uy<span class="sp">2</span> <span class="f150">(</span> 1 −</td> <td>B</td> +<tr><td rowspan="2">φ′ = ½Ux <span class="f150">(</span> 1 +</td> <td>A</td> +<td rowspan="2"><span class="f150">)</span>,   ψ′ = ½Uy<span class="sp">2</span> <span class="f150">(</span> 1 −</td> <td>B</td> <td rowspan="2"><span class="f150">)</span>.</td></tr> <tr><td class="denom">B<span class="su">0</span></td> <td class="denom">B<span class="su">0</span></td></tr></table> <div class="author">(6)</div> @@ -5728,7 +5689,7 @@ spheroid, then putting b<span class="sp">2</span> = pa, λ = λ&prim where a = ∞, we find for a paraboloid of revolution</p> <table class="math0" summary="math"> -<tr><td rowspan="2">B = </td> <td>p</td> +<tr><td rowspan="2">B = ½</td> <td>p</td> <td rowspan="2">,   </td> <td>B</td> <td rowspan="2">=</td> <td>p</td> <td rowspan="2">,</td></tr> @@ -5744,18 +5705,18 @@ where a = ∞, we find for a paraboloid of revolution</p> <p class="noind">with λ′ = 0 over the surface of the paraboloid; and then</p> -<p class="center">ψ′ = U [ y<span class="sp">2</span> − p √ (x<span class="sp">2</span> + y<span class="sp">2</span>) + px ];</p> +<p class="center">ψ′ = ½ U [ y<span class="sp">2</span> − p √ (x<span class="sp">2</span> + y<span class="sp">2</span>) + px ];</p> <div class="author">(9)</div> -<p class="center">ψ = − Up [ √ (x<span class="sp">2</span> + y<span class="sp">2</span>) − x ];</p> +<p class="center">ψ = −½ Up [ √ (x<span class="sp">2</span> + y<span class="sp">2</span>) − x ];</p> <div class="author">(10)</div> -<p class="center">φ = − Up log [ √ (x<span class="sp">2</span> + y<span class="sp">2</span>) + x ].</p> +<p class="center">φ = −½ Up log [ √ (x<span class="sp">2</span> + y<span class="sp">2</span>) + x ].</p> <div class="author">(11)</div> <p>The relative path of a liquid particle is along a stream line</p> -<p class="center">ψ′ = Uc<span class="sp">2</span>, a constant,</p> +<p class="center">ψ′ = ½ Uc<span class="sp">2</span>, a constant,</p> <div class="author">(12)</div> <table class="math0" summary="math"> @@ -5787,8 +5748,8 @@ where a = ∞, we find for a paraboloid of revolution</p> <p class="center">A = B = C = a<span class="sp">3</span> / 3r<span class="sp">3</span>,</p> <table class="math0" summary="math"> -<tr><td rowspan="2">φ = Ux</td> <td>a<span class="sp">3</span>/r<span class="sp">3</span> + 2 a<span class="sp">3</span>/a<span class="su">1</span><span class="sp">3</span></td> -<td rowspan="2">,   ψ = Uy<span class="sp">2</span></td> <td>a<span class="sp">3</span>/r<span class="sp">3</span> − a<span class="sp">3</span>/a<span class="su">1</span><span class="sp">3</span></td> +<tr><td rowspan="2">φ = ½ Ux</td> <td>a<span class="sp">3</span>/r<span class="sp">3</span> + 2 a<span class="sp">3</span>/a<span class="su">1</span><span class="sp">3</span></td> +<td rowspan="2">,   ψ = ½ Uy<span class="sp">2</span></td> <td>a<span class="sp">3</span>/r<span class="sp">3</span> − a<span class="sp">3</span>/a<span class="su">1</span><span class="sp">3</span></td> <td rowspan="2">;</td></tr> <tr><td class="denom">1 − a<span class="sp">4</span>/a<span class="su">1</span><span class="sp">2</span></td> <td class="denom">1 − a<span class="sp">3</span>/a<span class="su">1</span><span class="sp">3</span></td></tr></table> <div class="author">(2)</div> @@ -5797,7 +5758,7 @@ where a = ∞, we find for a paraboloid of revolution</p> <table class="math0" summary="math"> <tr><td>A<span class="su">0</span> + 2A<span class="su">1</span></td> -<td rowspan="2">W′ = </td> <td>a<span class="su">1</span><span class="sp">3</span> + 2a<span class="sp">3</span></td> +<td rowspan="2">W′ = ½</td> <td>a<span class="su">1</span><span class="sp">3</span> + 2a<span class="sp">3</span></td> <td rowspan="2">W′.</td></tr> <tr><td class="denom">2A<span class="su">0</span> − 2A<span class="su">1</span></td> <td class="denom">a<span class="su">1</span><span class="sp">3</span> − a<span class="sp">3</span></td></tr></table> <div class="author">(3)</div> @@ -5892,7 +5853,7 @@ Math.</i> xxii.).</p> that</p> <table class="math0" summary="math"> -<tr><td rowspan="2">ψ′ = Uy<span class="sp">2</span> <span class="f150">(</span> 1 −</td> <td>a<span class="su">1</span><span class="sp">3</span></td> +<tr><td rowspan="2">ψ′ = ½ Uy<span class="sp">2</span> <span class="f150">(</span> 1 −</td> <td>a<span class="su">1</span><span class="sp">3</span></td> <td rowspan="2">−</td> <td>a<span class="su">2</span><span class="sp">3</span></td> <td rowspan="2">+</td> <td>a<span class="sp">3</span></td> <td rowspan="2"><span class="f150">)</span>,</td></tr> @@ -5918,7 +5879,7 @@ from their centres.</p> <p>With a<span class="su">2</span> = ∞, these reduce to</p> <table class="math0" summary="math"> -<tr><td rowspan="2">ψ′ = Uy<span class="sp">2</span> <span class="f150">(</span> 1 −</td> <td>a<span class="sp">5</span></td> +<tr><td rowspan="2">ψ′ = ½Uy<span class="sp">2</span> <span class="f150">(</span> 1 −</td> <td>a<span class="sp">5</span></td> <td rowspan="2"><span class="f150">)</span></td> <td>x</td> <td rowspan="2">, or Uy <span class="f150">(</span> 1 −</td> <td>a<span class="sp">4</span></td> <td rowspan="2"><span class="f150">)</span></td> <td>x</td> @@ -5929,10 +5890,10 @@ from their centres.</p> <p class="noind">for a sphere or cylinder, and a diametral plane.</p> -<p>Two equal spheres, intersecting at 120, will require</p> +<p>Two equal spheres, intersecting at 120°, will require</p> <table class="math0" summary="math"> -<tr><td rowspan="2">ψ′ = Uy<span class="sp">2</span> <span class="f150">[</span></td> <td>x</td> +<tr><td rowspan="2">ψ′ = ½Uy<span class="sp">2</span> <span class="f150">[</span></td> <td>x</td> <td rowspan="2">−</td> <td>a<span class="sp">3</span></td> <td rowspan="2">+</td> <td>a<span class="sp">4</span> (a − 2x)</td> <td rowspan="2">+</td> <td>a<span class="sp">3</span></td> @@ -5944,7 +5905,7 @@ from their centres.</p> <div class="author">(11)</div> <p class="noind">with a similar expression for cylinders; so that the plane x = 0 -may be introduced as a boundary, cutting the surface at 60. The +may be introduced as a boundary, cutting the surface at 60°. The motion of these cylinders across the line of centres is the equivalent of a line doublet along each axis.</p> @@ -5967,7 +5928,7 @@ the motion if</p> <p class="noind">and that the continuity of the liquid is secured if</p> <table class="math0" summary="math"> -<tr><td rowspan="2">(a<span class="sp">2</span> + λ)<span class="sp">3/2</span> (b<span class="sp">2</span> + λ)<span class="sp">3/2</span> (c<span class="sp">2</span> + λ) </td> <td>dχ</td> +<tr><td rowspan="2">(a<span class="sp">2</span> + λ)<span class="sp">3/2</span> (b<span class="sp">2</span> + λ)<span class="sp">3/2</span> (c<span class="sp">2</span> + λ) ½</td> <td>dχ</td> <td rowspan="2">= constant,</td></tr> <tr><td class="denom">dλ</td></tr></table> <div class="author">(3)</div> @@ -5975,7 +5936,7 @@ the motion if</p> <table class="math0" summary="math"> <tr><td rowspan="2">χ = <span class="f150">∫</span><span class="sp1">∞</span><span class="su1">λ</span></td> <td>N dλ</td> <td rowspan="2">=</td> <td>N</td> -<td rowspan="2"></td> <td>B<span class="su">λ</span> − A<span class="su">λ</span></td> +<td rowspan="2">·</td> <td>B<span class="su">λ</span> − A<span class="su">λ</span></td> <td rowspan="2">;</td></tr> <tr><td class="denom">(a<span class="sp">2</span> + λ) (b<span class="sp">2</span> + λ) P</td> <td class="denom">abc</td> <td class="denom">a<span class="sp">2</span> − b<span class="sp">2</span></td></tr></table> @@ -5984,7 +5945,7 @@ the motion if</p> <p class="noind">and at the surface λ = 0,</p> <table class="math0" summary="math"> -<tr><td rowspan="2">R = −</td> <td>[ (1/a<span class="sp">2</span> + 1/b<span class="sp">2</span>) N/abc (B<span class="su">0</span> − A<span class="su">0</span>)/(a<span class="sp">2</span> − b<span class="sp">2</span>) ] − N/abc 1/a<span class="sp">2</span>b<span class="sp">2</span></td> +<tr><td rowspan="2">R = −</td> <td>[ (1/a<span class="sp">2</span> + 1/b<span class="sp">2</span>) · N/abc · (B<span class="su">0</span> − A<span class="su">0</span>)/(a<span class="sp">2</span> − b<span class="sp">2</span>) ] − N/abc · 1/a<span class="sp">2</span>b<span class="sp">2</span></td> <td rowspan="2">,</td></tr> <tr><td class="denom">1/b<span class="sp">2</span> − 1/a<span class="sp">2</span></td></tr></table> <div class="author">(5)</div> @@ -5993,7 +5954,7 @@ the motion if</p> <tr><td>N</td> <td rowspan="2">= R</td> <td>1/b<span class="sp">2</span> − 1/a<span class="sp">2</span></td> <td rowspan="2">,</td></tr> -<tr><td class="denom">abc</td> <td class="denom">1/a<span class="sp">2</span>b<span class="sp">2</span> − [ (1/a<span class="sp">2</span> + 1/b<span class="sp">2</span>) (B<span class="su">0</span> − A<span class="su">0</span>) / (a<span class="sp">2</span> − b<span class="sp">2</span>) ]</td></tr></table> +<tr><td class="denom">abc</td> <td class="denom">1/a<span class="sp">2</span>b<span class="sp">2</span> − [ (1/a<span class="sp">2</span> + 1/b<span class="sp">2</span>) · (B<span class="su">0</span> − A<span class="su">0</span>) / (a<span class="sp">2</span> − b<span class="sp">2</span>) ]</td></tr></table> <div class="author">(6)</div> <table class="math0" summary="math"> @@ -6072,14 +6033,14 @@ by a fixed ellipsoid λ = λ<span class="su">1</span> is made in a s <td rowspan="2">− 1 <span class="f150">)</span>,   Cλ = 0;</td></tr> <tr><td class="denom">a<span class="sp">2</span> − b<span class="sp">2</span></td> <td class="denom">b<span class="sp">2</span> + λ</td></tr></table> -<p class="noind">and then as above in 31, with</p> +<p class="noind">and then as above in § 31, with</p> <p class="center">a = c ch α, b = c sh α, a<span class="su">1</span> = √ (a<span class="sp">2</span> + λ) = c ch α<span class="su">1</span>, b<span class="su">1</span> = c sh α<span class="su">1</span></p> <div class="author">(13)</div> -<p class="noind">the ratio in (11) agrees with 31 (6).</p> +<p class="noind">the ratio in (11) agrees with § 31 (6).</p> -<p>As before in 31, the rotation may be resolved into a shear-pair, +<p>As before in § 31, the rotation may be resolved into a shear-pair, in planes perpendicular to Ox and Oy.</p> <p>A torsion of the ellipsoidal surface will give rise to a velocity @@ -6301,7 +6262,7 @@ expressed by (iii).</p> <p>If a fourth integral is obtainable, the solution is reducible to a quadrature, but this is not possible except in a limited series of cases, -investigated by H. Weber, F. Ktter, R. Liouville, Caspary, +investigated by H. Weber, F. Kötter, R. Liouville, Caspary, Jukovsky, Liapounoff, Kolosoff and others, chiefly Russian mathematicians; and the general solution requires the double-theta hyperelliptic function.</p> @@ -6311,9 +6272,9 @@ most general expression of the kinetic energy was shown by A. Clebsch to take the form</p> <table class="reg" summary="poem"><tr><td> <div class="poemr"> -<p>T = p (x<span class="su">1</span><span class="sp">2</span> + x<span class="su">2</span><span class="sp">2</span>) + p′x<span class="su">3</span><span class="sp">2</span></p> +<p>T = ½p (x<span class="su">1</span><span class="sp">2</span> + x<span class="su">2</span><span class="sp">2</span>) + ½p′x<span class="su">3</span><span class="sp">2</span></p> <p class="i05">+ q (x<span class="su">1</span>y<span class="su">1</span> + x<span class="su">2</span>y<span class="su">2</span>) + q′x<span class="su">3</span>y<span class="su">3</span></p> -<p class="i05">+ r (y<span class="su">1</span><span class="sp">2</span> + y<span class="su">2</span><span class="sp">2</span>) + r′y<span class="su">3</span><span class="sp">2</span></p> +<p class="i05">+ ½r (y<span class="su">1</span><span class="sp">2</span> + y<span class="su">2</span><span class="sp">2</span>) + ½r′y<span class="su">3</span><span class="sp">2</span></p> </div> </td></tr></table> <div class="author">(1)</div> @@ -6530,14 +6491,14 @@ Otherwise, if A is positive</p> <p>A number of cases are worked out in the American Journal of Mathematics (1907), in which the motion is made algebraical by the use of the pseudo-elliptic integral. To give a simple instance, -changing to the stereographic projection by putting tan θ = x,</p> +changing to the stereographic projection by putting tan ½θ = x,</p> <p class="center">(Nx e<span class="sp">ψi</span>)<span class="sp">3/2</span> = (x + 1) √ X<span class="su">1</span> + i (x − 1) √ X<span class="su">2</span>,</p> <div class="author">(27)</div> <table class="math0" summary="math"> <tr><td>X<span class="su">1</span></td> -<td rowspan="2">= ax<span class="sp">4</span> + 2ax<span class="sp">3</span> 3 (a + b) x<span class="sp">2</span> + 2bx b,</td></tr> +<td rowspan="2">= ± ax<span class="sp">4</span> + 2ax<span class="sp">3</span> ± 3 (a + b) x<span class="sp">2</span> + 2bx ± b,</td></tr> <tr><td class="denom">X<span class="su">2</span></td></tr></table> <div class="author">(28)</div> @@ -6617,7 +6578,7 @@ well as of the body from the vector OF to O′F′ requires an impulse couple, tending to increase the angle FOO′, of magnitude, in sec. foot-pounds</p> -<p class="center">FOO′sin FOO′ = FVt sin (θ − φ),</p> +<p class="center">F·OO′·sin FOO′ = FVt sin (θ − φ),</p> <div class="author">(4)</div> <p class="noind">equivalent to an incessant couple</p> @@ -6735,7 +6696,7 @@ centring, we obtain</p> of this quadratic in μ, and then</p> <table class="math0" summary="math"> -<tr><td rowspan="2">μ = </td> <td>C<span class="su">1</span></td> +<tr><td rowspan="2">μ = ½</td> <td>C<span class="su">1</span></td> <td rowspan="2">p sec θ,</td></tr> <tr><td class="denom">C<span class="su">2</span></td></tr></table> <div class="author">(7)</div> @@ -6762,13 +6723,13 @@ Rifling, and n the Pitch of Rifling in Calibres.</i></p> <table class="ws" summary="Contents"> <tr><td class="tccm allb" colspan="2"> </td> <td class="tccm allb" colspan="2">Cast-iron Common Shell<br />ƒ = <span class="spp">2</span>⁄<span class="suu">3</span>, S.G. 7.2.</td> - <td class="tccm allb" colspan="2">Palliser Shell<br />ƒ = , S.G. 8.</td> + <td class="tccm allb" colspan="2">Palliser Shell<br />ƒ = ½, S.G. 8.</td> <td class="tccm allb" colspan="2">Solid Steel Bullet<br />ƒ = 0, S.G. 8.</td> <td class="tccm allb" colspan="2">Solid Lead Bullet<br />ƒ = 0, S.G. 10.9.</td></tr> <tr><td class="tcc allb">x</td> <td class="tcc allb">β − α</td> <td class="tcc allb">δ</td> <td class="tcc allb">n</td> <td class="tcc allb">δ</td> <td class="tcc allb">n</td> <td class="tcc allb">δ</td> <td class="tcc allb">n</td> <td class="tcc allb">δ</td> <td class="tcc allb">n</td></tr> -<tr><td class="tcc lb rb">1.0</td> <td class="tcc rb">0.0000</td> <td class="tcr rb">0   0′</td> <td class="tcc rb">Infinity</td> <td class="tcr rb">0   0′</td> <td class="tcc rb">Infinity</td> <td class="tcr rb">0   0′</td> <td class="tcc rb">Infinity</td> <td class="tcr rb">0   0′</td> <td class="tcc rb">Infinity</td></tr> +<tr><td class="tcc lb rb">1.0</td> <td class="tcc rb">0.0000</td> <td class="tcr rb">0°   0′</td> <td class="tcc rb">Infinity</td> <td class="tcr rb">0°   0′</td> <td class="tcc rb">Infinity</td> <td class="tcr rb">0°   0′</td> <td class="tcc rb">Infinity</td> <td class="tcr rb">0°   0′</td> <td class="tcc rb">Infinity</td></tr> <tr><td class="tcc lb rb">2.0</td> <td class="tcc rb">0.4942</td> <td class="tcr rb">2   49</td> <td class="tcc rb">63.87</td> <td class="tcr rb">2   32</td> <td class="tcc rb">71.08</td> <td class="tcr rb">2   29</td> <td class="tcc rb">72.21</td> <td class="tcr rb">2   08</td> <td class="tcc rb">84.29</td></tr> <tr><td class="tcc lb rb">2.5</td> <td class="tcc rb">0.6056</td> <td class="tcr rb">3   46</td> <td class="tcc rb">47.91</td> <td class="tcr rb">3   23</td> <td class="tcc rb">53.32</td> <td class="tcr rb">3   19</td> <td class="tcc rb">54.17</td> <td class="tcr rb">2   51</td> <td class="tcc rb">63.24</td></tr> <tr><td class="tcc lb rb">3.0</td> <td class="tcc rb">0.6819</td> <td class="tcr rb">4   41</td> <td class="tcc rb">38.45</td> <td class="tcr rb">4   13</td> <td class="tcc rb">42.79</td> <td class="tcr rb">4   09</td> <td class="tcc rb">43.47</td> <td class="tcr rb">3   38</td> <td class="tcc rb">50.74</td></tr> @@ -6785,10 +6746,10 @@ Rifling, and n the Pitch of Rifling in Calibres.</i></p> which the rifling makes one turn in a pitch of n calibres or nd inches, so that the angle δ of the rifling is given by</p> -<p class="center">tan δ = πd / nd = dp / u,</p> +<p class="center">tan δ = πd / nd = ½ dp / u,</p> <div class="author">(10)</div> -<p class="noind">which is the ratio of the linear velocity of rotation dp to u, the +<p class="noind">which is the ratio of the linear velocity of rotation ½dp to u, the velocity of advance,</p> <table class="math0" summary="math"> @@ -6806,7 +6767,7 @@ velocity of advance,</p> <tr><td rowspan="2">1 +</td> <td>W′</td> <td rowspan="2">α</td></tr> <tr><td class="denom">W</td></tr></table></td> -<td rowspan="2"></td> <td><table class="math0" summary="math"> +<td rowspan="2">·</td> <td><table class="math0" summary="math"> <tr><td rowspan="2"><span class="f150">(</span> 1 +</td> <td>W′</td> <td rowspan="2">ε <span class="f150">)</span> <span class="f150">(</span></td> <td>k<span class="su">1</span></td> <td rowspan="2"><span class="f150">)</span></td> <td><span class="sp">2</span></td></tr> @@ -6846,7 +6807,7 @@ shot, this equation will give the value of δ and n required for stability of flight in the air.</p> <p>The ellipsoid is the only shape for which α and β have so far been -determined analytically, as shown already in 44, so we must restrict +determined analytically, as shown already in § 44, so we must restrict our calculation to an egg-shaped bullet, bounded by a prolate ellipsoid of revolution, in which, with b = c,</p> @@ -7023,7 +6984,7 @@ above. But if the body is perforated, the liquid can circulate through a hole, in reentrant stream lines linked with the body, even while the body is at rest; and no reaction from the surface can influence this circulation, which may be supposed started in the ideal manner -described in 29, by the application of impulsive pressure across an +described in § 29, by the application of impulsive pressure across an ideal membrane closing the hole, by means of ideal mechanism connected with the body. The body is held fixed, and the reaction of the mechanism and the resultant of the impulsive pressure on the @@ -7044,7 +7005,7 @@ deduced of a perforated solid in liquid, from considerations purely hydrodynamical.</p> <p>The effect of an external circulation of vortex motion on the -motion of a cylinder has been investigated in 29; a similar procedure +motion of a cylinder has been investigated in § 29; a similar procedure will show the influence of circulation through a hole in a solid, taking as the simplest illustration a ring-shaped figure, with uniplanar motion, and denoting by ξ the resultant axial linear @@ -7217,7 +7178,7 @@ the component ξ of the circulation.</p> body cannot describe loops; but with ξ, the influence may be great enough to make dx/dt change sign, and so loops occur, as shown in A. B. Basset’s <i>Hydrodynamics</i>, i. 192, resembling the trochoidal -curves, which can be looped, investigated in 29 for the motion of +curves, which can be looped, investigated in § 29 for the motion of a cylinder under gravity, when surrounded by a vortex.</p> <p>The branch of hydrodynamics which discusses wave motion in a @@ -7227,7 +7188,7 @@ the influence of viscosity is considered under <span class="sc"><a href="#artlin <p><span class="sc">References.</span>—For the history and references to the original memoirs see <i>Report to the British Association</i>, by G. G. Stokes (1846), and W. M. Hicks (1882). See also the <i>Fortschritte der Mathematik</i>, -and A. E. H. Love, “Hydrodynamik” in the <i>Encyklpadie der +and A. E. H. Love, “Hydrodynamik” in the <i>Encyklöpadie der mathematischen Wissenschaften</i> (1901).</p> </div> <div class="author">(A. G. G.)</div> @@ -8010,7 +7971,7 @@ budded from the founder.</td></tr> simple unbranched <i>Plumularia</i>-type. F, founder; 1-8, main axis formed by biserial budding from founder; <i>a-e</i>, pinnule formed -by uniserial budding from founder; <i>a</i>-<i>d</i>, +by uniserial budding from founder; <i>a</i>¹-<i>d</i>¹, branch formed by similar budding from 1; <i>a</i><span class="sp">2</span>-<i>d</i><span class="sp">2</span> from 2, and so forth.</td></tr></table> @@ -8156,7 +8117,7 @@ which starts a uniserial pinnule; and as a third bud I<span class="sp">7</span>, which starts a biserial branch (II<span class="sp">7</span>-VI<span class="sp">7</span>) that repeats the structure of the main stem and gives off pinnules. The main stem is indicated -by---, the new stem by .</td></tr></table> +by-·-·-·, the new stem by ······.</td></tr></table> <p class="pt2">In other colonies the two functions of the nutritive @@ -8276,7 +8237,7 @@ its tentacles have become rudimentary or absent. It is interesting to note that <i>Mnestra</i> has been shown by J. W. Fewkes -[<b>15</b>] and R. T. Gnther [<b>19</b>] to belong to the same family (<i>Cladonemidae</i>) +[<b>15</b>] and R. T. Günther [<b>19</b>] to belong to the same family (<i>Cladonemidae</i>) as <i>Cladonema</i> and <i>Clavatella</i>, and it is reasonable to suppose that the non-parasitic ancestor of <i>Mnestra</i> was, like the other two genera, an ambulatory @@ -8481,7 +8442,7 @@ thickly as to form a tough, supporting, “chondral” tissue, resemblin cartilage, chiefly developed at the margin of the umbrella and forming streaks or bars supporting the tentacles (“Tentakelspangen,” <i>peronia</i>) or the tentaculocysts -(“Gehrspangen,” <i>otoporpae</i>).</p> +(“Gehörspangen,” <i>otoporpae</i>).</p> <p>The muscular tissue of the Hydromedusae is entirely ectodermal. The @@ -9729,12 +9690,12 @@ medusa. Whether sporogony occurs also in the polyp or not remains to be proved.</p> <p>6. <i>Sexual Reproduction and Embryology.</i>—The ovum of Hydromedusae -is usually one of a large number of ogonia, and grows +is usually one of a large number of oögonia, and grows at the expense of its sister-cells. No regular follicle is formed, -but the ocyte absorbs nutriment from the remaining ogonia. -In <i>Hydra</i> the ocyte is a large amoeboid cell, which sends out -pseudopodia amongst the ogonia and absorbs nutriment from -them. When the ocyte is full grown, the residual ogonia +but the oöcyte absorbs nutriment from the remaining oögonia. +In <i>Hydra</i> the oöcyte is a large amoeboid cell, which sends out +pseudopodia amongst the oögonia and absorbs nutriment from +them. When the oöcyte is full grown, the residual oögonia die off and disintegrate.</p> <table class="pic" style="clear: both;" summary="Illustration"> @@ -10113,13 +10074,13 @@ Ussow [<b>54</b>].</p> Viguier is a remarkable floating marine form. See C. Viguier [<b>56</b>] and -Delage and Hrouard +Delage and Hérouard (Hydrozoa [<b>2</b>]).</p> <p><i>Haleremita</i> Schaudinn. See F. Schaudinn [<b>50</b>] and Delage and -Hrouard (<span class="sc">Hydrozoa</span> +Hérouard (<span class="sc">Hydrozoa</span> [<b>2</b>]).</p> <p>In all the above-mentioned @@ -10279,11 +10240,11 @@ produced, they may show all stages of degeneration.</p> <p><i>Classification.</i>—Until quite recently the hydroids (Gymnoblastea) and the medusae (Anthomedusae) have been classified separately, since the connexion between them was insufficiently known. Delage -and Hrouard (<span class="sc">Hydrozoa</span> [<b>2</b>]) were the first to make an heroic +and Hérouard (<span class="sc">Hydrozoa</span> [<b>2</b>]) were the first to make an heroic attempt to unite the two classifications into one, to which Hickson (<span class="sc">Hydrozoa</span> [<b>4</b>]) has made some additions and slight modifications. The classification given here is for the most part that of Delage and -Hrouard. It is certain, however, that no such classification can be +Hérouard. It is certain, however, that no such classification can be considered final at present, but must undergo continual revision in the future. With this reservation we may recognize fifteen well-characterized families and others of more doubtful nature. Certain @@ -10798,9 +10759,9 @@ numerous hollow tentacles bearing ocelli, and without otocysts. sessile gonophores. Many common or well-known genera belong here, such as <i>Halecium</i>, <i>Campanularia</i>, <i>Gonothyraea</i>, &c.</p> -<p>7. <i>Lafoidae.</i>—Trophosome as in the preceding; gonosome, free +<p>7. <i>Lafoëidae.</i>—Trophosome as in the preceding; gonosome, free medusae or gonophores, the medusae with large open otocysts. -The hydroid genus <i>Lafoa</i> is remarkable for producing gonothecae on +The hydroid genus <i>Lafoëa</i> is remarkable for producing gonothecae on the hydrorhiza, each containing a blastostyle which bears a single gonophore; this portion of the colony was formerly regarded as an independent parasitic hydroid, and was named <i>Coppinia</i>. Medusan @@ -11064,7 +11025,7 @@ Hydrozoa, especially the Calyptoblastea, than with any other existing group of the animal kingdom.</p> <div class="condensed"> -<p>See the treatise of Delage and Hrouard (<span class="sc">Hydrozoa</span>, [<b>4</b>]), and the +<p>See the treatise of Delage and Hérouard (<span class="sc">Hydrozoa</span>, [<b>4</b>]), and the article <span class="sc"><a href="#artlinks">Graptolites</a></span>.</p> </div> @@ -11122,7 +11083,7 @@ by budding.</p> <tr><td class="figright1"><img style="width:313px; height:652px" src="images/img155a.jpg" alt="" /></td></tr> <tr><td class="caption80">After Haeckel, <i>System der Medusen</i>, by permission of Gustav Fischer.</td></tr> -<tr><td class="caption"><span class="sc">Fig. 64.</span> <i>Olindias mlleri.</i></td></tr></table> +<tr><td class="caption"><span class="sc">Fig. 64.</span> <i>Olindias mülleri.</i></td></tr></table> <div class="condensed"> <p>The Trachomedusae are @@ -11150,7 +11111,7 @@ gonads; manubrium short; ring-canals giving off blind centripetal canals; tentaculocysts -enclosed. <i>Olindias mlleri</i> +enclosed. <i>Olindias mülleri</i> (fig. 64) is a common Mediterranean species. Other genera are <i>Aglauropsis</i>, @@ -11274,7 +11235,7 @@ tentacle as one of a pair of peronial canals, the limbs of the V-like figure already mentioned. The nerve-rings have a similar course. The tentaculocysts are implanted round the margins of the lobes of the umbrella and may be supported by prolongations -of the ectodermal rim termed <i>otoporpae</i> (<i>Gehrspangen</i>). +of the ectodermal rim termed <i>otoporpae</i> (<i>Gehörspangen</i>). The radial canals are represented by wide gastric pouches, and may be absent, so that the tentacles arise directly from the stomach (<i>Solmaridae</i>). The tentacles are always solid, as in @@ -11309,7 +11270,7 @@ its host. At the same time it produces buds from an aboral stolon. The buds become medusae by the direct method of budding described above. In some cases the buds do not become detached at once, but the stolon continues to grow and to produce -more buds, forming a “bud-spike” (<i>Knospenhre</i>), which +more buds, forming a “bud-spike” (<i>Knospenähre</i>), which consists of the axial stolon bearing medusa-buds in all stages of development. In such cases the original parent-actinula does not itself become a medusa, but remains arrested in development @@ -11616,14 +11577,14 @@ varieties have been termed “cystons” by Haeckel.</p> <p><span class="pagenum"><a name="page158" id="page158"></a>158</span></p> -<p>3. <i>Tentacles</i> (“<i>Fangfden</i>”), always present, and implanted one +<p>3. <i>Tentacles</i> (“<i>Fangfäden</i>”), always present, and implanted one at the base of each siphon (fig. 68, <i>f</i>). The tentacles of siphonophores may reach a great length and have a complex structure. They may bear accessory filaments or <i>tentilla</i> (<i>f</i>′), covered thickly with batteries of nematocysts, to which these organisms owe their great powers of offence and defence.</p> -<p>4. <i>Palpacles</i> (“<i>Tastfden</i>”), occurring together with palpons, one +<p>4. <i>Palpacles</i> (“<i>Tastfäden</i>”), occurring together with palpons, one implanted at the base of each palpon (fig. 68, <i>h</i>). Each palpacle is a tactile filament, very extensile, without accessory filaments or nematocysts.</p> @@ -11825,7 +11786,7 @@ Narcomedusan.</p> <p><i>Theories of Siphonophore Morphology.</i>—The many theories that have been put forward as to the interpretation of the cormus and the various parts are set forth and discussed in the -treatise of Y. Delage and E. Hrouard (<span class="sc">Hydrozoa</span> [<b>4</b>]) and more +treatise of Y. Delage and E. Hérouard (<span class="sc">Hydrozoa</span> [<b>4</b>]) and more recently by R. Woltereck [<b>59</b>], and only a brief analysis can be given here.</p> @@ -11980,7 +11941,7 @@ strictly comparable to a stolon.</p> </div> <p><i>Classification.</i>—The Siphonophora may be divided, following -Delage and Hrouard, into four sub-orders:</p> +Delage and Hérouard, into four sub-orders:</p> <p>I. <span class="sc">Chondrophorida</span> (<i>Disconectae</i> Haeckel, <i>Tracheophysae</i> Chun). With an apical chambered pneumatophore, from which @@ -12058,9 +12019,9 @@ general works cited in the article <span class="sc">Hydrozoa</span>, in some of full bibliographies will be found.</p> <p><b>1.</b> G. J. Allman, “A Monograph of the Gymnoblastic or Tubularian -Hydroids,” Ray Society (1871-1872); <b>2.</b> A. Brauer, “ber die +Hydroids,” Ray Society (1871-1872); <b>2.</b> A. Brauer, “Über die Entwickelung von Hydra,” <i>Zeitschr. f. wiss. Zool.</i> lii. (1891), pp. 169-216, -pls. ix.-xii.; <b>3.</b> “ber die Entstehung der Geschlechtsprodukte +pls. ix.-xii.; <b>3.</b> “Über die Entstehung der Geschlechtsprodukte und die Entwickelung von Tubularia mesembryanthemum Allm.,” <i>t.c.</i> pp. 551-579, pls. xxxiii.-xxxv.; <b>4.</b> W. K. Brooks, “The Life-History of the Hydromedusae: a discussion of the Origin of the @@ -12079,11 +12040,11 @@ the Freshwater Medusa liberated by <i>Microhydra ryderi</i>, Potts, and a Comparison with <i>Limnocodium</i>,” <i>Quart. Journ. Micr. Sci.</i> I (1906), pp. 635, 645, pl. xxxvii.; <b>10a.</b> “On the Freshwater Medusa <i>Limnocnida tanganicae</i>” <i>Budgett Memorial Volume</i> (Cambridge, -1908, pp. 471-482, pl. xxviii.; <b>11.</b> C. Claus, “ber die Struktur der -Muskelzellen und ber den Krperbau von Mnestra parasites +1908, pp. 471-482, pl. xxviii.; <b>11.</b> C. Claus, “Über die Struktur der +Muskelzellen und über den Körperbau von Mnestra parasites Krohn,” <i>Verhandl. zool. bot. Ges. Wien</i>, xxv. (1876), pp. 9-12, pl. i.; -<b>11a.</b> C. Dawydov, “Hydroctena salenskii,” <i>Mm. Acad. Imp. St. -Ptersbourg</i> (viii.) xiv. No. 9 (1903), 17 pp., 1 pl.; <b>12.</b> A. Dendy, +<b>11a.</b> C. Dawydov, “Hydroctena salenskii,” <i>Mém. Acad. Imp. St. +Pétersbourg</i> (viii.) xiv. No. 9 (1903), 17 pp., 1 pl.; <b>12.</b> A. Dendy, “On a Free-swimming Hydroid, <i>Pelagohydra mirabilis</i>,” n. gen. et sp., <i>Quart. Journ. Micr. Sci.</i> xlvi. (1903), pp. 1-24, pls. i. ii.; <b>13.</b> H. Driesch, “Tektonische Studien an Hydroidpolypen,” (1) <i>Jen. @@ -12096,39 +12057,39 @@ Vertreterin einer neuen Familie der Hydromedusen,” <i>Annot. Zool. Tokyo</i>, i. (1897), pp. 93-104, pl. vi., figs. 106-113; <b>17.</b> “The Craspe dote Medusa <i>Olindias</i> and some of its Natural Allies,” <i>Mark Anniversary Volume</i> (New York, 1903), pp. 1-22, 3 pls.; <b>18.</b> H. Grenacher, -“ber die Nesselkapseln von Hydra,” <i>Zool. Anz.</i> xviii. (1895), -pp. 310-321, 7 figs.; <b>19.</b> R. T. Gnther, “On the Structure and +“Über die Nesselkapseln von Hydra,” <i>Zool. Anz.</i> xviii. (1895), +pp. 310-321, 7 figs.; <b>19.</b> R. T. Günther, “On the Structure and Affinities of <i>Mnestra parasites</i> Krohn; with a revision of the Classification of the <i>Cladonemidae</i>,” <i>Mitt. Stat. Neapel</i>, xvi. (1903), pp. 35-62, pls. ii. iii.; <b>20.</b> E. Haeckel, “Das System der Medusen,” <i>Denkschr. med.-nat.-wiss. Ges.</i> (Jena, 1879-1881); <b>21.</b> “Deep Sea Medusae,” in <i>Reports of the Challenger Expedition</i>, Zool. iv. pt. 2 (London, 1882); <b>22.</b> P. Hallez, “Bougainvillia fruticosa Allm. est -le facis d’eau agite du Bougainvillia ramosa Van Ben.” <i>C.-R. Acad. +le faciès d’eau agitée du Bougainvillia ramosa Van Ben.” <i>C.-R. Acad. Sci. Paris</i>, cxl. (1905), pp. 457-459; <b>23.</b> O. & R. Hertwig, <i>Der Organismus der Medusen</i> (Jena, 1878), 70 pp., 3 pls.; <b>24.</b> <i>Das Nervensystem und die Sinnesorgane der Medusen</i> (Leipzig, 1878), 186 pp., 10 pls.; <b>25.</b> S. J. Hickson, “The Medusae of <i>Millepora</i>,” <i>Proc. Roy. Soc.</i> lxvi. (1899), pp. 6-10, 10 figs.; <b>26.</b> T. Hincks, <i>A History of British Hydroid Zoophytes</i> (2 vols., London, 1868); <b>27.</b> N. Iwanzov, -“ber den Bau, die Wirkungsweise und die Entwickelung der +“Über den Bau, die Wirkungsweise und die Entwickelung der Nesselkapseln von Coelenteraten,” <i>Bull. Soc. Imp. Natural, Moscou</i> (1896), pp. 323-355, 4 pls.; <b>28.</b> C. F. Jickeli, “Der Bau der Hydroidpolypen,” (1) <i>Morph. Jahrbuch</i>, viii. (1883), pp. 373-416, pls. xvi.-xviii.; (2) t.c., pp. 580-680, pls. xxv.-xxviii.; <b>29.</b> Albert Lang, -“ber die Knospung bei Hydra und einigen Hydropolypen,” +“Über die Knospung bei Hydra und einigen Hydropolypen,” <i>Zeitschr. f. wiss. Zool.</i> liv. (1892), pp. 365-384, pl. xvii.; <b>30.</b> Arnold -Lang, “Gastroblasta Raffaelei. Eine durch eine Art unvollstndiger +Lang, “Gastroblasta Raffaelei. Eine durch eine Art unvollständiger Theilung entstehende Medusen-Kolonie,” <i>Jena Zeitschr.</i> xix. (1886), pp. 735-762, pls. xx., xxi.; <b>31.</b> A. Linko, “Observations -sur les mduses de la mer Blanche,” <i>Trav. Soc. Imp. Nat. St Ptersbourg</i>, -xxix. (1899); <b>32.</b> “ber den Bau der Augen bei den Hydromedusen,” -<i>Zapiski Imp. Akad. Nauk (Mm. Acad. Imp. Sci.) St -Ptersbourg</i> (8) x. 3 (1900), 23 pp., 2 pls.; <b>33.</b> O. Maas, “Die craspedoten +sur les méduses de la mer Blanche,” <i>Trav. Soc. Imp. Nat. St Pétersbourg</i>, +xxix. (1899); <b>32.</b> “Über den Bau der Augen bei den Hydromedusen,” +<i>Zapiski Imp. Akad. Nauk (Mém. Acad. Imp. Sci.) St +Pétersbourg</i> (8) x. 3 (1900), 23 pp., 2 pls.; <b>33.</b> O. Maas, “Die craspedoten Medusen,” in <i>Ergebn. Plankton Expedition</i>, ii. (Kiel and Leipzig, 1893), 107 pp., 8 pls., 3 figs.; <b>34.</b> “Die Medusen,” <i>Mem. Mus. Comp. Zool. Harvard</i>, xxiii. (1897), i.; <b>35.</b> “On <i>Hydroctena</i>,” <i>Zool. -Centralbl.</i> xi. (1904), pp. 240-243; <b>36.</b> “Revision des mduses +Centralbl.</i> xi. (1904), pp. 240-243; <b>36.</b> “Revision des méduses appartenant aux familles des <i>Cunanthidae</i> et des <i>Aeginidae</i>, et groupement nouveau des genres,” <i>Bull. Mus. Monaco</i>, v. (1904), 8 pp.; <b>37.</b> “Revision der Cannotiden Haeckels,” <i>SB. K. Bayer. @@ -12141,13 +12102,13 @@ Polypomedusen),” <i>Fauna arctica</i>, iv. (1906), pp. 479-526; <b>41.</b> Mereschkowsky, “On a new Genus of Hydroids (<i>Monobrachium</i>) from the White Sea, with a short description of other new Hydroids,” <i>Ann. Mag. Nat. Hist.</i> (4) xx. (1877), pp. 220-229, pls. v. vi.; <b>42.</b> -E. Metchinkoft, “Studien ber die Entwickelung der Medusen und +E. Metchinkoft, “Studien über die Entwickelung der Medusen und Siphonophoren,” <i>Zeitschr. f. wiss. Zool.</i> xxiv. (1874), pp. 15-83, pls. i.-xii.; <b>43.</b> “Vergleichend-embryologische Studien” (<i>Geryoniden, Cunina</i>), <i>ibid.</i> xxxvi. (1882), pp. 433-458, pl. xxviii.; <b>44.</b> <i>Embryologische Studien an Medusen</i> (Vienna, 1886), 150 pp., 12 pls., 10 figs.; <b>45.</b> “Medusologische Mittheilungen,” <i>Arb. zool. Inst. Wien</i>, vi. -(1886), pp. 237-266, pls. xxii. xxiii.; <b>46.</b> L. Murbach, “Beitrge zur +(1886), pp. 237-266, pls. xxii. xxiii.; <b>46.</b> L. Murbach, “Beiträge zur Kenntnis der Anatomie und Entwickelung der Nesselorgane der Hydroiden,” <i>Arch. f. Naturgesch.</i> lx. i. (1894), pp. 217-254, pl. xii.; <b>47.</b> “Preliminary Note on the Life-History of <i>Gonionemus</i>,” <i>Journ. @@ -12156,27 +12117,27 @@ Morph.</i> xi. (1895), pp. 493-496; <b>48.</b> L. Murbach and C. Shearer, <i>Proc. Zool. Soc.</i> (1903), ii. pp. 164-191, pls. xvii.-xxii.; <b>49.</b> H. F. Perkins, “The Development of <i>Gonionema murbachii</i>,” <i>Proc. Acad. Nat. Sci. Philadelphia</i> (1902), pp. 750-790, pls. xxxi-xxxiv.; <b>50.</b> -F. Schaudinn, “ber Haleremita cumulans, n. g. n. sp., einen +F. Schaudinn, “Über Haleremita cumulans, n. g. n. sp., einen marinen Hydroidpolypen,” <i>SB. Ges. natforsch. Freunde Berlin</i> (1894), pp. 226-234, 8 figs.; <b>51.</b> F. E. Schulze, “On the Structure and Arrangement of the Soft Parts in <i>Euplectella aspergillum</i>” (<i>Amphibrachium</i>), <i>Tr. R. Soc. Edinburgh</i>, xxix. (1880), pp. 661-673, pl. -xvii.; <b>52.</b> O. Seeliger, “ber das Verhalten der Keimbltter bei -der Knospung der Clenteraten,” <i>Zeitschr. f. wiss. Zool.</i> lviii. (1894), +xvii.; <b>52.</b> O. Seeliger, “Über das Verhalten der Keimblätter bei +der Knospung der Cölenteraten,” <i>Zeitschr. f. wiss. Zool.</i> lviii. (1894), pp. 152-188, pls. vii.-ix.; <b>53.</b> W. B. Spencer, “A new Family of Hydroidea (<i>Clathrozoon</i>), together with a description of the Structure of a new Species of <i>Plumularia</i>,” <i>Trans. Roy. Soc. Victoria</i> (1890), pp. 121-140, 7 pls.; <b>54.</b> M. Ussow, “A new Form of Fresh-water Coelenterate” (<i>Polypodium</i>), <i>Ann. Mag. Nat. Hist.</i> (5) xviii. (1886), -pp. 110-124, pl. iv.; <b>55.</b> E. Vanhffen, “Versuch einer natrlichen +pp. 110-124, pl. iv.; <b>55.</b> E. Vanhöffen, “Versuch einer natürlichen Gruppierung der Anthomedusen,” <i>Zool. Anzeiger</i>, xiv. (1891), pp. -439-446; <b>56.</b> C. Viguier, “tudes sur les animaux infrieurs de la +439-446; <b>56.</b> C. Viguier, “Études sur les animaux inférieurs de la baie d’Alger” (<i>Tetraplatia</i>), <i>Arch. Zool. Exp. Gen.</i> viii. (1890), pp. 101-142, pls. vii.-ix.; <b>57.</b> J. Wagner, “Recherches sur l’organisation -de Monobrachium parasiticum Mrjk,” <i>Arch. biol.</i> x. (1890), +de Monobrachium parasiticum Méréjk,” <i>Arch. biol.</i> x. (1890), pp. 273-309, pls. viii. ix.; <b>58.</b> A. Weismann, <i>Die Entstehung der Sexualzellen bei den Hydromedusen</i> (Jena, 1883); <b>59.</b> R. Woltereck, -“Beitrge zur Ontogenie und Ableitung des Siphonophorenstocks,” +“Beiträge zur Ontogenie und Ableitung des Siphonophorenstocks,” <i>Zeitschr. f. wiss. Zool.</i> lxxxii. (1905), pp. 611-637, 21 text-figs.; <b>60.</b> J. Wulfert, “Die Embryonalentwickelung von Gonothyraea loveni Allm.,” <i>Zeitschr. f. wiss. Zool.</i> lxxi. (1902), pp. 296-326, pls. @@ -12198,7 +12159,7 @@ word Hydrozoa, it refers to the bibliography at the end of the article <hr class="art" /> -<p><span class="bold">HYDROMETER<a name="ar3" id="ar3"></a></span> (Gr. <span class="grk" title="hydr">ὕδωρ</span>, water, and <span class="grk" title="metron">μέτρον</span>, a measure), an +<p><span class="bold">HYDROMETER<a name="ar3" id="ar3"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, and <span class="grk" title="metron">μέτρον</span>, a measure), an instrument for determining the density of bodies, generally of fluids, but in some cases of solids. When a body floats in a fluid under the action of gravity, the weight of the body is equal @@ -12402,7 +12363,7 @@ of the excise, was provided with thirty-two weights to adapt it to spirits of different specific gravities, and eleven smaller weights, or “weather weights” as they were called, which were attached to the instrument in order to correct for variations of temperature. -The weights were adjusted for successive intervals of 5 F., but +The weights were adjusted for successive intervals of 5° F., but for degrees intermediate between these no additional correction was applied. The correction for temperature thus afforded was not sufficiently accurate for excise purposes, and William Speer @@ -12463,7 +12424,7 @@ W. Nicholson in the <i>Manchester Memoirs</i>, ii. 374:—</p> <div class="condensed"> <p>“AA represents a small scale. It may be taken off at D. Diameter -1 in., weight 44 grains.</p> +1½ in., weight 44 grains.</p> <p>“B a stem of hardened steel wire. Diameter <span class="spp">1</span>⁄<span class="suu">100</span> in.</p> @@ -12473,14 +12434,14 @@ W. Nicholson in the <i>Manchester Memoirs</i>, ii. 374:—</p> <p>“FF a stirrup of wire screwed to the globe at C.</p> <p>“G a small scale, serving likewise as a counterpoise. Diameter -1 in. Weight with stirrup 1634 grains.</p> +1½ in. Weight with stirrup 1634 grains.</p> <p>“The other dimensions may be had from the drawing, which is one-sixth of the linear magnitude of the instrument itself.</p> <p>“In the construction it is assumed that the upper scale shall constantly carry 1000 grains when the lower scale is empty, and the -instrument sunk in distilled water at the temperature of 60 Fahr. +instrument sunk in distilled water at the temperature of 60° Fahr. to the middle of the wire or stem. The length of the stem is arbitrary, as is likewise the distance of the lower scale from the surface of the globe. But, the length of the stem being settled, the lower scale may @@ -12573,10 +12534,10 @@ the cup) could be attached, and thus completely immersed. Atkins’s instrument was constructed so as to weigh 700 grains, and when immersed to the mark on the stem -in distilled water at 60 F. it carried 300 +in distilled water at 60° F. it carried 300 grains in the upper dish. The hydrometer therefore displaced 1000 grains of distilled -water at 60 F. and hence the specific gravity +water at 60° F. and hence the specific gravity of any other liquid was at once indicated by adding 700 to the number of grains in the pan required to make the instrument sink to @@ -12615,7 +12576,7 @@ adjusted for liquids of widely differing specific gravities by drawing out a sliding tube, thus changing the volume of the hydrometer while its weight remains constant.</p> -<p>The hydrometer of A. Baum, which has been extensively used in +<p>The hydrometer of A. Baumé, which has been extensively used in France, consists of a common hydrometer graduated in the following manner. Certain fixed points were first determined upon the stem of the instrument. The first of these was found by immersing the @@ -12637,14 +12598,14 @@ The instrument is so arranged that it floats in pure water with most of the stem above the surface. A solution containing 10% of pure salt is used to indicate the zero of the scale, and the point at which the instrument floats when immersed in distilled water at -10 R. (54 F.) is numbered 10. Equal divisions are then marked +10° R. (54½° F.) is numbered 10. Equal divisions are then marked off upwards along the stem as far as the 50th degree.</p> -<p>The densities corresponding to the several degrees of Baum’s +<p>The densities corresponding to the several degrees of Baumé’s hydrometer are given by Nicholson (<i>Journal of Philosophy</i>, i. 89) as follows:—</p> -<p class="pt2 center"><i>Baum’s Hydrometer for Spirits. Temperature 10 R.</i></p> +<p class="pt2 center"><i>Baumé’s Hydrometer for Spirits. Temperature 10° R.</i></p> <table class="ws" summary="Contents"> <tr><td class="tcc allb">Degrees.</td> <td class="tcc allb">Density.</td> <td class="tcc allb">Degrees.</td> <td class="tcc allb">Density.</td> <td class="tcc allb">Degrees.</td> <td class="tcc allb">Density.</td></tr> @@ -12683,11 +12644,11 @@ follows:—</p> <tr><td class="caption1"><span class="sc">Fig. 5.</span>—Jones’s Hydrometer.</td></tr></table> -<p>Carrier’s hydrometer was very similar to that of Baum, Cartier +<p>Carrier’s hydrometer was very similar to that of Baumé, Cartier having been employed by the latter to construct his instruments for the French revenue. The point at which the instrument floated in -distilled water was marked 10 by Cartier, and 30 -on Carrier’s scale corresponded to 32 on Baum’s.</p> +distilled water was marked 10° by Cartier, and 30° +on Carrier’s scale corresponded to 32° on Baumé’s.</p> <p>Perhaps the main object for which hydrometers have been constructed is the determination of the @@ -12701,8 +12662,8 @@ of an octagonal prism, and upon each of the eight faces a scale is engraved, indicating the percentage strength of the spirit corresponding to the several divisions of the scale, the eight scales being -adapted respectively to the temperature 35, 40, -45, 50, 55, 60, 65 and 70 F. Four small pins, +adapted respectively to the temperature 35°, 40°, +45°, 50°, 55°, 60°, 65° and 70° F. Four small pins, which can be inserted into the counterpoise of the instrument, serve to adapt the instrument to the temperatures intermediate between those for which @@ -12735,13 +12696,13 @@ which is marked W at the bottom of the fourth scale. One side of the stem AD is shown in fig. 5, the other three in fig. 6. The thermometer is also provided with four scales corresponding to the scales above mentioned. Each scale has its zero in the middle corresponding -to 60 F. If the mercury in the thermometer +to 60° F. If the mercury in the thermometer stand above this zero the spirit must be reckoned weaker than the hydrometer indicates by the number on the thermometer scale level with the top of the mercury, while if the thermometer indicate a temperature -lower than the zero of the scale (60 F.) the +lower than the zero of the scale (60° F.) the spirit must be reckoned stronger by the scale reading. At the side of each of the four scales on the stem of the hydrometer is engraved @@ -12769,23 +12730,23 @@ Hydrometer.</td></tr></table> <p>This instrument was adopted by the United States in 1790, but was subsequently discarded by the Internal Revenue Service for another type. In this latter form the observations have to be made -at the standard temperature of 60 F., at which the graduation 100 +at the standard temperature of 60° F., at which the graduation 100 corresponds to proof spirit and 200 to absolute alcohol. The need of adjustable weights is avoided by employing a set of five instruments, -graduated respectively 0-100, 80-120, 100-140, 130-170, -160-200. The reading gives the volume of +graduated respectively 0°-100°, 80°-120°, 100°-140°, 130°-170°, +160°-200°. The reading gives the volume of proof spirit equivalent to the volume of liquor; -thus the readings 80 and 120 mean that 100 +thus the readings 80° and 120° mean that 100 volumes of the test liquors contain the same amount of absolute alcohol as 80 and 120 volumes of proof spirit respectively. Proof spirit is defined in the United States as a mixture of alcohol and water which contains -equal volumes of alcohol and water at 60 F., +equal volumes of alcohol and water at 60° F., the alcohol having a specific gravity of 0.7939 -at 60 as compared with water at its maximum +at 60° as compared with water at its maximum density. The specific gravity of proof spirit is -0.93353 at 60; and 100 volumes of the +0.93353 at 60°; and 100 volumes of the mixture is made from 50 volumes of absolute alcohol and 53.71 volumes of water.</p> @@ -12805,7 +12766,7 @@ stem.</p> is described in <i>Nicholson’s Journal</i>, 8vo, ii. 276. It is made of brass, and is provided with a spheroidal bulb the axis of which is -2 in. in length, the conjugate diameter being 1 +2 in. in length, the conjugate diameter being 1½ in. The whole length of the instrument is 8 in., the stem square of about <span class="spp">1</span>⁄<span class="suu">8</span>-in. side, and the weight about 400 grains. It is provided with @@ -12829,7 +12790,7 @@ practically to 272. When no weight is attached the instrument indicates densities from .806 to .843; with No. 1 it registers from .843 to .880, with No. 2 from .880 to .918, with No. 3 from .918 to .958, and with No. 4 from .958 to 1.000, the temperature being -55 F. It will thus be seen that the whole length of the stem corresponds +55° F. It will thus be seen that the whole length of the stem corresponds to a difference of density of about .04, and one division to about .00074, indicating a difference of little more than <span class="spp">1</span>⁄<span class="suu">3</span>% in the strength of any sample of spirits.</p> @@ -12837,7 +12798,7 @@ strength of any sample of spirits.</p> <p>The instrument is provided with a sliding rule, with scales corresponding to the several weights, which indicate the specific gravity corresponding to the several divisions of the hydrometer scale compared -with water at 55 F. The slider upon the rule serves to adjust +with water at 55° F. The slider upon the rule serves to adjust the scale for different temperatures, and then indicates the strength of the spirit in percentages over or under proof. The slider is also provided with scales, marked respectively Dicas and Clarke, which @@ -12868,14 +12829,14 @@ and 329-341.</p> <p>In Gay-Lussac’s alcoholometer the scale is divided into 100 parts corresponding to the presence of 1, 2, ... % by volume of alcohol at -15 C., the highest division of the scale corresponding to the purest +15° C., the highest division of the scale corresponding to the purest alcohol he could obtain (density .7947) and the lowest division corresponding to pure water. A table provides the necessary corrections for other temperatures.</p> <p>Tralles’s hydrometer differs from Gay-Lussac’s only in being -graduated at 4 C. instead of 15 C., and taking alcohol of density -.7939 at 15.5 C. for pure alcohol instead of .7947 as taken by Gay-Lussac +graduated at 4° C. instead of 15° C., and taking alcohol of density +.7939 at 15.5° C. for pure alcohol instead of .7947 as taken by Gay-Lussac (Keene’s <i>Handbook of Hydrometry</i>).</p> <p>In Beck’s hydrometer the zero of the scale corresponds to density @@ -12890,9 +12851,9 @@ Hydrometer.</td></tr></table> <p>In the centesimal hydrometer of Francœur the volume of the stem between successive divisions of the scale is always <span class="spp">1</span>⁄<span class="suu">100</span>th of the whole volume immersed when the instrument floats -in water at 4 C. In order to graduate the stem +in water at 4° C. In order to graduate the stem the instrument is first weighed, then immersed in -distilled water at 4 C., and the line of flotation +distilled water at 4° C., and the line of flotation marked zero. The first degree is then found by placing on the top of the stem a weight equal to <span class="spp">1</span>⁄<span class="suu">100</span>th of the weight of the instrument, which increases @@ -12906,14 +12867,14 @@ of which would be equal to that of the hydrometer up to the zero graduation, Francœur called the “modulus” of the hydrometer. He constructed his instruments of glass, using different instruments -for different portions of the scale (Francœur, <i>Trait -d’aromtrie</i>, Paris, 1842).</p> +for different portions of the scale (Francœur, <i>Traité +d’aréométrie</i>, Paris, 1842).</p> -<p>Dr Boris of Montpellier constructed a hydrometer +<p>Dr Boriés of Montpellier constructed a hydrometer which was based upon the results of his experiments on mixtures of alcohol and water. The interval between the points corresponding to -pure alcohol and to pure water Boris divided +pure alcohol and to pure water Boriés divided into 100 equal parts, though the stem was prolonged so as to contain only 10 of these divisions, the other 90 being provided for by the addition of 9 @@ -12924,13 +12885,13 @@ purposes for nearly a century is that associated with the name of Bartholomew Sikes, who was correspondent to the Board of Excise from 1774 to 1783, and for some time collector of excise for Hertfordshire.</p> -<p>Sikes’s hydrometer, on account of its similarity to that of Boris, +<p>Sikes’s hydrometer, on account of its similarity to that of Boriés, appears to have been borrowed from that instrument. It is made of gilded brass or silver, and consists of a spherical ball A (fig. 8), 1.5 in. in diameter, below which is a weight B connected with the ball by a short conical stem C. The stem D is rectangular in section -and about 3 in. in length. This is divided into ten equal parts, each -of which is subdivided into five. As in Boris’s instrument, a series +and about 3½ in. in length. This is divided into ten equal parts, each +of which is subdivided into five. As in Boriés’s instrument, a series of 9 weights, each of the form shown at E, serves to extend the scale <span class="pagenum"><a name="page165" id="page165"></a>165</span> to 100 principal divisions. In the centre of each weight is a hole @@ -12952,7 +12913,7 @@ that saccharic acid contained in some spirits attacked brass behind the gilding.</p> <p>The following table gives the specific gravities corresponding to the -principal graduations on Sikes’s hydrometer at 60 F. and 62 F., +principal graduations on Sikes’s hydrometer at 60° F. and 62° F., together with the corresponding strengths of spirits. The latter are based upon the tables of Charles Gilpin, clerk to the Royal Society, for which the reader is referred to the <i>Phil. Trans.</i> for 1794. Gilpin’s @@ -12966,7 +12927,7 @@ are at once converted into percentage of proof-spirit.</p> Sike’s Hydrometer.</i></p> <table class="ws f90" summary="Contents"> -<tr><td class="tccm allb" rowspan="2">Sike’s<br />Indications.</td> <td class="tccm allb" colspan="2">60 F.</td> <td class="tccm allb" colspan="2">62 F.</td></tr> +<tr><td class="tccm allb" rowspan="2">Sike’s<br />Indications.</td> <td class="tccm allb" colspan="2">60° F.</td> <td class="tccm allb" colspan="2">62° F.</td></tr> <tr><td class="tccm allb">Density.</td> <td class="tccm allb">Proof<br />Spirit<br />per<br />cent.</td> <td class="tccm allb">Density.</td> <td class="tccm allb">Proof<br />Spirit<br />per<br />cent.</td></tr> @@ -13105,12 +13066,12 @@ of the customs or excise, denote such spirits to be.” This act came into force on January 5, 1817, and was to have remained in force until August 1, 1818, but was repealed by 58 Geo. III. c. 28, which established Sikes’s hydrometer on a permanent footing. By 3 and 4 Will. IV. -c. 52, 123, it was further enacted that the same instruments and +c. 52, § 123, it was further enacted that the same instruments and methods should be employed in determining the duty upon imported spirits as should in virtue of any Act of Parliament be employed in the determination of the duty upon spirits distilled at home. It is the practice of the officers of the inland revenue to adjust -Sikes’s hydrometer at 62 F., that being the temperature at which the +Sikes’s hydrometer at 62° F., that being the temperature at which the imperial gallon is defined as containing 10 ℔ avoirdupois of distilled water. The specific gravity of any sample of spirits thus determined, when multiplied by ten, gives the weight in pounds per imperial @@ -13140,7 +13101,7 @@ as mentioned above.</p> the determination of the quality of milk. It resembles Sikes’s hydrometer in other respects, but is provided with eight weights. It is also provided with a thermometer and slide rule, to reduce the -readings to the standard temperature of 55 F. Any determination +readings to the standard temperature of 55° F. Any determination of density can be taken only as affording prima facie evidence of the quality of milk, as the removal of cream and the addition of water are operations which tend to compensate each other in their influence on @@ -13158,7 +13119,7 @@ are employed for taking observations of the density of sea-water.</p> the strength of the brine in marine boilers in which sea-water is employed. Saunders’s salinometer consists of a hydrometer which floats in a chamber through which the water from the boiler is -allowed to flow in a gentle stream, at a temperature of 200 F. +allowed to flow in a gentle stream, at a temperature of 200° F. The peculiarity of the instrument consists in the stream of water, as it enters the hydrometer chamber, being made to impinge against a disk of metal, by which it is broken into drops, thus liberating the @@ -13211,7 +13172,7 @@ is little more than the vehicle, and not the only one. Thermotherapeutics (or thermotherapy) is a term less open to objection.</p> <p>Hydropathy, as a formal system, dates from about 1829, -when Vincenz Priessnitz (1801-1851), a farmer of Grfenberg +when Vincenz Priessnitz (1801-1851), a farmer of Gräfenberg in Silesia, Austria, began his public career in the paternal homestead, extended so as to accommodate the increasing numbers attracted by the fame of his cures. Two English @@ -13234,18 +13195,18 @@ in 1797, and soon after translated into German by Michaelis placed the subject on a scientific basis. Hahn’s writings had meanwhile created much enthusiasm among his countrymen, societies having been everywhere formed to promote the medicinal -and dietetic use of water; and in 1804 Professor rtel of Ansbach +and dietetic use of water; and in 1804 Professor Örtel of Ansbach republished them and quickened the popular movement by unqualified commendation of water drinking as a remedy for all diseases. In him the rising Priessnitz found a zealous advocate, and doubtless an instructor also.</p> -<p>At Grfenberg, to which the fame of Priessnitz drew people of +<p>At Gräfenberg, to which the fame of Priessnitz drew people of every rank and many countries, medical men were conspicuous by their numbers, some being attracted by curiosity, others by the desire of knowledge, but the majority by the hope of cure for ailments which had as yet proved incurable. Many records -of experiences at Grfenberg were published, all more or less +of experiences at Gräfenberg were published, all more or less favourable to the claims of Priessnitz, and some enthusiastic in their estimate of his genius and penetration; Captain Claridge introduced hydropathy into England in 1840, his writings and @@ -13272,10 +13233,10 @@ who, impressed in his own person with the severities as well as the benefits of “the cold water cure,” practised among his workpeople a milder form of hydropathy, and began about 1852 a new era in its history, founding at Matlock a counterpart of the -establishment at Grfenberg.</p> +establishment at Gräfenberg.</p> -<p>Ernst Brand (1826-1897) of Berlin, Rljen and Theodor von -Jrgensen of Kiel, and Karl Liebermeister (1833-1901) of +<p>Ernst Brand (1826-1897) of Berlin, Räljen and Theodor von +Jürgensen of Kiel, and Karl Liebermeister (1833-1901) of Basel, between 1860 and 1870, employed the cooling bath in abdominal typhus with striking results, and led to its introduction to England by Dr Wilson Fox. In the Franco-German @@ -13314,7 +13275,7 @@ detail.</p> <p>(<i>b</i>) Hot air baths, the chief of which is the Turkish (properly, the Roman) bath, consisting of two or more chambers ranging in -temperature from 120 to 212 or higher, but mainly used at 150 for +temperature from 120° to 212° or higher, but mainly used at 150° for curative purposes. Exposure is from twenty minutes up to two hours according to the effect sought, and is followed by a general bath, and occasionally by soaping and shampooing. It is stimulating, derivative, @@ -13364,7 +13325,7 @@ electricity, &c., are adjuncts largely employed.</p> <p><span class="sc">Bibliography.</span>—Among the numerous earlier works on hydropathy, the following are worth mention: Balbirnie, <i>Water Cure in Consumption</i> (1847), <i>Hydropathic Aphorisms</i> (1856) and <i>A Plea for -the Turkish Bath</i> (1862); Beni-Barde, <i>Trait d’hydrothrapie</i> (1874); +the Turkish Bath</i> (1862); Beni-Barde, <i>Traité d’hydrothérapie</i> (1874); Claridge, <i>Cold Water Cure, or Hydropathy</i> (1841), <i>Facts and Evidence in Support of Hydropathy</i> (1843) and <i>Cold Water, Tepid Water and Friction Cure</i> (1849); Dunlop, <i>Philosophy of the Bath</i> (1873); Floyer, @@ -13759,7 +13720,7 @@ made known upon the subject. The malady was regarded with universal horror and dread, and the unfortunate sufferers were generally abandoned by all around them and left to their terrible fate. In later times the investigations of Boerhaave, Gerard -van Swieten (1700-1772), John Hunter, Franois Magendie +van Swieten (1700-1772), John Hunter, François Magendie (1783-1855), Gilbert Breschet (1784-1845), Virchow, Albert Reder, as also of William Youatt (1776-1847), George Fleming, Meynell, Karl Hertwig (1798-1881), and others, have furnished @@ -14122,7 +14083,7 @@ Medicine</i>.</p> <hr class="art" /> -<p><span class="bold">HYDROSPHERE<a name="ar6" id="ar6"></a></span> (Gr. <span class="grk" title="hydr">ὕδωρ</span>, water, and <span class="grk" title="sphaira">σφαῖρα</span>, sphere), in +<p><span class="bold">HYDROSPHERE<a name="ar6" id="ar6"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, and <span class="grk" title="sphaira">σφαῖρα</span>, sphere), in physical geography, a name given to the whole mass of the water of the oceans, which fills the depressions in the earth’s crust, and covers nearly three-quarters of its surface. The name is @@ -14136,7 +14097,7 @@ covering all the products of human intelligence.</p> <hr class="art" /> -<p><span class="bold">HYDROSTATICS<a name="ar7" id="ar7"></a></span> (Gr. <span class="grk" title="hydr">ὕδωρ</span>, water, and the root <span class="grk" title="sta">στα</span>-, to cause +<p><span class="bold">HYDROSTATICS<a name="ar7" id="ar7"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, and the root <span class="grk" title="sta">στα</span>-, to cause to stand), the branch of hydromechanics which discusses the equilibrium of fluids (see <span class="sc"><a href="#artlinks">Hydromechanics</a></span>).</p> @@ -14173,13 +14134,13 @@ methyl alcohol and then adding sodium methylate. The precipitated sodium chloride is filtered, and the solution of hydroxylamine distilled in order to remove methyl alcohol, and finally fractionated under reduced pressure. The free base is a colourless, -odourless, crystalline solid, melting at about 30 C., and boiling -at 58 C. (under a pressure of 22 mm.). It deliquesces and +odourless, crystalline solid, melting at about 30° C., and boiling +at 58° C. (under a pressure of 22 mm.). It deliquesces and oxidizes on exposure, inflames in dry chlorine and is reduced to ammonia by zinc dust. Its aqueous solution is strongly alkaline, and with acids it forms well-defined stable salts. E. Ebler and E. Schott (<i>J. pr. Chem.</i>, 1908, 78, p. 289) regard it as acting with -the formula NH<span class="su">2</span>OH towards bases, and as NH<span class="su">3</span>:O towards acids, +the formula NH<span class="su">2</span>·OH towards bases, and as NH<span class="su">3</span>:O towards acids, the salts in the latter case being of the oxonium type. It is a strong reducing agent, giving a precipitate of cuprous oxide from alkaline copper solutions at ordinary temperature, converting @@ -14193,7 +14154,7 @@ resulted in the formation of trimethyloxamine, N(CH<span class="su">3</span>)<sp <div class="condensed"> <p>Many substituted hydroxylamines are known, substitution taking place either in the α or β position <img style="width:74px; height:28px; vertical-align: middle;" src="images/img171.jpg" alt="" />. β-phenylhydroxyl-amine, -C<span class="su">6</span>H<span class="su">5</span>NHOH, is obtained in the reduction of nitrobenzene +C<span class="su">6</span>H<span class="su">5</span>NH·OH·, is obtained in the reduction of nitrobenzene in neutral solution (<i>e.g.</i> by the action of the aluminium-mercury couple and water), but better, according to C. Goldschmidt (<i>Ber.</i>, 1896, 29, p. 2307) by dissolving nitrobenzene in ten times its weight @@ -14202,7 +14163,7 @@ with excess of zinc dust and anhydrous calcium chloride for three hours on a water bath. It also appears as an intermediate product in the electrolytic reduction of nitrobenzene in sulphuric acid solution. By gentle oxidation it yields nitrosobenzene. Derivatives -of the type R<span class="su">2</span>NOH result in the action of the Grignard reagent on +of the type R<span class="su">2</span>N·OH result in the action of the Grignard reagent on amyl nitrite. Dihydroxy-ammonia or nitroxyl, NH(OH)<span class="su">2</span>, a very unstable and highly reactive substance, has been especially studied by A. Angeli (see A. W. Stewart, <i>Recent Advances in Physical and @@ -14493,8 +14454,8 @@ systematic accounts will be found under these headings.</p> <p><span class="sc">General Works on Hydrozoa.</span>—C. Chun, “Coelenterata (Hohlthiere),” <i>Bronn’s Klassen und Ordnungen des Thier-Reichs</i> -ii. 2 (1889 et seq.); Y. Delage, and E. Hrouard, <i>Trait de zoologie -concrte</i>, ii. part 2, <i>Les Coelentrs</i> (1901); G. H. Fowler, “The +ii. 2 (1889 et seq.); Y. Delage, and E. Hérouard, <i>Traité de zoologie +concrète</i>, ii. part 2, <i>Les Coelentérés</i> (1901); G. H. Fowler, “The Hydromedusae and Scyphomedusae” in E. R. Lankester’s <i>Treatise on Zoology</i>, ii. chapters iv. and v. (1900); S. J. Hickson, “Coelenterata and Ctenophora,” <i>Cambridge Natural History</i>, i. chapters @@ -14591,13 +14552,13 @@ Italy.</p> <hr class="art" /> -<p><span class="bold">HYRES,<a name="ar11" id="ar11"></a></span> a town in the department of the Var in S.E. France, +<p><span class="bold">HYÈRES,<a name="ar11" id="ar11"></a></span> a town in the department of the Var in S.E. France, 11 m. by rail E. of Toulon. In 1906 the population of the commune was 17,790, of the town 10,464; the population of the former was more than doubled in the last decade of the 19th century. -Hyres is celebrated (as is also its fashionable suburb, Costebelle, +Hyères is celebrated (as is also its fashionable suburb, Costebelle, nearer the seashore) as a winter health resort. The town proper -is situated about 2 m. from the seashore, and on the south-western +is situated about 2½ m. from the seashore, and on the south-western slope of a steep hill (669 ft., belonging to the Maurettes chain, 961 ft.), which is one of the westernmost spurs of the thickly wooded Montagnes des Maures. It is sheltered from the @@ -14617,7 +14578,7 @@ are: the house (Rue Rabaton, 7) where J. B. Massillon (1663-1742), the famous pulpit orator, was born; the parish church of St Louis, built originally in the 13th century by the Cordelier or Franciscan friars, but completely restored in the earlier part -of the 19th century; and the site of the old chteau, on the +of the 19th century; and the site of the old château, on the summit of the hill, now occupied by a villa. The plain between the new town and the sea is occupied by large nurseries, an excellent <i>jardin d’acclimatation</i>, and many market gardens, which @@ -14625,24 +14586,24 @@ supply Paris and London with early fruits and vegetables, especially artichokes, as well as with roses in winter. There are extensive salt beds (<i>salines</i>) both on the peninsula of Giens, S. of the town, and also E. of the town. To the east of the Giens -peninsula is the fine natural harbour of Hyres, as well as three +peninsula is the fine natural harbour of Hyères, as well as three thinly populated islands (the Stoechades of the ancients), Porquerolles, Port Cros and Le Levant, which are grouped -together under the common name of les d’Hyres.</p> +together under the common name of Îles d’Hyères.</p> -<p>The town of Hyres seems to have been founded in the 10th +<p>The town of Hyères seems to have been founded in the 10th century, as a place of defence against pirates, and takes its name -from the aires (<i>hierbo</i> in the Provenal dialect), or threshing-floors +from the aires (<i>hierbo</i> in the Provençal dialect), or threshing-floors for corn, which then occupied its site. It passed from the possession of the viscounts of Marseilles to Charles of Anjou, count of Provence, and brother of St Louis (the latter landed -here in 1254, on his return from Egypt). The chteau was +here in 1254, on his return from Egypt). The château was <span class="pagenum"><a name="page175" id="page175"></a>175</span> dismantled by Henri IV., but thanks to its walls, the town resisted in 1707 an attack made by the duke of Savoy.</p> <div class="condensed"> -<p>See Ch. Lenthric, <i>La Provence Maritime ancienne et moderne</i> +<p>See Ch. Lenthéric, <i>La Provence Maritime ancienne et moderne</i> (chap. 5) (Paris, 1880).</p> </div> <div class="author">(W. A. B. C.)</div> @@ -14690,14 +14651,14 @@ giving food or drink to a serpent out of a dish.</p> <div class="condensed"> <p>See the article by H. Lechat in Daremberg and Saglio’s <i>Dictionnaire -des antiquits</i>, with full references to authorities; and E. -Thrmer in Roscher’s <i>Lexikon der Mythologie</i>, with a special section +des antiquités</i>, with full references to authorities; and E. +Thrämer in Roscher’s <i>Lexikon der Mythologie</i>, with a special section on the modern theories of Hygieia.</p> </div> <hr class="art" /> -<p><span class="bold">HYGIENE<a name="ar13" id="ar13"></a></span> (Fr. <i>hygine</i>, from Gr. <span class="grk" title="hygiainein">ὑγιαίνειν</span>, to be healthy), +<p><span class="bold">HYGIENE<a name="ar13" id="ar13"></a></span> (Fr. <i>hygiène</i>, from Gr. <span class="grk" title="hygiainein">ὑγιαίνειν</span>, to be healthy), the science of preserving health, its practical aim being to render “growth more perfect, decay less rapid, life more vigorous, death more remote.” The subject is thus a very wide one, @@ -14849,7 +14810,7 @@ The lists vary greatly in different versions, but the above seems the most reasonable selection of readings to be made. For “Hellenic” see below. The supposed connexion with the Israelites has made the problem of the Hyksos attractive, but -light is coming upon it very slowly. In 1847 E. de Roug +light is coming upon it very slowly. In 1847 E. de Rougé proved from a fragment of a story in the papyri of the British Museum, that Apopi was one of the latest of the Hyksos kings, corresponding to Aphobis; he was king of the “pest” and @@ -14870,7 +14831,7 @@ of Apopi engraved lightly on the shoulder; this was evidently a usurper’s mark, but from the whole circumstances it was concluded that these, and others of the same type of features found elsewhere, must have belonged to the Hyksos. This -view held the field until 1893, when Golnischeff produced an +view held the field until 1893, when Golénischeff produced an inferior example bearing its original name, which showed that in this case it represented Amenemhe III. In consequence it is now generally believed that they all belong to the twelfth @@ -14926,8 +14887,8 @@ armies of Tethmosis to the Euphrates.</p> <div class="condensed"> <p>Besides the histories of Egypt, see J. H. Breasted, <i>Ancient Records of Egypt</i>; Historical Documents ii. 4, 125; G. Maspero, -<i>Contes populaires</i>, 3me d. p. 236; W. M. F. Petrie, <i>Hyksos -and Israelite Cities</i>, p. 67; Golnischeff in <i>Recueil de travaux</i>, xv. +<i>Contes populaires</i>, 3me éd. p. 236; W. M. F. Petrie, <i>Hyksos +and Israelite Cities</i>, p. 67; Golénischeff in <i>Recueil de travaux</i>, xv. p. 131.</p> </div> <div class="author">(F. Ll. G.)</div> @@ -14958,13 +14919,13 @@ of a boy was thrown into the water, signifying the dying vegetation-spirit of the year.</p> <div class="condensed"> -<p>See G. Trk in <i>Breslauer Philologische Abhandlungen</i>, vii. (1895); +<p>See G. Türk in <i>Breslauer Philologische Abhandlungen</i>, vii. (1895); W. Mannhardt, <i>Mythologische Forschungen</i> (1884).</p> </div> <hr class="art" /> -<p><span class="bold">HYLOZOISM<a name="ar20" id="ar20"></a></span> (Gr. <span class="grk" title="hyl">ὕλη</span>, matter, <span class="grk" title="z">ζωή</span>, life), in philosophy, a +<p><span class="bold">HYLOZOISM<a name="ar20" id="ar20"></a></span> (Gr. <span class="grk" title="hylê">ὕλη</span>, matter, <span class="grk" title="zôê">ζωή</span>, life), in philosophy, a term applied to any system which explains all life, whether physical or mental, as ultimately derived from matter (“cosmic matter,” <i>Weldstoff</i>). Such a view of existence has been common @@ -15009,12 +14970,12 @@ Hymenaeus being invoked at the end of each portion.</p> <div class="condensed"> <p>See R. Schmidt, <i>De Hymenaeo el Talasio</i> (1886), and J. A. Hild in -Daremberg and Saglis’s <i>Dictionnaire des antiquits</i>.</p> +Daremberg and Saglis’s <i>Dictionnaire des antiquités</i>.</p> </div> <hr class="art" /> -<p><span class="bold">HYMENOPTERA<a name="ar22" id="ar22"></a></span> (Gr. <span class="grk" title="hymn">ὑμήν</span>, a membrane, and <span class="grk" title="pteron">πτερόν</span>, a wing), +<p><span class="bold">HYMENOPTERA<a name="ar22" id="ar22"></a></span> (Gr. <span class="grk" title="hymên">ὑμήν</span>, a membrane, and <span class="grk" title="pteron">πτερόν</span>, a wing), a term used in zoological classification for one of the most important orders of the class <i>Hexapoda</i> (<i>q.v.</i>). The order was founded by Linnaeus (<i>Systema Naturae</i>, 1735), and is still recognized by @@ -15056,7 +15017,7 @@ Soc. Zool. France</i> (1898).</td></tr> <tr><td class="tcl f90"><span class="sc">Fig. 2.</span>—Jaws of Hive-bee (<i>Apis mellifica</i>). Magnified -about 6 times. +about 6½ times. <i>a</i>, mandible; <i>b</i>, <i>c</i>, palp and lacinia of first maxilla; @@ -15651,18 +15612,18 @@ elaboration of a wonderful insect-society. (See <span class="sc"><a href="#artli Hymenoptera will be found under the articles <span class="sc"><a href="#artlinks">Ant</a></span>, <span class="sc"><a href="#artlinks">Bee</a></span>, <span class="sc"><a href="#artlinks">Ichneumon-Fly</a></span>, <span class="sc"><a href="#artlinks">Wasp</a></span>, &c., referred to above. Among earlier students on structure may be mentioned P. A. Latreille, <i>Familles naturelles du -rgne animal</i> (Paris, 1825), who recognized the nature of the +règne animal</i> (Paris, 1825), who recognized the nature of the “median segment.” C. Gerstaecker (<i>Arch. f. Naturg.</i> xx., 1867) and F. Brauer (<i>Sitzb. K. Akad. Wiss. Wien.</i> lxxxv., 1883) should also be consulted on this subject. For internal anatomy, specially -the digestive organs, see L. Dufour, <i>Mm. savants trangers</i>, vii. +the digestive organs, see L. Dufour, <i>Mém. savants étrangers</i>, vii. (1841), and <i>Ann. Sci. Nat. Zool.</i> (4), i. 1854. For nervous system H. Viallanes, <i>Ann. Sci. Nat. Zool.</i> (7), ii. iv. 1886-1887, and F. C. Kenyon, <i>Journ. Comp. Neurol.</i> vi., 1896. For poison and other glands, see L. Bordas, <i>Ann. Sci. Nat. Zool.</i> (7) xix., 1895. For the sting and ovipositor H. Dewitz, <i>Zeits. wiss. Zool.</i> xxv., 1874, xxviii., 1877, and F. Zander, <i>ib.</i> lxvi., 1899. For male genital -armature S. A. Peytoureau, <i>Morphologie de l’armure gnitale des</i> +armature S. A. Peytoureau, <i>Morphologie de l’armure génitale des</i> <span class="pagenum"><a name="page181" id="page181"></a>181</span> <i>insectes</i> (Bordeaux, 1895), and E. Zander, Zeits. wiss. Zool. lxvii., 1900. The systematic student of Hymenoptera is greatly helped @@ -15672,7 +15633,7 @@ Leipzig, 1893-1902). For general classifications see F. W. Konow, xxiii., 1901; the latter paper deals also especially with the Ichneumonoidea of the globe. For habits and life histories of Hymenoptera see J. Lubbock (Lord Avebury), <i>Ants, Bees and Wasps</i> (9th ed., -London, 1889); C. Janet, <i>tudes sur les fourmis, les gupes et les +London, 1889); C. Janet, <i>Études sur les fourmis, les guêpes et les abeilles</i> (Paris, &c., 1893 and onwards); and G. W. and E. G. Peckham, <i>Instincts and Habits of Solitary Wasps</i> (Madison, Wis. U.S.A., 1898). Monographs of most of the families of British @@ -15707,7 +15668,7 @@ from its aromatic herbs; their fame still persists. The spring mentioned by Ovid (<i>Ars Amat.</i> iii. 687) is probably to be recognized near the monastery of Syriani or Kaesariani on the western slope. This may be identical with that known as <span class="grk" title="Kyllon -Pra">Κύλλον Πήρα</span>, said to be a remedy for barrenness in women. The marble +Pêra">Κύλλον Πήρα</span>, said to be a remedy for barrenness in women. The marble of Hymettus, which often has a bluish tinge, was used extensively for building in ancient Athens, and also, in early times, for sculpture; but the white marble of Pentelicus was preferred @@ -15798,20 +15759,20 @@ David the son of Jesse”), in Ps. lxv. 1, and also in the Greek titles of the 6th, 54th, 55th, 67th and 76th (this numbering of the psalms being that of the English version, not of the LXX.). The 44th chapter of Ecclesiasticus, “Let us now praise famous -men,” &c., is entitled in the Greek <span class="grk" title="patern hymnos">πατέρων ὕμνος</span>, “The Fathers’ +men,” &c., is entitled in the Greek <span class="grk" title="paterôn hymnos">πατέρων ὕμνος</span>, “The Fathers’ Hymn.” Bede speaks of the whole book of Psalms as called “liber hymnorum,” by the universal consent of Hebrews, Greeks and Latins.</p> <p>In the New Testament we find our Lord and His apostles -singing a hymn (<span class="grk" title="hymnsantes exlthon">ὑμνήσαντες ἐξῆλθον</span>), after the institution of +singing a hymn (<span class="grk" title="hymnêsantes exêlthon">ὑμνήσαντες ἐξῆλθον</span>), after the institution of the Lord’s Supper; St Paul and Silas doing the same (<span class="grk" title="hymnoun ton theon">ὕμνουν τὸν θεόν</span>) in their prison at Philippi; St James recommending -psalm-singing (<span class="grk" title="psallet">ψαλλέτω</span>), and St Paul “psalms and hymns -and spiritual songs” (<span class="grk" title="psalmois kai hymnois kai dais pneumatikais">ψαλμοῖς καὶ ὕμνοις καὶ ῲδαῖς πνευματικαῖς</span>) +psalm-singing (<span class="grk" title="psalletô">ψαλλέτω</span>), and St Paul “psalms and hymns +and spiritual songs” (<span class="grk" title="psalmois kai hymnois kai ôdais pneumatikais">ψαλμοῖς καὶ ὕμνοις καὶ ῲδαῖς πνευματικαῖς</span>) St Paul also, in the 14th chapter of the first epistle to the Corinthians, -speaks of singing (<span class="grk" title="psal">ψαλῶ</span>) and of every man’s psalm -(<span class="grk" title="hekastos hymn psalmon echei">ἕκαστος ὑμῶν ψαλμὸν ἕχει</span>). In a context which plainly has reference +speaks of singing (<span class="grk" title="psalô">ψαλῶ</span>) and of every man’s psalm +(<span class="grk" title="hekastos hymôn psalmon echei">ἕκαστος ὑμῶν ψαλμὸν ἕχει</span>). In a context which plainly has reference to the assemblies of the Corinthian Christians for common worship. All the words thus used were applied by the LXX. to the Davidical psalms; it is therefore possible that these only @@ -15873,7 +15834,7 @@ into a choir”), to “sing praise to the Father in Christ Jesus.” A statement of Theodoret has sometimes been supposed to refer the origin of antiphonal singing to a much later date; but this seems to relate only to the singing of Old Testament -Psalms (<span class="grk" title="tn Dauidikn meldian">τὴν Δαυιδικὴν μελῳδίαν</span>), the alternate chanting of +Psalms (<span class="grk" title="tên Dauidikên melôdian">τὴν Δαυιδικὴν μελῳδίαν</span>), the alternate chanting of which, by a choir divided into two parts, was (according to that statement) first introduced into the church of Antioch by two monks famous in the history of their time, Flavianus and Diodorus, @@ -15898,8 +15859,8 @@ the <i>Apostolical Constitutions</i>, and which are also mentioned in the “Tract on Virginity” printed with the works of St Athanasius, and in St Basil’s treatise upon the Holy Spirit, to belong to the same family. Clement’s hymn, in a short anapaestic -metre, beginning <span class="grk" title="stomion pln adan">στόμιον πώλων ἀδαῶν</span> (or, according to some -editions, <span class="grk" title="basileu hagin, loge pandamatr">βασιλεῦ ἁγίων, λόγε πανδαμάτωρ</span>—translated by the +metre, beginning <span class="grk" title="stomion pôlôn adaôn">στόμιον πώλων ἀδαῶν</span> (or, according to some +editions, <span class="grk" title="basileu hagiôn, loge pandamatôr">βασιλεῦ ἁγίων, λόγε πανδαμάτωρ</span>—translated by the Rev. A. Chatfield, “O Thou, the King of Saints, all-conquering Word”), is rapid, spirited and well-adapted for singing. The Greek “Morning Hymn” (which, as divided into verses by @@ -15912,7 +15873,7 @@ relinquished the use of liturgies. The Latin form of this hymn translation) is said, by Bede and other ancient writers, to have been brought into use at Rome by Pope Telesphorus, as early as the time of the emperor Hadrian. A third, the Vesper or “Lamp-lighting” -hymn (“<span class="grk" title="phs hilaron hagias doxs">φῶς ἱλαρὸν ἁγίας δόξης</span>”—translated by +hymn (“<span class="grk" title="phôs hilaron hagias doxês">φῶς ἱλαρὸν ἁγίας δόξης</span>”—translated by Canon Bright “Light of Gladness, Beam Divine”), holds its <span class="sidenote">3rd century.</span> place to this day in the services of the Greek rite. @@ -15974,10 +15935,10 @@ too much depreciated by the admirers of the later Greek “Melodists.” They have found an able English translator in the Rev. Allen Chatfield (<i>Songs and Hymns of Earliest Greek Christian Poets</i>, London, 1876). Among the most striking of -their works are <span class="grk" title="mneo Christe">μνώεο Χριστέ</span> (“Lord Jesus, think of me”), by -Synesius; <span class="grk" title="se ton aphthiton monarchn">σὲ τὸν ἄφθιτον μονάρχην</span> (“O Thou, the One Supreme”) +their works are <span class="grk" title="mnôeo Christe">μνώεο Χριστέ</span> (“Lord Jesus, think of me”), by +Synesius; <span class="grk" title="se ton aphthiton monarchên">σὲ τὸν ἄφθιτον μονάρχην</span> (“O Thou, the One Supreme”) and <span class="grk" title="ti soi theleis genesthai">τί σοι θέλεις γενέσθαι</span> (“O soul of mine, repining”), by Gregory; -also <span class="grk" title="anthen parthenoi">ἄνωθεν παρθένοι</span> (“The Bridegroom cometh”), by Methodius. +also <span class="grk" title="anôthen parthenoi">ἄνωθεν παρθένοι</span> (“The Bridegroom cometh”), by Methodius. There continued to be Greek metrical hymn-writers, in a similar style, till a much later date. Sophronius, patriarch of Jerusalem <span class="pagenum"><a name="page183" id="page183"></a>183</span> @@ -16530,7 +16491,7 @@ which its chief writer belonged) has been called “Victorine.” Most Missals appear to have contained some of both kinds. In the majority of those from which Neale’s specimens are taken, the metrical kind largely prevailed; but in some (<i>e.g.</i> those of Sarum -and Lige) the greater number were Notkerian.</p> +and Liége) the greater number were Notkerian.</p> </div> <p>Of the sequence on the Holy Ghost, sent by Notker (according @@ -16732,7 +16693,7 @@ justifiable upon the principle of correcting supposed corruptions of the original text. Of these, the transposition, “Urbs Jerusalem beata,” instead of “Urbs beata Hierusalem,” may be taken as a typical example. The next revision was in 1670-1680, -under Cardinal Prfixe, preceptor of Louis XIV., and Francis +under Cardinal Péréfixe, preceptor of Louis XIV., and Francis Harlay, successively archbishops of Paris, who employed for this purpose Claude Santeul, of the monastery of St Magloire, and, through him, obtained the assistance of other French scholars, including @@ -16789,7 +16750,7 @@ Rev. Isaac Williams and the Rev. John Chandler appear (from the title-page of the latter, and the prefaces of both) to have supposed their hymns to be “ancient” and “primitive.” Among the other authors associated with them, perhaps the first place is due to the -Abb Besnault, of Sens, who contributed to the book of 1735 the +Abbé Besnault, of Sens, who contributed to the book of 1735 the “Urbs beata vera pacis Visio Jerusalem,” in the opinion of Neale “much superior” to the “Caelestis urbs Jerusalem” of the Roman Breviary. This stood side by side with the “Urbs Jerusalem beata” @@ -16859,7 +16820,7 @@ in 1525. Some of their works are still popular in Germany. Weiss’s “Funeral Hymn,” “Nun lasst uns den Leib begraben” (“Now lay we calmly in the grave”); Eber’s “Herr Jesu Christ, wahr Mensch und Gott” (“Lord Jesus Christ, true Man -and God”), and “Wenn wir in hchsten Nthen sein” (“When +and God”), and “Wenn wir in höchsten Nöthen sein” (“When in the hour of utmost need”); Walther’s “New Heavens and new Earth” (“Now fain my joyous heart would sing”); Decius’s “To God on high be thanks and praise”; and Speratus’s @@ -16926,7 +16887,7 @@ known in other branches of literature. All these wrote some good hymns. They were succeeded by men of another sort, to whom F. A. Cunz gives the name of “master-singers,” as having raised both the poetical -and the musical standard of German hymnody:—Bartholomus +and the musical standard of German hymnody:—Bartholomäus Ringwaldt, Ludwig Helmbold, Johannes Pappus, Martin Schalling, Rutilius and Sigismund Weingartner. The principal topics of their hymns (as if with some foretaste of the calamities @@ -16941,7 +16902,7 @@ with fine chorales, two years afterwards. One of these (the “Sleepers wake! a voice is calling,” of Mendelssohn’s oratorio, <i>St Paul</i>) belongs to the family of Advent or New Jerusalem hymns. The other, a “Song of the believing soul concerning the -Heavenly Bridegroom” (“Wie schn leucht’t uns der Morgenstern”—“O +Heavenly Bridegroom” (“Wie schön leucht’t uns der Morgenstern”—“O morning Star, how fair and bright”), became the favourite marriage hymn of Germany.</p> @@ -16960,16 +16921,16 @@ original genius, exercised much power as a critic. Some of the best of these works were by men who wrote little. In the famous battle-song of Gustavus Adolphus, published (1631) after the victory of Breitenfeld, for the use of his army, “Verzage nicht -du Huflein klein” (“Fear not, O little flock, the foe”), we have +du Häuflein klein” (“Fear not, O little flock, the foe”), we have almost certainly a composition of the hero-king himself, the versification corrected by his chaplain Jakob Fabricius (1593-1654) and the music composed by Michael Altenburg, whose name has been given to the hymn. This, with Luther’s paraphrase of the 67th Psalm, was sung by Gustavus and his soldiers -before the battle of Ltzen in 1632. Two very fine hymns, +before the battle of Lützen in 1632. Two very fine hymns, one of prayer for deliverance and peace, the other of trust in God under calamities, were written about the same time by -Matthus Lwenstern, a saddler’s son, poet, musician and +Matthäus Löwenstern, a saddler’s son, poet, musician and statesman, who was ennobled after the peace by the emperor <span class="pagenum"><a name="page189" id="page189"></a>189</span> Ferdinand III. Martin Rinckhart, in 1636, wrote the “Chorus @@ -16982,7 +16943,7 @@ ye mighty gates”), and J. M. Meyfart, professor of theology at Erfurt, in 1642, a fine adaptation of the ancient “Urbs beata Hierusalem.” The hymn of trust in Providence by George Neumark, librarian to that duke of Weimar (“Wer nur den -lieben Gott lsst walten”—“Leave God to order all thy ways”), +lieben Gott lässt walten”—“Leave God to order all thy ways”), is scarcely, if at all, inferior to that of Paul Gerhardt on the same theme. Paul Flemming, a great traveller and lover of nature, who died in 1639, also wrote excellent compositions, coloured @@ -17020,7 +16981,7 @@ Heermann, and written, upon the whole, in a more manly spirit. <span class="sidenote">Dach.</span> Next to Heermann and Rist in fertility of production, and above them in poetical genius, was Simon Dach, -professor of poetry at Knigsberg, who died in 1659. Miss +professor of poetry at Königsberg, who died in 1659. Miss Winkworth ranks him high among German poets, “for the sweetness of form and depth of tender contemplative emotion to be found in his verses.”</p> @@ -17096,13 +17057,13 @@ less fertile writers of the same school. The “Auf hinauf zu deiner Freude” (“Up, yes, upward to thy gladness”) of Schade may recall to an English reader a hymn by Seagrave, and more than one by Lyte; the “Malabarian hymn” (as it was called by -Jacobi) of Johann Schtz, “All glory to the Sovereign Good,” +Jacobi) of Johann Schütz, “All glory to the Sovereign Good,” has been popular in England as well as Germany; and one of the most exquisite strains of pious resignation ever written is “Whate’er my God ordains is right,” by Samuel Rodigast.</p> -<p>Joachim Neander, a schoolmaster at Dsseldorf, and a friend -of Spener and Schtz (who died before the full development of +<p>Joachim Neander, a schoolmaster at Düsseldorf, and a friend +of Spener and Schütz (who died before the full development of the “Pietistic” school), was the first man of eminence in the “Reformed” or Calvinistic Church who imitated <span class="sidenote">Neander.</span> @@ -17145,13 +17106,13 @@ Schmolke. Few hymns, of the subjective kind, are better than his “I will not let Thee go, Thou Help in time of need,” “O Friend of souls, how well is me,” and “Now, the pearly gates unfold.” Hiller (1699-1769), was a pastor -in Wrttemberg who, falling into ill-health during the -latter part of his ministry, published a <i>Geistliche Liederhstlein</i> in a +in Württemberg who, falling into ill-health during the +latter part of his ministry, published a <i>Geistliche Liederhöstlein</i> in a didactic vein, with more taste than power, but (as Miss Winkworth says) in a tone of “deep, thoughtful, practical piety.” They were so well adapted to the wants of his people that to this day Hiller’s Casket is prized, next to their Bibles, by the peasantry of -Wrttemberg; and the numerous emigrants from that part of +Württemberg; and the numerous emigrants from that part of Germany to America and other foreign countries generally <span class="sidenote">Arnold.</span> take it with them wherever they go. Arnold, a @@ -17172,7 +17133,7 @@ were with the Moravians and with Zinzendorf, was, of all the more copious German hymn-writers after Luther, perhaps the most remarkable man. Pietist, mystic and missionary, he was also a great religious poet. His 111 hymns were published In 1731, in -a volume called <i>Geistlicher Blumengrtlein inniger</i> Seelen. +a volume called <i>Geistlicher Blumengärtlein inniger</i> Seelen. They are intensely individual, meditative and subjective. Wesley’s adaptations of two—“Lo! God is here; let us adore,” and “Thou hidden Love of God, whose source”—are well known. @@ -17232,15 +17193,15 @@ Lyre</i>) are artificial and much too elaborate.</p> <p>Of the “romantic” school, which came in with the French Revolution, the two leading writers are Friedrich Leopold von Hardenberg, called “Novalis,” and Friedrich de la Motte -Fouqu, the celebrated author of <i>Undine</i> and <i>Sintram</i>—both +Fouqué, the celebrated author of <i>Undine</i> and <i>Sintram</i>—both romance-writers, as well as poets. The genius of Novalis was early lost to the world; he died in 1801, not thirty years old. Some of his hymns are very beautiful; but even in such works as “Though all to Thee were faithless,” and “If only He is mine,” there is a feeling of insulation and of despondency as to good in the actual world, which was perhaps inseparable from his -<span class="sidenote">Fouqu.</span> -ecclesiastical idealism. Fouqu survived till 1843. +<span class="sidenote">Fouqué.</span> +ecclesiastical idealism. Fouqué survived till 1843. In his hymns there is the same deep flow of feeling, richness of imagery and charm of expression which distinguishes his prose works. The two missionary hymns—“Thou, solemn @@ -18377,27 +18338,27 @@ link the sympathies of the writer and the listener, and aim at expressing the feeling prompted by the hymn under treatment.</p> <p><span class="sc">Bibliography</span>: I. Ancient.—George Cassander, <i>Hymni ecclesiastici</i> -(Cologne, 1556); Georgius Fabricius, <i>Potarum veterum +(Cologne, 1556); Georgius Fabricius, <i>Poëtarum veterum ecclesiasticorum</i> (Frankfort, 1578); Cardinal J. M. Thomasius, <i>Hymnarium in Opera</i>, ii. 351 seq. (Rome, 1747); A. J. Rambach, -<i>Anthologie christlicher Gesnge</i> (Altona, 1817); H. A. Daniel, +<i>Anthologie christlicher Gesänge</i> (Altona, 1817); H. A. Daniel, <i>Thesaurus hymnologicus</i> (Leipzig, 5 vols., 1841-1856); J. M. Neale, <i>Hymni ecclesiae et sequentiae</i> (London, 1851-1852); and <i>Hymns of the Eastern Church</i> (1863). The dissertation prefixed to the second volume of the <i>Acta sanctorum</i> of the Bollandists; Cardinal J. -B. Pitra, <i>Hymnographie de l’glise grecque</i> (1867), <i>Analecta sacra</i> +B. Pitra, <i>Hymnographie de l’église grecque</i> (1867), <i>Analecta sacra</i> (1876); W. Christ and M. Paranikas, <i>Anthologia Graeca carminum Christianorum</i> (Leipzig, 1871); F. A. March, <i>Latin Hymns with English Notes</i> (New York, 1875); R. C. Trench, <i>Sacred Latin Poetry</i> (London, 4th ed., 1874); J. Pauly, <i>Hymni breviarii Romani</i> (Aix-la-Chapelle, -3 vols., 1868-1870); Pimont, <i>Les Hymnes du brviaire romain</i> +3 vols., 1868-1870); Pimont, <i>Les Hymnes du bréviaire romain</i> (vols. 1-3, 1874-1884, unfinished); A. W. F. Fischer, <i>Kirchenlieder-Lexicon</i> -(Gotha, 1878-1879); J. Kayser, <i>Beitrge zur Geschichte der -ltesten Kirchenhymnen</i> (1881); M. Manitius, <i>Geschichte der christlichen +(Gotha, 1878-1879); J. Kayser, <i>Beiträge zur Geschichte der +ältesten Kirchenhymnen</i> (1881); M. Manitius, <i>Geschichte der christlichen lateinischen Poesie</i> (Stuttgart, 1891); John Julian, <i>Dictionary of Hymnology</i> (1892, new ed. 1907). For criticisms of metre, see -also Huemer, <i>Untersuchungen ber die ltesten christlichen Rhythmen</i> -(1879); E. Bouvy, <i>Potes et mlodes</i> (Nmes, 1886); C. Krumbacher, +also Huemer, <i>Untersuchungen über die ältesten christlichen Rhythmen</i> +(1879); E. Bouvy, <i>Poètes et mélodes</i> (Nîmes, 1886); C. Krumbacher, <i>Geschichte der byzantinischen Literatur</i> (Munich, 1897, p. 700 seq.); J. M. Neale, Latin dissertation prefixed to Daniel’s <i>Thesaurus</i>, vol. 5; and D. J. Donahoe, <i>Early Christian Hymns</i> (London, 1909).</p> @@ -18405,16 +18366,16 @@ and D. J. Donahoe, <i>Early Christian Hymns</i> (London, 1909).</p> <p>II. Medieval.—Walafrid Strabo’s treatise, ch. 25, <i>De hymnis, &c.</i>; Radulph of Tongres, <i>De psaltario observando</i> (14th century); Clichtavaens, <i>Elucidatorium ecclesiasticum</i> (Paris, 1556); Faustinus -Arevalus, <i>Hymnodia Hispanica</i> (Rome, 1786); E. du Mril, <i>Posies -populaires latines antrieures au XIII<span class="sp">e</span> sicle</i> (Paris, 1843); J. Stevenson, +Arevalus, <i>Hymnodia Hispanica</i> (Rome, 1786); E. du Méril, <i>Poésies +populaires latines antérieures au XIII<span class="sp">e</span> siècle</i> (Paris, 1843); J. Stevenson, <i>Latin Hymns of the Anglo-Saxon Church</i> (Surtees Society, Durham, 1851); Norman, <i>Hymnarium Sarisburiense</i> (London, 1851); J. D. Chambers, <i>Psalter, &c.</i>, according to the Sarum use (1852); F. J. Mone, <i>Lateinische Hymnen des Mittelalters</i> (Freiburg, 3 vols., 1853-1855); -Ph. Wackernagel, <i>Das deutsche Kirchenlied von der ltesten +Ph. Wackernagel, <i>Das deutsche Kirchenlied von der ältesten Zeit bis zum Anfang des 17. Jahrhunderts</i>, vol. i. (Leipzig, 1864); E. -Dmmler, <i>Potae latini aevi Carolini</i> (1881-1890); the <i>Hymnologische -Beitrge: Quellen und Forschungen zur Geschichte der lateinischen +Dümmler, <i>Poëtae latini aevi Carolini</i> (1881-1890); the <i>Hymnologische +Beiträge: Quellen und Forschungen zur Geschichte der lateinischen Hymnendichtung</i>, edited by C. Blume and G. M. Dreves (Leipzig, 1897); G. C. F. Mohnike, <i>Hymnologische Forschungen</i>; Klemming, <i>Hymni et sequentiae in regno Sueciae</i> (Stockholm, 4 vols., @@ -18422,10 +18383,10 @@ Hymnendichtung</i>, edited by C. Blume and G. M. Dreves (Leipzig, Severin Meister, 1862, vol. ii. by W. Baumker, 1883); the “Hymnodia Hiberica,” <i>Spanische Hymnen des Mittelalters</i>, vol. xvi. (1894); the “Hymnodia Gotica,” <i>Mozarabische Hymnen des -altspanischen Ritus</i>, vol. xxvii. (1897); J. Dank, <i>Vetus hymnarium +altspanischen Ritus</i>, vol. xxvii. (1897); J. Dankó, <i>Vetus hymnarium ecclesiasticae Hungariae</i> (Budapest, 1893); J. H. Bernard and R. Atkinson, <i>The Irish Liber Hymnorum</i> (2 vols., London, 1898); -C. A. J. Chevalier, <i>Posie liturgique du moyen ge</i> (Paris, 1893).</p> +C. A. J. Chevalier, <i>Poésie liturgique du moyen âge</i> (Paris, 1893).</p> <p>III. Modern.—J. C. Jacobi, <i>Psalmodia Germanica</i> (1722-1725 and 1732, with supplement added by J. Haberkorn, 1765); F. A. @@ -18446,20 +18407,20 @@ Modern</i> (1867); Daniel Sedgwick, <i>Comprehensive Index of Names of Original Authors of Hymns</i> (2nd ed., 1863); R. E. Prothero, <i>The Psalms in Human Life</i> (1907); C. J. Brandt and L. Helweg, <i>Den danske Psalmedigtning</i> (Copenhagen, 1846-1847); J. N. Skaar, -<i>Norsk Salmehistorie</i> (Bergen, 1879-1880); H. Schck, <i>Svensk +<i>Norsk Salmehistorie</i> (Bergen, 1879-1880); H. Schück, <i>Svensk Literaturhistoria</i> (Stockholm, 1890); Rudolf Wolkan, <i>Geschichte der -deutschen Literatur in Bhmen</i>, 246-256, and <i>Das deutsche Kirchenlied -der bhm. Brder</i> (Prague, 1891); Zahn, <i>Die geistlichen Lieder der -Brder in Bhmen, Mhren u. Polen</i> (Nuremberg, 1875); and J. -Mller, “Bohemian Brethren’s Hymnody,” in J. Julian’s <i>Dictionary +deutschen Literatur in Böhmen</i>, 246-256, and <i>Das deutsche Kirchenlied +der böhm. Brüder</i> (Prague, 1891); Zahn, <i>Die geistlichen Lieder der +Brüder in Böhmen, Mähren u. Polen</i> (Nuremberg, 1875); and J. +Müller, “Bohemian Brethren’s Hymnody,” in J. Julian’s <i>Dictionary of Hymnology</i>.</p> <p>For account of hymn-tunes, &c., see W. Cowan and James Love, <i>Music of the Church Hymnody and the Psalter in Metre</i> (London, 1901); and Dickinson, <i>Music in the History of the Western Church</i> -(New York, 1902); S. Kmmerle, <i>Encyklopdie der evangelischen +(New York, 1902); S. Kümmerle, <i>Encyklopädie der evangelischen Kirchenmusik</i> (4 vols., 1888-1895); Chr. Palmer, <i>Evangelische -Hymnologie</i> (Stuttgart, 1865); and P. Urto Kornmller, <i>Lexikon +Hymnologie</i> (Stuttgart, 1865); and P. Urto Kornmüller, <i>Lexikon der kirchlichen Tonkunst</i> (1891).</p> </div> @@ -18501,7 +18462,7 @@ Psalm is associated with its proper text.</p> <hr class="art" /> <p><span class="bold">HYPAETHROS<a name="ar25" id="ar25"></a></span> (Gr. <span class="grk" title="hypaithros">ὕπαιθρος</span>, beneath the sky, in the open -air, <span class="grk" title="hypo">ὑπό</span>, beneath, and <span class="grk" title="aithr">αἰθήρ</span>, air), the Greek term quoted by +air, <span class="grk" title="hypo">ὑπό</span>, beneath, and <span class="grk" title="aithêr">αἰθήρ</span>, air), the Greek term quoted by Vitruvius (iii. 2) for the opening in the middle of the roof of decastyle temples, of which “there was no example in Rome, but one in Athens in the temple of Jupiter Olympius, which is @@ -18553,7 +18514,7 @@ Crete now in the British Museum shows a pierced tile on each side of the roof, and a large number of pierced tiles have been found in Pompeii, some of them surrounded with a rim identical with that of the marble tiles at Bassae. On the other hand, -there are many authorities, among them Dr W. Drpfeld, who +there are many authorities, among them Dr W. Dörpfeld, who have adhered to their original opinion that it was only through the open doorway that light was ever admitted into the cella, and with the clear atmosphere of Greece and the reflections @@ -18613,7 +18574,7 @@ some kind which Orestes knew how to open.</p> <hr class="art" /> -<p><span class="bold">HYPALLAGE<a name="ar26" id="ar26"></a></span> (Gr. <span class="grk" title="hypallag">ὑπαλλαγή</span>, interchange or exchange), a +<p><span class="bold">HYPALLAGE<a name="ar26" id="ar26"></a></span> (Gr. <span class="grk" title="hypallagê">ὑπαλλαγή</span>, interchange or exchange), a rhetorical figure, in which the proper relation between two words according to the rules of syntax are inverted. The stock instance is that in Virgil, <i>Aen.</i> iii. 61, where <i>dare classibus austros</i>, to @@ -18634,7 +18595,7 @@ recognized head of the Neoplatonic school there (<i>c.</i> 400). Her great eloquence and rare modesty and beauty, combined with her remarkable intellectual gifts, attracted to her class-room a large number of pupils. Among these was Synesius, afterwards -(<i>c.</i> 410) bishop of Ptolemas, several of whose letters to her, +(<i>c.</i> 410) bishop of Ptolemaïs, several of whose letters to her, full of chivalrous admiration and reverence, are still extant. Suidas, misled by an incomplete excerpt in Photius from the life of Isidorus (the Neoplatonist) by Damascius, states that Hypatia @@ -18668,7 +18629,7 @@ than of Porphyry and Iamblichus. Zeller, however, in his that “she appears to have taught the Neoplatonic doctrine in the form in which Iamblichus had stated it.” A Latin letter to Cyril on behalf of Nestorius, printed in the <i>Collectio nova conciliorum</i>, -i. (1623), by Stephanus Baluzius (tienne Baluze, <i>q.v.</i>), +i. (1623), by Stephanus Baluzius (Étienne Baluze, <i>q.v.</i>), and sometimes attributed to her, is undoubtedly spurious. The story of Hypatia appears in a considerably disguised yet still recognizable form in the legend of St Catherine as recorded in @@ -18685,8 +18646,8 @@ epigram by Palladas in the Greek Anthology (ix. 400). See Fabricius, Stephan Wolf (Czernowitz, 1879), H. Ligier (Dijon, 1880) and W. A. Meyer (Heidelberg, 1885), who devotes attention to the relation of Hypatia to the chief representatives of Neoplatonism; J. B. Bury, -<i>Hist. of the Later Roman Empire</i> (1889), i. 208,317; A. Gldenpenning, -<i>Geschichte des ostrmischen Reiches unter Arcadius und Theodosius II.</i> +<i>Hist. of the Later Roman Empire</i> (1889), i. 208,317; A. Güldenpenning, +<i>Geschichte des oströmischen Reiches unter Arcadius und Theodosius II.</i> (Halle, 1885), p. 230; Wetzer and Welte, <i>Kirchenlexikon</i>, vi. (1889), from a Catholic standpoint. The story of Hypatia also forms the basis of the well-known historical romance by Charles Kingsley @@ -18742,9 +18703,9 @@ hyperbola.</p> <p>Some properties of the curve will be briefly stated: If PN be the ordinate of the point P on the curve, AA’ the vertices, X the meet of -the directrix and axis and C the centre, then PN<span class="sp">2</span>: ANNA′: : -SX<span class="sp">2</span>: AXA′X, <i>i.e.</i> PN<span class="sp">2</span> is to ANNA′ in a constant ratio. The circle -on AA’ as diameter is called the auxiliarly circle; obviously ANNA’ +the directrix and axis and C the centre, then PN<span class="sp">2</span>: AN·NA′: : +SX<span class="sp">2</span>: AX·A′X, <i>i.e.</i> PN<span class="sp">2</span> is to AN·NA′ in a constant ratio. The circle +on AA’ as diameter is called the auxiliarly circle; obviously AN·NA’ equals the square of the tangent to this circle from N, and hence the ratio of PN to the tangent to the auxiliarly circle from N equals the ratio of the conjugate axis to the transverse. We may observe @@ -18765,7 +18726,7 @@ these chords is its conjugate diameter. Any diameter is a mean proportional between the transverse axis and the focal chord parallel to the diameter. Any line cuts off equal distances between the curve and the asymptotes. If the tangent at P meets the asymptotes in -R, R′, then CRCR′ = CS<span class="sp">2</span>. The geometry of the rectangular hyperbola +R, R′, then CR·CR′ = CS<span class="sp">2</span>. The geometry of the rectangular hyperbola is simplified by the fact that its principal axes are equal.</p> <p>Analytically the hyperbola is given by ax<span class="sp">2</span> + 2hxy + by<span class="sp">2</span> + 2gx + 2fy + c = 0 @@ -18775,11 +18736,11 @@ principal axes of the curve, the equation is further simplified to Ax<span class="sp">2</span> − By<span class="sp">2</span> = C, or if the semi-transverse axis be a, and the semi-conjugate b, x<span class="sp">2</span>/a<span class="sp">2</span> − y<span class="sp">2</span>/b<span class="sp">2</span> = 1. This is the most commonly used form. In the rectangular hyperbola a = b; hence its equation is x<span class="sp">2</span> − y<span class="sp">2</span> = 0. -The equations to the asymptotes are x/a = y/b and x = y respectively. +The equations to the asymptotes are x/a = ±y/b and x = ±y respectively. Referred to the asymptotes as axes the general equation becomes xy = k<span class="sp">2</span>; obviously the axes are oblique in the general hyperbola and rectangular in the rectangular hyperbola. The values -of the constant k<span class="sp">2</span> are (a<span class="sp">2</span> + b<span class="sp">2</span>) and a<span class="sp">2</span> respectively. (See +of the constant k<span class="sp">2</span> are ½(a<span class="sp">2</span> + b<span class="sp">2</span>) and ½a<span class="sp">2</span> respectively. (See <span class="sc"><a href="#artlinks">Geometry</a></span>: <i>Analytical</i>; <i>Projective</i>.)</p> </div> @@ -18798,13 +18759,13 @@ name does not occur in the <i>Iliad</i> or the <i>Odyssey</i>, but Herodotus (iv. 32) states that they were mentioned in Hesiod and in the <i>Epigoni</i>, an epic of the Theban cycle. According to Herodotus, two maidens, Opis and Arge, and later two others, Hyperoche -and Laodice, escorted by five men, called by the Delians Perpheres, +and Laodice, escorted by five men, called by the Delians Perphereës, were sent by the Hyperboreans with certain offerings to Delos. Finding that their messengers did not return, the Hyperboreans adopted the plan of wrapping the offerings in wheat-straw and requested their neighbours to hand them on to the next nation, and so on, till they finally reached Delos. -The theory of H. L. Ahrens, that Hyperboreans and Perpheres +The theory of H. L. Ahrens, that Hyperboreans and Perphereës are identical, is now widely accepted. In some of the dialects of northern Greece (especially Macedonia and Delphi) φ had a tendency to become β. The original form of <span class="grk" title="Perpherees">Περφερέες</span> was @@ -18814,7 +18775,7 @@ becoming <span class="grk" title="hyperboroi">ὑπέρβ	 were thus the bearers of the sacrificial gifts to Apollo over land and sea, irrespective of their home, the name being given to Delphians, Thessalians, Athenians and Delians. It is -objected by O. Schrder that the form <span class="grk" title="Perpherees">Περφερέες</span> requires a passive +objected by O. Schröder that the form <span class="grk" title="Perpherees">Περφερέες</span> requires a passive meaning, “those who are carried round the altar,” perhaps dancers like the whirling dervishes; distinguishing them from the Hyperboreans, he explains the latter as those who live “above @@ -18854,8 +18815,8 @@ as far apart from each other as they both are from the Mongolo-Tatar stock.</p> <div class="condensed"> -<p>See O. Crusius in Roscher’s <i>Lexikon der Mythologie</i>; O. Schrder -in <i>Archiv fr Religionswissenschaft</i> (1904), viii. 69; W. Mannhardt, +<p>See O. Crusius in Roscher’s <i>Lexikon der Mythologie</i>; O. Schröder +in <i>Archiv für Religionswissenschaft</i> (1904), viii. 69; W. Mannhardt, <i>Wald- und Feldkulte</i> (1905); L. R. Farnell, <i>Cults of the Greek States</i> (1907), iv. 100.</p> </div> @@ -18920,7 +18881,7 @@ over Leosthenes and his comrades who had fallen in the Lamian war, the best extant specimen of epideictic oratory (see <span class="sc"><a href="#artlinks">Babington</a></span>, <span class="sc"><a href="#artlinks">Churchill</a></span>). Towards the end of the century further discoveries were made of the conclusion of the speech <i>Against Philippides</i> -(dealing with a <span class="grk" title="graph paranomn">γραφὴ παρανόμων</span>, or indictment for the proposal of +(dealing with a <span class="grk" title="graphê paranomôn">γραφὴ παρανόμων</span>, or indictment for the proposal of an unconstitutional measure, arising out of the disputes of the Macedonian and anti-Macedonian parties at Athens), and of the whole of the <i>Against Athenogenes</i> (a perfumer accused of fraud in the sale @@ -18937,7 +18898,7 @@ Teubner series), to which may be added I. Bassi, <i>Le Quattro Orazioni di Iperide</i> (introduction and notes, 1888), and J. E. Sandys in <i>Classical Review</i> (January 1895) (a review of the editions of Kenyon and Blass). For the discourse against Athenogenes see H. Weil, -<i>tudes sur l’antiquit grecque</i> (1900).</p> +<i>Études sur l’antiquité grecque</i> (1900).</p> </div> @@ -18950,10 +18911,10 @@ where as in other poets the vowel -<i>i</i>- though really long, is shortened for metrical reasons) Hyperion is used for Apollo as expressive of the idea of beauty. The name is often used as an epithet of Helios, who is himself sometimes called simply -Hyperion. It is explained as (1) he who moves above (<span class="grk" title="hyper-in">ὑπερ-ιων</span>), +Hyperion. It is explained as (1) he who moves above (<span class="grk" title="hyper-iôn">ὑπερ-ιων</span>), but the quantity of the vowel is against this; (2) he who is -above (<span class="grk" title="hyperi-n">ὑπερι-ων</span>). Others take it to be a patronymic in form, -like <span class="grk" title="Kronin, Molin">Κρονῖων, Μολῖων</span>.</p> +above (<span class="grk" title="hyperi-ôn">ὑπερι-ων</span>). Others take it to be a patronymic in form, +like <span class="grk" title="Kroniôn, Moliôn">Κρονῖων, Μολῖων</span>.</p> <hr class="art" /> @@ -18979,7 +18940,7 @@ purposes.</p> <hr class="art" /> -<p><span class="bold">HYPERTROPHY<a name="ar35" id="ar35"></a></span> (Gr. <span class="grk" title="hyper">ὑπέρ</span>, over, and <span class="grk" title="troph">τροφή</span>, nourishment), +<p><span class="bold">HYPERTROPHY<a name="ar35" id="ar35"></a></span> (Gr. <span class="grk" title="hyper">ὑπέρ</span>, over, and <span class="grk" title="trophê">τροφή</span>, nourishment), a term in medicine employed to designate an abnormal increase in bulk of one or more of the organs or component tissues of the body (see <span class="sc"><a href="#artlinks">Pathology</a></span>). In its strict sense this term can only @@ -19176,7 +19137,7 @@ objects, which are thereby rendered potent to cure disease.</p> the artificial somnambulism which for nearly a century was called mesmeric or magnetic sleep, and which is now familiar as hypnosis of a well-marked degree. It was observed and described about -the year 1780 by the marquis de Puysgur, a disciple of Mesmer, +the year 1780 by the marquis de Puységur, a disciple of Mesmer, who showed that, while subjects were in this state, not only could some of their diseases be cured, but also their movements could be controlled by the “magnetizer,” and that they usually @@ -19184,7 +19145,7 @@ remembered nothing of the events of the period of sleep when restored to normal consciousness. These are three of the most important features of hypnosis, and the modern study of hypnotism may therefore be said to have been initiated at this date by -Puysgur. For, though it is probable that this state had often +Puységur. For, though it is probable that this state had often been induced by the earlier magnetists, they had not recognized that the peculiar behaviour of their patients resulted from their being plunged into this artificial sleep, but had attributed all @@ -19294,7 +19255,7 @@ very nearly, though not quite, extinct.</p> may distinguish three lines, the physiological, the psychological and the pathological. The last may be dismissed in a few words. Its principal representative was J. M. Charcot, who taught at -the Salptrire in Paris that hypnosis is essentially a symptom +the Salpêtrière in Paris that hypnosis is essentially a symptom of a morbid condition of hysteria or hystero-epilepsy. This doctrine, which, owing to the great repute enjoyed by Charcot, <span class="pagenum"><a name="page203" id="page203"></a>203</span> @@ -19318,9 +19279,9 @@ all the phenomena. This dates from 1884, when H. Bernheim, professor of medicine at Nancy, published his work <i>De la Suggestion</i> (republished in 1887 with a second part on the therapeutics of hypnotism). Bernheim was led to the study of hypnotism -by A. A. Libeault, who for twenty years had used it very +by A. A. Liébeault, who for twenty years had used it very largely and successfully in his general practice among the poor -of Nancy. Libeault rediscovered independently, and Bernheim +of Nancy. Liébeault rediscovered independently, and Bernheim made known to the world the truths, twice previously discovered and twice lost sight of, that expectation is a most important factor in the induction of hypnosis, that increased suggestibility @@ -19510,7 +19471,7 @@ of himself. He may then assent and describe the photograph in some detail, and, what is more astonishing, he may pick out the card as the one bearing the photograph, after it has been mixed with other similar blank cards. This seems to be due to the part -played by <i>points de repre</i>, insignificant details of surface or +played by <i>points de repère</i>, insignificant details of surface or texture, which serve as an objective basis around which the hallucinatory image is constructed by the pictorial imagination of the subject. A negative hallucination may be induced by @@ -19958,12 +19919,12 @@ the same journal by other hands; chapter on Hypnotism in <i>Human Personality and its Survival of bodily Death</i>, by F. W. H. Myers (London, 1903); <i>The Psychology of Suggestion</i>, by Boris Sidis, Ph.D. (New York, 1898); “Zur Psychologie der Suggestion,” by Prof. -Th. Lipp, and other papers in the <i>Zeitschrift fr Hypnotismus</i>. Of -special historical interest are the following:—<i>tude sur le zoomagntisme</i>, -par A. A. Libeault (Paris, 1883); <i>Hypnotisme, suggestion, -psycho-thrapie</i>, par Prof. Bernheim (Paris, 1891); <i>Braid on +Th. Lipp, and other papers in the <i>Zeitschrift für Hypnotismus</i>. Of +special historical interest are the following:—<i>Étude sur le zoomagnétisme</i>, +par A. A. Liébeault (Paris, 1883); <i>Hypnotisme, suggestion, +psycho-thérapie</i>, par Prof. Bernheim (Paris, 1891); <i>Braid on Hypnotism</i> (a new issue of James Braid’s <i>Neurypnology</i>), edited by -A. E. Waite (London, 1899); <i>Trait du somnambulisme</i>, by A. +A. E. Waite (London, 1899); <i>Traité du somnambulisme</i>, by A. Bertrand (Paris, 1826). A full bibliography is appended to Dr Milne Bramwell’s <i>Hypnotism</i>.</p> </div> @@ -19985,7 +19946,7 @@ concrete covered with layers of pounded bricks and marble cement, on which the marble pavement in slabs or tesserae was laid. In colder countries, as for instance in Germany and England, the living rooms were all heated in a similar way, and -round Trves (Trier) both systems have been found in two or +round Trèves (Trier) both systems have been found in two or three Roman villas, with the one flue for the ordinary rooms and several wall flues for the hot baths. In England these hypocausts are found in every Roman settlement, and the chief @@ -20066,7 +20027,7 @@ of Rome (cf. Routh, <i>Rel. Sacr.</i> iii. 373) condemns the attempt to sever the Godhead into three separate <i>hypostases</i> and three deities, and the Nicene Creed in the anathemas speaks of <span class="pagenum"><a name="page208" id="page208"></a>208</span> -<span class="grk" title="ex heteras hypostases ousias">ὲξ ἑτέρας ὑποστάσεως ἢ οὐσίας</span>. Alongside, however, of this persistent +<span class="grk" title="ex heteras hypostaseôs ê ousias">ὲξ ἑτέρας ὑποστάσεως ἢ οὐσίας</span>. Alongside, however, of this persistent interchange there was a desire to distinguish between the terms, and to confine <span class="grk" title="hypostasis">ὑπόστασις</span> to the Divine <i>persons</i>. This tendency arose in Alexandria, and its progress may be seen in @@ -20075,7 +20036,7 @@ writer, in view of the Arian trouble, felt that it was better to speak of <span class="grk" title="ousia">οὐσία</span> as “the common undifferentiated substance of Deity,” and <span class="grk" title="hypostasis">ὑπόστασις</span> as “Deity existing in a personal mode, the substance of Deity with certain special properties” (<span class="grk" title="ousia -meta tinn idimatn">οὐσία μετά τινων ἰδιωμάτων</span>). At the council of Alexandria in 362 the +meta tinôn idiômatôn">οὐσία μετά τινων ἰδιωμάτων</span>). At the council of Alexandria in 362 the phrase <span class="grk" title="treis hypostaseis">τρεῖς ὑποστάσεις</span> was permitted, and the work of this council was supplemented by Basil, Gregory of Nazianzus and Gregory of Nyssa in the formula <span class="grk" title="mia ousia, treis hypostaseis">μία οὐσία, τρεῖς ὑποστάσεις</span> or @@ -20109,7 +20070,7 @@ which Bernthsen showed to be H<span class="su">2</span>S<span class="su">2</span <hr class="art" /> -<p><span class="bold">HYPOTHEC<a name="ar43" id="ar43"></a></span> (Lat. <i>hypotheca</i>, Gr. <span class="grk" title="hypothk">ὑποθήκη</span>), in Roman law, +<p><span class="bold">HYPOTHEC<a name="ar43" id="ar43"></a></span> (Lat. <i>hypotheca</i>, Gr. <span class="grk" title="hypothêkê">ὑποθήκη</span>), in Roman law, the most advanced form of the contract of pledge. A specific thing may be given absolutely to a creditor on the understanding that it is to be given back when the creditor’s debt is paid; @@ -20186,7 +20147,7 @@ by which rigorous tests may be applied. This test is roughly of two kinds, first by the ultimate principles or presuppositions on which a particular branch of knowledge rests, and second by the comparison of correlative facts. Useful light is shed on -this distinction by Lotze, who contrasts (<i>Logic</i>, 273) <i>postulates</i> +this distinction by Lotze, who contrasts (<i>Logic</i>, § 273) <i>postulates</i> (“absolutely necessary assumptions without which the content of the observation with which we are dealing would contradict the laws of our thought”) with <i>hypotheses</i>, which he defines @@ -20212,15 +20173,15 @@ technically in the phrases “hypothetical judgment” and “hypothetical syllogism.” (See <span class="sc"><a href="#artlinks">Logic</a></span> and <span class="sc"><a href="#artlinks">Syllogism</a></span>.)</p> <div class="condensed"> -<p>See Naville, <i>La Logique de l’hypothse</i> (1880), and textbooks of +<p>See Naville, <i>La Logique de l’hypothèse</i> (1880), and textbooks of logic, <i>e.g.</i> those of Jevons, Bosanquet, Joseph; Liebmann, <i>Der Klimax d. Theorien</i>.</p> </div> <hr class="art" /> -<p><span class="bold">HYPOTRACHELIUM<a name="ar45" id="ar45"></a></span> (Gr. <span class="grk" title="hypotrachlion">ὑποτραχήλιον</span>, the lower part of -the neck, <span class="grk" title="trachlos">τράχηλος</span>), in classical architecture, the space between +<p><span class="bold">HYPOTRACHELIUM<a name="ar45" id="ar45"></a></span> (Gr. <span class="grk" title="hypotrachêlion">ὑποτραχήλιον</span>, the lower part of +the neck, <span class="grk" title="trachêlos">τράχηλος</span>), in classical architecture, the space between the annulet of the echinus and the upper bed of the shafts, including, according to C. R. Cockerell, the three grooves or sinkings found in some of the older examples, as in the temple @@ -20281,7 +20242,7 @@ which has been anglicized into “dassie.”</p> <div class="condensed"> <p>As regards the recent forms, the dentition in the fully adult animal -consists only of incisors and cheek-teeth, the formula being <i>i.</i> , +consists only of incisors and cheek-teeth, the formula being <i>i.</i> ½, <i>c.</i> <span class="spp">0</span>⁄<span class="suu">0</span>, <i>p.</i> <span class="spp">4</span>⁄<span class="suu">4</span> <i>m.</i> <span class="spp">3</span>⁄<span class="suu">3</span>. There is, however, a minute upper canine developed at first, which is early shed; and in extinct forms this tooth was functional and molar-like. The upper incisors have persistent @@ -20514,7 +20475,7 @@ blossom from June to September. Varieties of the plant occur in gardens with red and white flowers, also one having variegated leaves. The leaves have a warm, aromatic, bitter taste, and are believed to owe their properties to a volatile oil which is present -in the proportion of to %. Hyssop is a native of the south +in the proportion of ¼ to ½%. Hyssop is a native of the south of Europe, its range extending eastward to central Asia. A strong tea made of the leaves, and sweetened with honey, was formerly used in pulmonary and catarrhal affections, and externally as an @@ -20533,7 +20494,7 @@ quantities it acts as a purgative, diuretic and emetic when taken internally. It was formerly official in the Edinburgh Pharmacopoeia, being esteemed as a remedy for dropsy. It is said to have formed the basis of a celebrated nostrum for gout, called -<i>Eau mdicinale</i>, and in former times was called <i>Gratia Dei</i>. +<i>Eau médicinale</i>, and in former times was called <i>Gratia Dei</i>. When growing in abundance, as it does in some damp pastures in Switzerland, it becomes dangerous to cattle. G. <i>peruviana</i> is known to possess similar properties.</p> @@ -20551,7 +20512,7 @@ the discussion of their several claims. By Tristram (<i>Oxford Bible for Teachers</i>, 1880) and others the caper plant (<i>Capparis spinosa</i>) is supposed to be meant; but, apart from other difficulties, this identification is open to the objection that the caper seems to be, -at least in one passage (Eccl. xii. 5), otherwise designated (<i>’abiy-ynah</i>). +at least in one passage (Eccl. xii. 5), otherwise designated (<i>’abiy-yônah</i>). Thenius (on 1 Kings v. 13) suggests <i>Orthotrichum saxatile</i>. <span class="pagenum"><a name="page211" id="page211"></a>211</span> The most probable opinion would seem to be that found in Maimonides @@ -20591,7 +20552,7 @@ Zoroastrianism itself (see <span class="sc"><a href="#artlinks">Persia</a></span <hr class="art" /> -<p><span class="bold">HYSTERESIS<a name="ar52" id="ar52"></a></span> (Gr. <span class="grk" title="hystersis">ὑστέρησις</span>, from <span class="grk" title="hysterein">ὑστέρειν</span>, to lag behind), +<p><span class="bold">HYSTERESIS<a name="ar52" id="ar52"></a></span> (Gr. <span class="grk" title="hysterêsis">ὑστέρησις</span>, from <span class="grk" title="hysterein">ὑστέρειν</span>, to lag behind), a term added to the vocabulary of physical science by J. A. Ewing, who defines it as follows: When there are two qualities M and N such that cyclic variations of N cause cyclic variations @@ -20637,7 +20598,7 @@ name). This view is now universally recognized to be erroneous. The term “functional” is often used by English neurologists as synonymous with hysterical, a nomenclature which is tentatively advantageous since it is at least non-committal. P. J. -Mbius has defined hysteria as “a state in which ideas control +Möbius has defined hysteria as “a state in which ideas control the body and produce morbid changes in its functions.” P. Janet, who has done much to popularize the psychical origin of the affection, holds that there is “a limitation of the field @@ -20761,13 +20722,13 @@ a hospital ward or nursing home, are essential, in order that full benefit may be derived from psychotherapeutic measures.</p> <div class="condensed"> -<p><span class="sc">Bibliography.</span>—Charcot, <i>Leons sur les maladies du systme +<p><span class="sc">Bibliography.</span>—Charcot, <i>Leçons sur les maladies du système nerveuse</i> (1877); S. Weir Mitchell, <i>Lectures on Diseases of the Nervous System especially in Women</i> (1885); Buzzard, <i>Simulation of Hysteria -by Organic Nervous Disease</i> (1891); Pitres, <i>Leons cliniques sur -l’hystrie et l’hypnotisme</i> (1891); Richer, <i>tudes cliniques sur la -grande hystrie</i> (1891); Gilles de la Tourette, <i>Trait clinique et -thrapeutique de l’hystrie</i> (1891); Bastian, <i>Hysterical or Functional +by Organic Nervous Disease</i> (1891); Pitres, <i>Leçons cliniques sur +l’hystérie et l’hypnotisme</i> (1891); Richer, <i>Études cliniques sur la +grande hystérie</i> (1891); Gilles de la Tourette, <i>Traité clinique et +thérapeutique de l’hystérie</i> (1891); Bastian, <i>Hysterical or Functional Paralysis</i> (1893); Ormerod, Art. “Hysteria,” in Clifford Allbutt’s <i>System of Medicine</i> (1899); Camus and Pagnez, <i>Isolement et Psychotherapie</i> (1904).</p> @@ -20813,7 +20774,7 @@ antiquity but unknown date, founded originally for the reception of lepers. A government school of musketry, in which instructors for the army are trained, was established in 1854, and has been extended since, and the Shorncliffe military camp is within -2 m. of the town.</p> +2½ m. of the town.</p> <p>Lympne, which is now 3 m. inland, is thought to have been the original harbour which gave Hythe a place among the Cinque @@ -20836,7 +20797,7 @@ were held. A mile north from Hythe is Saltwood Castle, of very ancient origin, but rebuilt in the time of Richard II. The castle was granted to the see of Canterbury in 1026, but escheated to the crown in the time of Henry II., when the murder of Thomas - Beckett is said to have been concerted here, and having been +à Beckett is said to have been concerted here, and having been restored to the archbishops by King John remained a residence of theirs until the time of Henry VIII. It was restored as a residence in 1882. About 2 m. N.W. of Saltwood are remains @@ -21021,7 +20982,7 @@ epistle of Iamblichus.</p> to harmonize the principles of the various Greek schools. At the head of his system he placed the transcendent incommunicable one (<span class="grk" title="hen amethekton">ἓν ἀμέθεκτον</span>), whose first-begotten is intellect (<span class="grk" title="nous">νοῦς</span>), from -which proceeds soul (<span class="grk" title="psych">ψυχή</span>), which in turn gives birth to <span class="grk" title="physis">φύσις</span>, the +which proceeds soul (<span class="grk" title="psychê">ψυχή</span>), which in turn gives birth to <span class="grk" title="physis">φύσις</span>, the <span class="pagenum"><a name="page214" id="page214"></a>214</span> realm of nature. Immediately after the absolute one, Iamblichus introduced a second superexistent unity to stand between it and @@ -21031,14 +20992,14 @@ undergo various modifications. He speaks of them as intellectual (<span class="grk" title="theoi noeroi">θεοὶ νοεροί</span>), supramundane (<span class="grk" title="hyperkosmioi">ὑπερκόσμιοι</span>), and mundane gods (<span class="grk" title="egkosmioi">ἐγκόσμιοι</span>). The first of these—which Plotinus represented under the three stages of (objective) being (<span class="grk" title="on">ὄν</span>), -(subjective) life (<span class="grk" title="z">ζωή</span>), and (realized) intellect (<span class="grk" title=" nous">νοῦς</span>)—is distinguished -by him into spheres of intelligible gods (<span class="grk" title="theoi notoi">θεοὶ νοεροί</span>) and +(subjective) life (<span class="grk" title="zôê">ζωή</span>), and (realized) intellect (<span class="grk" title=" nous">νοῦς</span>)—is distinguished +by him into spheres of intelligible gods (<span class="grk" title="theoi noêtoi">θεοὶ νοεροί</span>) and of intellectual gods (<span class="grk" title="theoi noeroi">θεοὶ νοεροί</span>), each subdivided into triads, the latter sphere being the place of ideas, the former of the archetypes of these ideas. Between these two worlds, at once separating and uniting them, some scholars think there was inserted by Iamblichus, as afterwards by Proclus, a third sphere partaking -of the nature of both (<span class="grk" title="theoi notoi kai noeroi">θεοὶ νοητοὶ καὶ νοεροί</span>). But this supposition +of the nature of both (<span class="grk" title="theoi noêtoi kai noeroi">θεοὶ νοητοὶ καὶ νοεροί</span>). But this supposition depends on a merely conjectural emendation of the text. We read, however, that “in the intellectual hebdomad he assigned the third rank among the fathers to the Demiurge.” @@ -21046,7 +21007,7 @@ The Demiurge, Zeus, or world-creating potency, is thus identified with the perfected <span class="grk" title="nous">νοῦς</span>, the intellectual triad being increased to a hebdomad, probably (as Zeller supposes) through the subdivision of its first two members. As in Plotinus <span class="grk" title="nous">νοῦς</span> produced -nature by mediation of <span class="grk" title="psych">ψυχή</span>, so here the intelligible gods are +nature by mediation of <span class="grk" title="psychê">ψυχή</span>, so here the intelligible gods are followed by a triad of psychic gods. The first of these is incommunicable and supramundane, while the other two seem to be mundane though rational. In the third class, or mundane @@ -21064,11 +21025,11 @@ offerings.</p> <p>The whole of this complex theory is ruled by a mathematical formulism of triad, hebdomad, &c., while the first principle is -identified with the monad, <span class="grk" title="nous">νοῦς</span> with the dyad, and <span class="grk" title="psych">ψυχή</span> with +identified with the monad, <span class="grk" title="nous">νοῦς</span> with the dyad, and <span class="grk" title="psychê">ψυχή</span> with the triad, symbolic meanings being also assigned to the other numbers. “The theorems of mathematics,” he says, “apply absolutely to all things,” from things divine to original matter -(<span class="grk" title="hyl">ὕλη</span>). But though he thus subjects all things to number, he +(<span class="grk" title="hylê">ὕλη</span>). But though he thus subjects all things to number, he holds elsewhere that numbers are independent existences, and occupy a middle place between the limited and unlimited.</p> @@ -21150,8 +21111,8 @@ worship of images of the gods, though his master held that these hand of man or (as he believed) fallen from heaven. But images could easily be dispensed with from the point of view of the writer, who not only held that all things were full of gods (<span class="grk" title="panta -plr then">πάντα πλήρη θεῶν</span>, as Thales said), but thought that each man had a -special divinity of his own—an <span class="grk" title="idios daimn">ἴδιος δαίμων</span>—as his guard and +plêrê theôn">πάντα πλήρη θεῶν</span>, as Thales said), but thought that each man had a +special divinity of his own—an <span class="grk" title="idios daimôn">ἴδιος δαίμων</span>—as his guard and companion.</p> <div class="condensed"> @@ -21162,13 +21123,13 @@ authorities used see E. Rohde in <i>Rheinisches Museum</i>, xxvi., xxvii. (1871, 1872); Eng. trans. by Thomas Taylor (1818), (2) The <i>Exhortation to Philosophy</i> (<span class="grk" title="Logos protreptikos eis philosophian">Λόγος προτρεπτικὸς εἰς φιλοσοφίαν</span>), ed. T. Kiessling (1813); H. Piselli (1888). (3) The treatise <i>On the General Science -of Mathematics</i> (<span class="grk" title="Peri ts koins mathmatks epistms">Περὶ τῆς κοινῆς μαθηματικῆς ἐπιστήμης</span>), ed. J. G. Friis +of Mathematics</i> (<span class="grk" title="Peri tês koinês mathêmatkês epistêmês">Περὶ τῆς κοινῆς μαθηματικῆς ἐπιστήμης</span>), ed. J. G. Friis (Copenhagen, 1790), N. Festa (Leipzig, 1891). (4) The book <i>On the -Arithmetic of Nicomachus</i> (<span class="grk" title="Peri ts Nikomachou arithmtiks eisaggs">Περὶ τῆς Νικομάχου ἀριθμητικῆς εἰσαγωγῆς</span>), -along with fragments on fate (<span class="grk" title="Peri heimarmens">Περὶ εἱμαρμένης</span>) and prayer (<span class="grk" title="Peri -euchs">Περὶ εὐχῆς</span>), ed. S. Tennulius (1688), the <i>Arithmetic</i> by H. Pistelli (1894). -(5) The <i>Theological Principles of Arithmetic</i> (<span class="grk" title="Theologoumena ts -arithmtiks">Θεολογούμενα τῆς ἀριθμητικῆς</span>)—the seventh book of the series—by F. Ast (Leipzig, +Arithmetic of Nicomachus</i> (<span class="grk" title="Peri tês Nikomachou arithmêtikês eisagôgês">Περὶ τῆς Νικομάχου ἀριθμητικῆς εἰσαγωγῆς</span>), +along with fragments on fate (<span class="grk" title="Peri heimarmenês">Περὶ εἱμαρμένης</span>) and prayer (<span class="grk" title="Peri +euchês">Περὶ εὐχῆς</span>), ed. S. Tennulius (1688), the <i>Arithmetic</i> by H. Pistelli (1894). +(5) The <i>Theological Principles of Arithmetic</i> (<span class="grk" title="Theologoumena tês +arithmêtikês">Θεολογούμενα τῆς ἀριθμητικῆς</span>)—the seventh book of the series—by F. Ast (Leipzig, 1817). Two lost books, treating of the physical and ethical signification of numbers, stood fifth and sixth, while books on music, geometry and astronomy followed. The emperor Julian had a great admiration @@ -21185,10 +21146,10 @@ Taylor (1821).</p> <p>There is a monograph on Iamblichus by G. E. Hebenstreit (<i>De Iamblichi, philosophi Syri, doctrina</i>, Leipzig, 1764), and one of the -<i>De myst.</i> by Harless (<i>Das Buch v. d. gypt. Myst.</i>, Munich, 1858). +<i>De myst.</i> by Harless (<i>Das Buch v. d. ägypt. Myst.</i>, Munich, 1858). The best accounts of Iamblichus are those of Zeller, <i>Phil. d. Griechen</i>, -iii. 2, pp. 613 sq., 2nd ed.; E. Vacherot, <i>Hist. de l’cole d’Alexandrie</i> -(1846), ii. 57 sq.; J. Simon, <i>Hist. de l’cole d’Alexandrie</i> (1845); A. E. +iii. 2, pp. 613 sq., 2nd ed.; E. Vacherot, <i>Hist. de l’école d’Alexandrie</i> +(1846), ii. 57 sq.; J. Simon, <i>Hist. de l’école d’Alexandrie</i> (1845); A. E. Chaignet, <i>Histoire de la psychologie des Grecs</i> (Paris, 1893) v. 67-108; T. Whittaker, <i>The Neo-Platonists</i> (Cambridge, 1901).</p> </div> @@ -21206,7 +21167,7 @@ in <i>Comment. Soc. Reg. Sci. Gott.</i>, vol. iv., 1781, p. 77.</p> <hr class="art" /> <p><span class="bold">IAMBLICHUS,<a name="ar59" id="ar59"></a></span> of Syria, the earliest of the Greek romance writers, flourished in the 2nd century <span class="scs">A.D.</span> He was the author -of <span class="grk" title="Babylniaka">Βαβυλωνιακά</span>, the loves of Rhodanes and Sinonis, of which an +of <span class="grk" title="Babylôniaka">Βαβυλωνιακά</span>, the loves of Rhodanes and Sinonis, of which an epitome is preserved in Photius (cod. 94). Garmus, a legendary king of Babylon, forces Sinonis to marry him and throws Rhodanes into prison. The lovers manage to escape, and after many @@ -21231,7 +21192,7 @@ preserved, in addition to Photius’s epitome.</p> <hr class="art" /> <p><span class="bold">IANNINA<a name="ar60" id="ar60"></a></span> (<i>i.e.</i> “the city of St John”; Gr. <i>Ioannina</i>; Turk -<i>Yani</i>; also written Janina, Jannina, and, according to its +<i>Yaniá</i>; also written Janina, Jannina, and, according to its Albanian pronunciation, Yanina), the capital of the vilayet of Iannina, Albania, European Turkey. Pop. (1905) about 22,000. The largest ethnical groups in the population are the Albanian and @@ -21258,7 +21219,7 @@ the commercial importance of Iannina has notably declined since the cession of Arta and Thessaly to Greece in 1881. Iannina had previously been one of the chief centres of the Thessalian grain trade; it now exports little except cheese, hides, bitumen and -sheepskins to the annual value of about 120,000; the imports, +sheepskins to the annual value of about £120,000; the imports, which supply only the local demand for provisions, textile goods, hardware, &c., are worth about double that sum.</p> @@ -21312,7 +21273,7 @@ things is described as warring against the new order under Zeus, and is naturally relegated to Tartarus.</p> <div class="condensed"> -<p>See F. G. Welcker, <i>Griechische Gtterlehre</i>, i. (1857); C. H. Vlcker, +<p>See F. G. Welcker, <i>Griechische Götterlehre</i>, i. (1857); C. H. Völcker, <i>Die Mythologie des Iapetischen Geschlechtes</i> (1824); M. Mayer, <i>Giganten und Titanen</i> (1887).</p> </div> @@ -21345,7 +21306,7 @@ but subsequently rebelled.</p> which the object of this science was held to be “not to make gold but to prepare medicines.” This doctrine dominated chemical thought during the 16th century, its foremost supporters -being Paracelsus, van Helmont and de la Bo Sylvius. +being Paracelsus, van Helmont and de la Boë Sylvius. But it gave way to the new definition formulated by Boyle, viz. that the proper domain of chemistry was “to determine the composition of substances.” (See <span class="sc"><a href="#artlinks">Chemistry</a></span>: I. <i>History</i>; @@ -21405,10 +21366,10 @@ Ibadan.</p> <hr class="art" /> -<p><span class="bold">IBAGU,<a name="ar66" id="ar66"></a></span> or <span class="sc">San Bonifacio de Ibagu</span>, a city of Colombia, +<p><span class="bold">IBAGUÉ,<a name="ar66" id="ar66"></a></span> or <span class="sc">San Bonifacio de Ibagué</span>, a city of Colombia, and capital of the department of Tolima, about 60 m. W. of -Bogot and 18 m. N.W. of the Nevado de Tolima. Pop. (1900, -estimate) 13,000. Ibagu is built on a beautiful plain between +Bogotá and 18 m. N.W. of the Nevado de Tolima. Pop. (1900, +estimate) 13,000. Ibagué is built on a beautiful plain between the Chipalo and Combeima, small affluents of the Cuello, a western tributary of the Magdalena. Its elevation, 4300 ft. above the sea, gives it a mild, subtropical climate. The plain @@ -21417,7 +21378,7 @@ sugar-cane. There are two thermal springs in the vicinity, and undeveloped mines of sulphur and silver. The city has an endowed college. It is an important commercial centre, being on the road which crosses the Quindio pass, or <i>paramo</i>, into the -Cauca valley. Ibagu was founded in 1550 and was the capital +Cauca valley. Ibagué was founded in 1550 and was the capital of the republic for a short time in 1854.</p> @@ -21445,7 +21406,7 @@ more severely from earthquakes, that of 1859 causing great damage to its public buildings, and the greater one of the 16th of August 1868 almost completely destroyed the town and killed a large number of its inhabitants. The village of Carranqui, -1 m. from Ibarra, is the birthplace of Atahualpa, the Inca +1¼ m. from Ibarra, is the birthplace of Atahualpa, the Inca sovereign executed by Pizarro, and close by is the small lake called Yaguarcocha where the army of Huaynacapac, the father of Atahualpa, inflicted a bloody defeat on the Carranquis. @@ -21456,7 +21417,7 @@ or Indian burial mounds.</p> <hr class="art" /> -<p><span class="bold">IBERIANS<a name="ar68" id="ar68"></a></span> (Iberi, <span class="grk" title="Ibres">Ἲβηρες</span>), an ancient people inhabiting +<p><span class="bold">IBERIANS<a name="ar68" id="ar68"></a></span> (Iberi, <span class="grk" title="Ibêres">Ἲβηρες</span>), an ancient people inhabiting parts of the Spanish peninsula. Their ethnic affinities are not known, and our knowledge of their history is comparatively slight. It is almost impossible to make any statement in regard @@ -21469,7 +21430,7 @@ The principal sources of information about the Iberians are earlier Greek navigators to the peoples who inhabited the eastern coast of Spain; probably it originally meant those who dwelt by the river Iberus (mod. <i>Ebro</i>). It is possible (Boudard, -<i>tudes sur l’alphabet ibrien</i> (Paris, 1852) that the river-name +<i>Études sur l’alphabet ibérien</i> (Paris, 1852) that the river-name itself represents the Basque phrase <i>ibay-erri</i> “the country of the river.” On the other hand, even in older Greek usage (as in Thuc. vi. 1) the term Iberia is said to have embraced the country @@ -21525,7 +21486,7 @@ authenticated by their occurrence on the inscribed coins, and to link it with other traces of non-Aryan speech round the shores of the Western Mediterranean and on the Atlantic seaboard of Europe. This phase of Iberian theory opens with K. W. -Humboldt (<i>Prfung der Untersuchungen ber die Urbewohner +Humboldt (<i>Prüfung der Untersuchungen über die Urbewohner Hispaniens vermittelst der waskischen Sprache</i>, Berlin, 1821), <span class="pagenum"><a name="page217" id="page217"></a>217</span> who contended that there existed once a single great Iberian @@ -21540,10 +21501,10 @@ mainly raged. The principal evidence which Humboldt adduced in its support was the possibility of explaining a vast number of the ancient topographical names of Spain, and of other asserted Iberian districts, by the forms and significations of Basque. -In reply, Graslin (<i>De l’Ibrie</i>, Paris, 1839), maintained that the +In reply, Graslin (<i>De l’Ibérie</i>, Paris, 1839), maintained that the name Iberia was nothing but a Greek misnomer of Spain, and that there was no proof that the Basque people had ever -occupied a wider area than at present; and Blad (<i>Origine des +occupied a wider area than at present; and Bladé (<i>Origine des Basques</i>, Paris, 1869) took the same line of argument, holding that Iberia is a purely geographical term, that there was no proper Iberian race, that the Basques were always shut in by @@ -21587,60 +21548,60 @@ no misunderstanding as to the steps by which the term <i>Iberian</i> attained its meaning in modern anthropology.</p> <div class="condensed"> -<p><span class="sc">Authorities.</span>—K. W. von Humboldt, “ber die cantabrische +<p><span class="sc">Authorities.</span>—K. W. von Humboldt, “Über die cantabrische oder baskische Sprache” in Adelung, <i>Mithridates</i> iv. (1817), and -<i>Prfung d. Untersuchungen . die Urbewohner Hispaniens vermittelst -der waskischen Sprache</i> (Berlin, 1821); L. F. Graslin, <i>De l’Ibrie</i> -(Paris, 1838); T. B. G. M. Bory de St Vincent, <i>Essai gologique sur +<i>Prüfung d. Untersuchungen ü. die Urbewohner Hispaniens vermittelst +der waskischen Sprache</i> (Berlin, 1821); L. F. Graslin, <i>De l’Ibérie</i> +(Paris, 1838); T. B. G. M. Bory de St Vincent, <i>Essai géologique sur le genre humain</i> (1838); G. Lagneau, “Sur l’ethnologie des peuples -ibriens,” in <i>Bull. soc. anthrop.</i> (1867), pp. 146-161; J. F. Blad, -<i>tudes sur l’origine des Basques</i> (Paris, 1869), <i>Dfense des tudes</i>, &c. +ibériens,” in <i>Bull. soc. anthrop.</i> (1867), pp. 146-161; J. F. Bladé, +<i>Études sur l’origine des Basques</i> (Paris, 1869), <i>Défense des études</i>, &c. (Paris, 1870); Phillips, <i>Die Einwanderung der Iberer in die pyren. -Halbinsel</i> (Vienna, 1870), <i>ber das iberische Alphabet</i> (Vienna, 1870); +Halbinsel</i> (Vienna, 1870), <i>Über das iberische Alphabet</i> (Vienna, 1870); W. Boyd Dawkins, “The Northern Range of the Basques,” in <i>Fortnightly Rev.</i> N.S. xvi. 323-337 (1874); W. T. van Eys, “La -Langue ibrienne et la langue basque,” in <i>Revue de linguistique</i>, +Langue ibérienne et la langue basque,” in <i>Revue de linguistique</i>, pp. 3-15 (1874); W. Webster, “The Basque and the Kelt,” in <i>Journ. Anthrop. Inst.</i> v. 5-29 (1875); F. M. Tubino, <i>Los Aborigines ibericos o los Berberos en la peninsula</i> (Madrid, 1876); A. Luchaire, <i>Les Origines linguistiques de l’Aquitaine</i> (Paris, 1877); W. Boyd Dawkins, <i>Early Man in Britain</i> (London, 1880); A. Castaing, “Les Origines -des Aquitains,” <i>Mm. Soc. Eth.</i> N.S. 1, pp. 183-328 (1884); G. C. C. -Gerland, “Die Basken und die Iberer” in Grber, <i>Grundriss d. roman. +des Aquitains,” <i>Mém. Soc. Eth.</i> N.S. 1, pp. 183-328 (1884); G. C. C. +Gerland, “Die Basken und die Iberer” in Gröber, <i>Grundriss d. roman. Philologie</i>, 1, pp. 313-334 (1888); M. H. d’Arbois de Jubainville, -<i>Les Premiers habitants de l’Europe</i> (1889-1894); J. F. Blad, <i>Les -Vascons avant leur tablissement en Novempopulanie</i>, Agen. (1891); +<i>Les Premiers habitants de l’Europe</i> (1889-1894); J. F. Bladé, <i>Les +Vascons avant leur établissement en Novempopulanie</i>, Agen. (1891); W. Webster, “The Celt-iberians,” <i>Academy</i> xl. 268-269 (and consequent correspondence) (1891); J. Rhys, “The Inscriptions and Language of the Northern Picts,” <i>Proc. Soc. Ant. Scot.</i> xxvi. 263-351 -(1892); F. Fita, “El Vascuence en las inscripciones gmicas,” +(1892); F. Fita, “El Vascuence en las inscripciones ógmicas,” <i>Bol. Real. Acad. Hist. Madrid</i> (June 1893), xxii. 579-587; G. v. d. Gabelentz, “Baskisch u. Berberisch,” <i>Sitz. k. preuss. Akad. Wiss.</i> 593-613 (Berlin, 1893), <i>Die Verwandtschaft der Baskischen mit der Berber-Sprache Nordafrikas nachgewiesen</i> (Braunschweig, 1894); M. H. d’Arbois de Jubainville, “Les Celtes en Espagne,” <i>Rev. -celtique</i>, xiv. 357-395 (1894); G. Buschan, “ber die iberische -Rasse,” <i>Ausland</i>, lxvi. 342-344 (1894); F. Olriz y Aguilera, <i>Distribucion -geografica del indice cefalico en Espaa</i> (Madrid, 1894), -“La Talla humana en Espaa” in <i>Discursos R. Acad. Medicina</i> +celtique</i>, xiv. 357-395 (1894); G. Buschan, “Über die iberische +Rasse,” <i>Ausland</i>, lxvi. 342-344 (1894); F. Olóriz y Aguilera, <i>Distribucion +geografica del indice cefalico en España</i> (Madrid, 1894), +“La Talla humana en España” in <i>Discursos R. Acad. Medicina</i> xxxvi. 389 (Madrid, 1896); R. Collignon, “La Race basque,” <i>L’Anthropologie</i>, v. 276-287 (1894); T. de Aranzadi, “Le Peuple -basque, rsum” <i>Bull. soc. d’anth.</i> 510-520 (1894), “Consideraciones +basque, résumé” <i>Bull. soc. d’anth.</i> 510-520 (1894), “Consideraciones acerca de la raza basca” <i>Euskel-Erria</i> xxxv. 33, 65, 97, 129 (1896); -H. Schuchhardt, <i>Baskische Studien</i>, i. “ber die Entstehung der +H. Schuchhardt, <i>Baskische Studien</i>, i. “Über die Entstehung der Bezugsformen des baskischen Zeitworts”; <i>Denkschriften der K. Akad. der Wiss.</i>, Phil.-Hist., Classe, Bd. 42, Abh. 3. (Wien, 1893); -Ph. Salmon, <i>Rev. mens. c. d’anthr.</i> v. 155-181, 214-220 (1895); -R. Collignon, “Anthr. du S.-O. de la France,” <i>Mm. Soc. Anthr.</i> - 3. 1. 4. p. 1-129 (1895), <i>Ann. de gogr.</i> v. 156-166 (1896), and with -J. Deniker, “Les Maures de Sngal,” <i>L’Anthr.</i> vii. 57-69 (1897); -G. Herv, <i>Rev. mens. c. d’anthr.</i> vi. 97-109 (1896); G. Sergi, +Ph. Salmon, <i>Rev. mens. Éc. d’anthr.</i> v. 155-181, 214-220 (1895); +R. Collignon, “Anthr. du S.-O. de la France,” <i>Mém. Soc. Anthr.</i> +§ 3. 1. 4. p. 1-129 (1895), <i>Ann. de géogr.</i> v. 156-166 (1896), and with +J. Deniker, “Les Maures de Sénégal,” <i>L’Anthr.</i> vii. 57-69 (1897); +G. Hervé, <i>Rev. mens. Éc. d’anthr.</i> vi. 97-109 (1896); G. Sergi, <i>Africa: Anthropologia della stirpe Camitica</i> (Turin, 1897), <i>Arii ed -Italici</i> (1898); L. de Hoyos Sainz, “L’Anthropologie et la prhistorique +Italici</i> (1898); L. de Hoyos Sainz, “L’Anthropologie et la préhistorique en Espagne et en Portugal en 1897,” <i>L’Anthropologie</i>, ix. 37-51 (1898); J. Deniker (see Collignon) “Les Races de l’Europe,” -<i>L’Anthropologie</i>, ix. 113-133 (1898); M. Gze, “De quelques rapports -entre les langues berbre et basque,” <i>Mm. soc. arch. du Midi de +<i>L’Anthropologie</i>, ix. 113-133 (1898); M. Gèze, “De quelques rapports +entre les langues berbère et basque,” <i>Mém. soc. arch. du Midi de la France</i>, xiii. See also the works quoted in the footnotes; and the bibliography under <span class="sc"><a href="#artlinks">Basques</a></span>.</p> </div> @@ -21651,22 +21612,22 @@ bibliography under <span class="sc"><a href="#artlinks">Basques</a></span>.</p> <p><a name="ft1f" id="ft1f" href="#fa1f"><span class="fn">1</span></a> For the prehistoric civilization of the peninsula as a whole see <span class="sc"><a href="#artlinks">Spain</a></span>.</p> -<p><a name="ft2f" id="ft2f" href="#fa2f"><span class="fn">2</span></a> P. A. Boudard’s <i>tudes sur l’alphabet ibrien</i> (Paris, 1852). -and <i>Numismatique ibrienne</i> (Bziers, 1859); Aloiss Heiss, <i>Notes -sur les monnaies celtibriennes</i> (Paris, 1865), and <i>Description gnrale -des monnaies antiques de l’Espagne</i> (Paris, 1870); Phillips, <i>ber das +<p><a name="ft2f" id="ft2f" href="#fa2f"><span class="fn">2</span></a> P. A. Boudard’s <i>Études sur l’alphabet ibérien</i> (Paris, 1852). +and <i>Numismatique ibérienne</i> (Béziers, 1859); Aloiss Heiss, <i>Notes +sur les monnaies celtibériennes</i> (Paris, 1865), and <i>Description générale +des monnaies antiques de l’Espagne</i> (Paris, 1870); Phillips, <i>Über das iberische Alphabet</i> (Vienna, 1870), <i>Die Einwanderung der Iberer in die pyren. Halbinsel</i> (Vienna, 1870); W. M. Flinders Petrie, <i>Journ. -Anthr. Inst.</i> xxix. (1899) 204, and above all E. Hbner, <i>Monumenta +Anthr. Inst.</i> xxix. (1899) 204, and above all E. Hübner, <i>Monumenta linguae Ibericae</i>.</p> -<p><a name="ft3f" id="ft3f" href="#fa3f"><span class="fn">3</span></a> W. van Eys, for example, “La Langue ibrienne et la langue +<p><a name="ft3f" id="ft3f" href="#fa3f"><span class="fn">3</span></a> W. van Eys, for example, “La Langue ibérienne et la langue basque,” in <i>Revue de linguistique</i>, goes against Humboldt; but Prince Napoleon and to a considerable extent A. Luchaire maintain the justice of his method and the value of many of his results. See Luchaire, <i>Les Origines linguistiques de l’Aquitaine</i> (Paris, 1877).</p> -<p><a name="ft4f" id="ft4f" href="#fa4f"><span class="fn">4</span></a> Compare the interesting rsum of the whole question in Boyd +<p><a name="ft4f" id="ft4f" href="#fa4f"><span class="fn">4</span></a> Compare the interesting résumé of the whole question in Boyd Dawkins’s <i>Early Man in Britain</i> (London, 1880).</p> </div> @@ -21678,7 +21639,7 @@ ibex</i>. Formerly the ibex was common on the mountain-ranges of Germany, Switzerland and Tirol, but is now confined to the Alps which separate Valais from Piedmont, and to the lofty peaks of Savoy, where its existence is mainly due to game-laws. -The ibex is a handsome animal, measuring about 4 ft. in length +The ibex is a handsome animal, measuring about 4½ ft. in length and standing about 40 in. at the shoulder. The skin is covered in summer with a short fur of an ashy-grey colour, and in winter with much longer yellowish-brown hair concealing a dense fur @@ -21749,9 +21710,9 @@ Bruce identified this bird with the <i>Abu-Hannes</i> or “Father John” of the Abyssinians, and in 1790 it received from Latham (<i>Index ornithologicus</i>, p. 706) the name of <i>Tantalus aethiopicus</i>. This determination was placed beyond question by Cuvier (<i>Ann. -du Musum</i>, iv. 116-135) and Savigny (<i>Hist. nat. et mythol. +du Muséum</i>, iv. 116-135) and Savigny (<i>Hist. nat. et mythol. de l’ibis</i>) in 1805. They, however, removed it from the Linnaean -genus <i>Tantalus</i> and, Lacpde having some years before founded +genus <i>Tantalus</i> and, Lacépède having some years before founded a genus <i>Ibis</i>, it was transferred thither, and is now generally known as <i>I. aethiopica</i>, though some speak of it as <i>I. religiosa</i>. No attempt can here be made to treat the ibis from a mythological @@ -21771,7 +21732,7 @@ have failed to meet with it there<a name="fa2g" id="fa2g" href="#ft2g"><span cla the birds of Egypt is limited to those which frequent the country in winter), and writers have denied generally to this species a place in its modern fauna (cf. Shelley, <i>Birds of Egypt</i>, p. 261). -However, in 1864, von Heuglin (<i>Journ. fr Ornithologie</i>, 1865, +However, in 1864, von Heuglin (<i>Journ. für Ornithologie</i>, 1865, p. 100) saw a young bird which had been shot in the Delta, and E. C. Taylor (<i>Ibis</i>, 1878, p. 372) saw an adult which had been killed near Lake Menzal in 1877. The story told to Herodotus @@ -21844,9 +21805,9 @@ him Linnaeus.</p> Society in London, and even reared its young there.</p> <p><a name="ft4g" id="ft4g" href="#fa4g"><span class="fn">4</span></a> For some account of these may be consulted Dr Reichenow’s -paper in <i>Journ. fr Ornithologie</i> (1877), pp. 143-156; Elliot’s in +paper in <i>Journ. für Ornithologie</i> (1877), pp. 143-156; Elliot’s in <i>Proc. Zool. Society</i> (1877), pp. 477-510; and that of Oustalet in -<i>Nouv. Arch. du Musum</i>, ser. 2, vols. i. pp. 167-184.</p> +<i>Nouv. Arch. du Muséum</i>, ser. 2, vols. i. pp. 167-184.</p> <p><a name="ft5g" id="ft5g" href="#fa5g"><span class="fn">5</span></a> It is a popular error—especially among painters—that this bird was the sacred ibis of the Egyptians.</p> @@ -21946,7 +21907,7 @@ the German Oriental Society</i>, xxxv. 148, and Goldziher’s criticism of ancient and modern Arabic verse. Some of his letters have been published by D. S. Margoliouth “On the Royal Correspondence of Diya ed-Din el-Jazari” in the <i>Actes du -dixime congrs international des orientalistes</i>, sect. 3, pp. 7-21.</p> +dixième congrès international des orientalistes</i>, sect. 3, pp. 7-21.</p> <p>The brother best known by the simple name of Ibn Athīr was <span class="sc">Abu-l-Ḥasan ‘Izzuddīn Mahommed Ibn ul-Athīr</span> (1160-1234), @@ -21964,8 +21925,8 @@ additions. Ibn Athīr also wrote a history of the Atabegs of Mosul, published in the <i>Recueil des historiens des croisades</i> (vol. ii., Paris); a work (<i>Usd ul-Ghāba</i>), giving an account of 7500 companions of Mahomet (5 vols., Cairo, 1863), and a compendium -(the <i>Lubāb</i>) of Sam‘āni’s <i>Kitāb ul-Anṣāb</i> (cf. F. Wstenfeld’s -<i>Specimen el-Lobabi</i>, Gttingen, 1835).</p> +(the <i>Lubāb</i>) of Sam‘āni’s <i>Kitāb ul-Anṣāb</i> (cf. F. Wüstenfeld’s +<i>Specimen el-Lobabi</i>, Göttingen, 1835).</p> <div class="author">(G. W. T.)</div> @@ -22006,11 +21967,11 @@ travelled into Kipchak (the Mongol khanate of Russia), and joined the camp of the reigning khan Mahommed Uzbeg, from whom the great and heterogeneous <i>Uzbeg</i> race is perhaps named. Among other places in this empire he travelled to Bolghar -(54 54′ N.) in order to witness the shortness of the summer +(54° 54′ N.) in order to witness the shortness of the summer night, and desired to continue his travels north into the “Land of Darkness” (in the extreme north of Russia), of which wonderful things were told, but was obliged to forego this. Returning -to the khan’s camp he joined the cortge of one of the Khatuns, +to the khan’s camp he joined the cortège of one of the Khatuns, who was a Greek princess by birth (probably illegitimate) and in her train travelled to Constantinople, where he had an interview with the emperor Andronikos III. the Younger (1328-1341). @@ -22123,7 +22084,7 @@ which attracted much interest. The French capture of Constantina afforded MSS. of the complete work, one of them the autograph of Ibn Juzai. And from these, after versions of fragments by various French scholars, was derived at last (1858-1859) the standard edition -and translation of the whole by M. Dfrmery and Dr Sanguinetti, +and translation of the whole by M. Défrémery and Dr Sanguinetti, in 4 vols. See also Sir Henry Yule, Cathay, ii. 397-526; C. Raymond Beazley, <i>Dawn of Modern Geography</i>, iii. 535-538. Though there are some singular chronological difficulties in the narrative, and a @@ -22160,7 +22121,7 @@ edited by A. Haitsma (1773) E. Scheidius (1786) and N. Boyesen Brockelmann, <i>Gesch. der ar. Lit.</i>, i. 211 ff., Weimar, 1898), The <i>Jamhara fi-l-Lugha</i> is a large dictionary written in Persian but not printed. Another work is the <i>Kitāb ul-Ishtiqāq</i> (“Book of -Etymology”), edited by F. Wstenfeld (Gttingen, 1854); it was +Etymology”), edited by F. Wüstenfeld (Göttingen, 1854); it was written in opposition to the anti-Arabian party to show the etymological connexion of the Arabian tribal names.</p> </div> @@ -22299,33 +22260,33 @@ of Oxford</i> (Oxford, 1850); Dukes, <i>Shīrē Shelomoh</i> (Hanover, 1 S. Sachs, <i>Shīr ha-shīrīm asher li-Shelomoh</i> (Paris, 1868, incomplete); Brody, <i>Die weltlichen Gedichte des ... Gabirol</i> (Berlin, 1897, &c.).</p> -<p>“Avencebrolis Fons Vitae” (Latin text) in Clemens Bumker’s -<i>Beitrge zur Gesch. d. Philosophie</i>, Bd. i. Hefte 2-4 (Mnster, 1892); +<p>“Avencebrolis Fons Vitae” (Latin text) in Clemens Bäumker’s +<i>Beiträge zur Gesch. d. Philosophie</i>, Bd. i. Hefte 2-4 (Münster, 1892); <i>The Improvement of the Moral Qualities</i> [Arabic and English] ed. by S. S. Wise (New York, 1901); <i>A Choice of Pearls</i> [Hebrew and English] ed. by Ascher (London, 1859).</p> -<p>On the philosophy in general: S. Munk, <i>Mlanges</i> (quoted above); -Guttmann, <i>Die Philosophie des Sal.-ibn Gabirol</i> (Gttingen, 1889); -D. Kaufmann, <i>Studien ber Sal.-ibn Gabirol</i> (Budapest, 1899); +<p>On the philosophy in general: S. Munk, <i>Mélanges</i> (quoted above); +Guttmann, <i>Die Philosophie des Sal.-ibn Gabirol</i> (Göttingen, 1889); +D. Kaufmann, <i>Studien über Sal.-ibn Gabirol</i> (Budapest, 1899); S. Horovitz, “Die Psychologie Ibn Gabirols,” in the <i>Jahresbericht -des jd. theol. Seminars Frnckel’scher Stiftung</i> (Breslau, 1900); -Wittmann, “Zur Stellung Avencebrols ...” (in Bumker’s -<i>Beitrge</i>, Bd. v. Heft 1, Mnster, 1905).</p> +des jüd. theol. Seminars Fränckel’scher Stiftung</i> (Breslau, 1900); +Wittmann, “Zur Stellung Avencebrols ...” (in Bäumker’s +<i>Beiträge</i>, Bd. v. Heft 1, Münster, 1905).</p> </div> <div class="author">(A. Cy.)</div> <hr class="foot" /> <div class="note"> -<p><a name="ft1h" id="ft1h" href="#fa1h"><span class="fn">1</span></a> <i>Jud. Har. Macam</i>, ed. Lagarde (Gttingen, 1883), p. 89, l. 61.</p> +<p><a name="ft1h" id="ft1h" href="#fa1h"><span class="fn">1</span></a> <i>Jud. Har. Macamæ</i>, ed. Lagarde (Göttingen, 1883), p. 89, l. 61.</p> -<p><a name="ft2h" id="ft2h" href="#fa2h"><span class="fn">2</span></a> See the passage quoted by Munk, <i>Mlanges de philosophie arabe +<p><a name="ft2h" id="ft2h" href="#fa2h"><span class="fn">2</span></a> See the passage quoted by Munk, <i>Mélanges de philosophie arabe et juive</i> (Paris, 1859), pp. 264 and 517.</p> <p><a name="ft3h" id="ft3h" href="#fa3h"><span class="fn">3</span></a> <i>Liber Juchassin</i>, ed. Filipowski (London, 1857), p. 217.</p> -<p><a name="ft4h" id="ft4h" href="#fa4h"><span class="fn">4</span></a> <i>Hebr. bersetzungen</i> (Berlin, 1893), 219, note 70; cf. Kaufmann, -<i>Studien ber Sal.-ibn Gabirol</i> (Budapest, 1899), p. 79, note 2.</p> +<p><a name="ft4h" id="ft4h" href="#fa4h"><span class="fn">4</span></a> <i>Hebr. Übersetzungen</i> (Berlin, 1893), § 219, note 70; cf. Kaufmann, +<i>Studien über Sal.-ibn Gabirol</i> (Budapest, 1899), p. 79, note 2.</p> <p><a name="ft5h" id="ft5h" href="#fa5h"><span class="fn">5</span></a> See Munk, <i>op. cit.</i> pp. 515-516, transl. on pp. 263-264. Metre had been already used by Dunash.</p> @@ -22344,7 +22305,7 @@ An anonymous epitome of the book was written in 1233.</p> <div class="condensed"> <p>See M. J. de Goeje, “Die Iṣṭahrī-Balhī Frage,” in the <i>Zeitschrift -der deutschen Morgenlndischen Gesellschaft</i>, xxv. 42 sqq.</p> +der deutschen Morgenländischen Gesellschaft</i>, xxv. 42 sqq.</p> </div> @@ -22390,9 +22351,9 @@ Ayyūb ul-Himyarī] (d. 834), Arabian biographer, studied in Kufa but lived afterwards in Fostāt (old Cairo), where he gained a name as a grammarian and student of language and history. His chief work is his edition of Ibn Isḥāq’s (<i>q.v.</i>) <i>Life of the -Apostle of God</i>, which has been edited by F. Wstenfeld (Gttingen, +Apostle of God</i>, which has been edited by F. Wüstenfeld (Göttingen, 1858-1860). An abridged German translation has -been made by G. Weil (Stuttgart, 1864; cf. P. Brnnle, <i>Die +been made by G. Weil (Stuttgart, 1864; cf. P. Brönnle, <i>Die Commentatoren des Ibn Isḥaq und ihre Scholien</i>, Halle, 1895). Ibn Hishām is said to have written a work explaining the difficult words which occur in poems on the life of the Apostle, @@ -22461,11 +22422,11 @@ Africa (1364), where he was received with great cordiality by the sultan of Bougie, Abu Abdallah, who had been formerly his companion in prison. On the fall of Abu Abdallah Ibn Khaldūn raised a large force amongst the desert Arabs, and entered the -service of the sultan of Tlemen. A few years later he was taken +service of the sultan of Tlemçen. A few years later he was taken prisoner by Abdalaziz (‘Abd ul ‘Azīz), who had defeated the -sultan of Tlemen and seized the throne. He then entered a +sultan of Tlemçen and seized the throne. He then entered a monastic establishment, and occupied himself with scholastic -duties, until in 1370 he was sent for to Tlemen by the new +duties, until in 1370 he was sent for to Tlemçen by the new sultan. After the death of ‘Abd ul ‘Azīz he resided at Fez, enjoying the patronage and confidence of the regent. After some further vicissitudes in 1378 he entered the service of the @@ -22511,13 +22472,13 @@ tribes and of the kingdoms founded by that race in North Africa. The introduction is an elaborate treatise on the science of history and the development of society, and the autobiography contains the history, not only of the author himself, but of his family and of -the dynasties which ruled in Fez, Tunis and Tlemen during his +the dynasties which ruled in Fez, Tunis and Tlemçen during his lifetime. An edition of the Arabic text has been printed at Būlāq, (7 vols., 1867) and a part of the work has been translated by the late -Baron McG. de Slane under the title of <i>Histoire des Berbres</i> (Algiers, +Baron McG. de Slane under the title of <i>Histoire des Berbères</i> (Algiers, 1852-1856); it contains an admirable account of the author and analysis of his work. Vol. i., the <i>Muqaddama</i> (preface), was published -by M. Quatremre (3 vols., Paris, 1858), often republished in the +by M. Quatremère (3 vols., Paris, 1858), often republished in the East, and a French translation was made by McG. de Slane (3 vols., Paris, 1862-1868). The parts of the history referring to the expeditions of the Franks into Moslem lands were edited by C. J. Tornberg @@ -22551,7 +22512,7 @@ most celebrated persons of Moslem history and literature, except those of Mahomet, the four caliphs and the companions of Mahomet and their followers (the <i>Tābiūn</i>). The work is anecdotal and contains many brief extracts from the poetry of the writers. It was -published by F. Wstenfeld (Gttingen, 1835-1843), in part by McG. +published by F. Wüstenfeld (Göttingen, 1835-1843), in part by McG. de Slane (Paris, 1838-1842), and also in Cairo (1859 and 1882). An English translation by McG. de Slane was published for the Oriental Translation Fund in 4 vols. (London, 1842-1871). Thirteen @@ -22580,10 +22541,10 @@ Studien</i>, ii. 136, Halle, 1890), his chief works were directed to the training of the ideal secretary. Of these five may be said to form a series. The <i>Adab ul-Kātib</i> (“Training of the Secretary”) contains instruction in writing and is a compendium of Arabic -style. It has been edited by Max Grnert (Leiden, 1900). +style. It has been edited by Max Grünert (Leiden, 1900). The <i>Kitāb ush-Sharāb</i> is still in manuscript. The <i>Kitāb -ul-Ma’ārif</i> has been edited by F. Wstenfeld as the <i>Handbuch der -Geschichte</i><a name="fa1i" id="fa1i" href="#ft1i"><span class="sp">1</span></a> (Gttingen, 1850); the <i>Kitāb ush-Shi’r +ul-Ma’ārif</i> has been edited by F. Wüstenfeld as the <i>Handbuch der +Geschichte</i><a name="fa1i" id="fa1i" href="#ft1i"><span class="sp">1</span></a> (Göttingen, 1850); the <i>Kitāb ush-Shi’r wash-Shu’arāi</i> (“Book of Poetry and Poets”) edited by M. J. de Goeje (Leiden, 1904).<a name="fa2i" id="fa2i" href="#ft2i"><span class="sp">2</span></a> The fifth and most important is the <i>’Uyūn ul-Akhbār</i>, which deals in ten books with lordship, war, nobility, @@ -22603,8 +22564,8 @@ writers) see C. Brockelmann, <i>Gesch. der arabischen Literatur</i>, vol. i. <p><a name="ft1i" id="ft1i" href="#fa1i"><span class="fn">1</span></a> Summary in E. G. Browne, <i>A Literary History of Persia</i> (London, 1902), pp. 387 f.</p> -<p><a name="ft2i" id="ft2i" href="#fa2i"><span class="fn">2</span></a> The preface was translated into German by Theodor Nldeke -in his <i>Beitrge</i> (Hanover, 1864), pp. 1-51.</p> +<p><a name="ft2i" id="ft2i" href="#fa2i"><span class="fn">2</span></a> The preface was translated into German by Theodor Nöldeke +in his <i>Beiträge</i> (Hanover, 1864), pp. 1-51.</p> </div> @@ -22676,7 +22637,7 @@ in 1708 and has been reprinted since. A Spanish translation by F. Pons Boigues was published at Saragossa (1900). Another work of Ibn Ṭufail, the <i>Kitāb Asrār ul-Hikma ul-mashraqīyya</i> (“Secrets of Eastern Science”), was published at Bulāq (1882); cf. S. Munk, -<i>Mlanges</i> (1859), pp. 410 sqq., and T. J. de Boer, <i>Geschichte der Philosophie +<i>Mélanges</i> (1859), pp. 410 sqq., and T. J. de Boer, <i>Geschichte der Philosophie im Islam</i> (Stuttgart, 1901), pp. 160 sqq. (also an English translation).</p> </div> <div class="author">(G. W. T.)</div> @@ -22697,7 +22658,7 @@ though it is uncertain whether the new edition was made public in the lifetime of the author.</p> <div class="condensed"> -<p>Edition by A. Mller (Knigsberg, 1884).</p> +<p>Edition by A. Müller (Königsberg, 1884).</p> </div> <div class="author">(G. W. T.)</div> @@ -22706,12 +22667,12 @@ in the lifetime of the author.</p> <p><span class="bold">IBO,<a name="ar92" id="ar92"></a></span> a district of British West Africa, on the lower Niger immediately above the delta, and mainly on the eastern bank of the river. The chief town, frequently called by the same -name (more correctly Abo or boh), lies on a creek which falls +name (more correctly Abo or Áboh), lies on a creek which falls into the main stream about 150 m. from its mouth and contains from 6000 to 8000 inhabitants. The Ibo are a strong well-built Negro race. Their women are distinguished by their embonpoint. The language of the Ibo is one of the most widely spoken -on the lower Niger. The Rev. J. F. Schn began its reduction +on the lower Niger. The Rev. J. F. Schön began its reduction in 1841, and in 1861 he published a grammar (<i>Oku Ibo Grammatical Elements</i>, London, Church Miss. Soc.). (See <span class="sc"><a href="#artlinks">Nigeria</a></span>.)</p> @@ -22779,7 +22740,7 @@ end of September 1818 he had forced the Wahhabi leader to surrender, and had taken Deraiya, which he ruined. On the 11th of December 1819 he made a triumphal entry into Cairo. After his return he gave effective support to the Frenchman, -Colonel Sve (Suleiman Pasha), who was employed to drill +Colonel Sève (Suleiman Pasha), who was employed to drill the army on the European model. Ibrahim set an example by submitting to be drilled as a recruit. When in 1824 Mehemet Ali was appointed governor of the Morea by the sultan, who @@ -22819,7 +22780,7 @@ Beilan on the 29th of July, invaded Asia Minor, and finally routed the grand vizier at Konia on the 21st of December. The convention of Kutaiah on the 6th of May left Syria for a time in the hands of Mehemet Ali. Ibrahim was undoubtedly helped -by Colonel Sve and the European officers in his army, but his +by Colonel Sève and the European officers in his army, but his intelligent docility to their advice, as well as his personal hardihood and energy, compare most favourably with the sloth, ignorance and arrogant conceit of the Turkish generals opposed @@ -22844,8 +22805,8 @@ became imbecile in 1848 he held the regency till his own death on the 10th of November 1848.</p> <div class="condensed"> -<p>See Edouard Gouin, <i>L’gypte au XIX<span class="sp">e</span> sicle</i> (Paris, 1847); Aim -Vingtrinier, <i>Soliman-Pasha</i> (<i>Colonel Sve</i>) (Paris, 1886). A great +<p>See Edouard Gouin, <i>L’Égypte au XIX<span class="sp">e</span> siècle</i> (Paris, 1847); Aimé +Vingtrinier, <i>Soliman-Pasha</i> (<i>Colonel Sève</i>) (Paris, 1886). A great deal of unpublished material of the highest interest with regard to Ibrahim’s personality and his system in Syria is preserved in the British Foreign Office archives; for references to these see <i>Cambridge @@ -22876,7 +22837,7 @@ published his first work, the blank-verse tragedy of <i>Catilina</i>, under the pseudonym Brynjolf Bjarme. A second drama, <i>The Viking’s Barrow</i>, was acted (but not printed) a few months later; Ibsen was at this time entirely under the influence of the -Danish poet Oehlenschlger. During the next year or two he +Danish poet Oehlenschläger. During the next year or two he made a very precarious livelihood in Christiania as a journalist, but in November 1851 he had the good fortune to be appointed “stage-poet” at the little theatre of Bergen, with a small but @@ -22885,7 +22846,7 @@ he also received a travelling stipend. In 1852, therefore, he went for five months to study the stage, to Copenhagen and to Dresden. Among many dramatic experiments which Ibsen made in Bergen, the most considerable and most satisfactory is the -saga-drama of <i>Mistress Inger at straat</i>, which was produced in +saga-drama of <i>Mistress Inger at Östraat</i>, which was produced in 1855; and printed at Christiania in 1857; here are already perceptible some qualities of his mature character. Much less significant, although at the time more successful, is <i>The Feast at @@ -22935,7 +22896,7 @@ which added to his embarrassment. In 1862 his theatre became bankrupt, and he was glad to accept the poorly-paid post of “aesthetic adviser” at the other house. An attempt to obtain a poet’s pension (<i>digtergage</i>) was unsuccessful; the Storthing, -which had just voted one to Bjrnson, refused to do the same for +which had just voted one to Björnson, refused to do the same for Ibsen. His cup was full of disillusion and bitterness, and in April 1864 he started, by Berlin and Trieste, ultimately to settle in Rome. His anger and scorn gave point to the satirical arrows @@ -22965,7 +22926,7 @@ for perfectly natural and yet pregnant dialogue. Ibsen was in Egypt, in October 1869, when his comedy was put on the stage in Christiania, amid violent expressions of hostility; on hearing the news, he wrote his brilliant little poem of defiance, called -<i>At Port Sad</i>. By this time, however, he had become a successful +<i>At Port Saïd</i>. By this time, however, he had become a successful author; <i>Brand</i> sold largely, and has continued to be the most popular of Ibsen’s writings. In 1866, moreover, the Storthing had been persuaded to vote him a “poet’s pension,” and there @@ -22979,7 +22940,7 @@ his writings were for the first time mentioned to the English public. At this time he was revising his old works, which were out of print, and which he would not resign again to the reading world until he had subjected them to what in some instances -(for example, <i>Mistress Inger at straat</i>) amounted to practical +(for example, <i>Mistress Inger at Östraat</i>) amounted to practical recomposition. In 1873 he published a double drama, each part of which was of unusual bulk, the whole forming the tragedy of <i>Emperor and Galilean</i>; this, Ibsen’s latest historical play, has @@ -23061,7 +23022,7 @@ figure of the play is an unhealthy, unlucky enthusiast, who goes <span class="pagenum"><a name="page226" id="page226"></a>226</span> about making hopeless mischief by exposing weak places in the sordid subterfuges of others. This drama contains a figure, -Hjlmar Ekdal, who claims the bad pre-eminence of being the +Hjálmar Ekdal, who claims the bad pre-eminence of being the meanest scoundrel in all drama. <i>The Wild Duck</i> is the darkest, the least relieved, of Ibsen’s studies of social life, and his object in composing it is not obvious. With <i>Rosmersholm</i> (1886) he @@ -23130,17 +23091,17 @@ Sigurd Ibsen, in 1904 (Eng. trans., 1905). Critical studies on the writings and position of Ibsen are innumerable, and only those which were influential in guiding opinion, during the early part of his career, in the various countries, can be mentioned here: -Georg Brandes <i>sthetiske Studier</i> (Copenhagen, 1868); Les Quesnel, -<i>Posie scandinave</i> (Paris 1874); Valfrid Valsenius, <i>Henrik Ibsen</i> +Georg Brandes <i>Ästhetiske Studier</i> (Copenhagen, 1868); Les Quesnel, +<i>Poésie scandinave</i> (Paris 1874); Valfrid Valsenius, <i>Henrik Ibsen</i> (Helsingfors, 1879); Edmund Gosse, <i>Studies in Northern Literature</i> (London, 1879); L. Passarge, <i>Henrik Ibsen</i> (Leipzig, 1883); G. -Brandes, <i>Bjrnson och Ibsen</i> (Stockholm, 1882); Henrik Jaeger, +Brandes, <i>Björnson och Ibsen</i> (Stockholm, 1882); Henrik Jaeger, <i>Henrik Ibsen 1828-1888</i> (Copenhagen, 1888; Eng. trans., 1890); T. Terwey, <i>Henrik Ibsen</i> (Amsterdam, 1882); G. Bernard Shaw, <i>The Quintessence of Ibsen</i> (London, 1892). In France Count Moritz Prozor carried on an ardent propaganda in favour of Ibsen from -1885, and Jules Lematre’s articles in his <i>Les Contemporains</i> and -<i>Impressions de thtre</i> did much to encourage discussion. W. Archer +1885, and Jules Lemaître’s articles in his <i>Les Contemporains</i> and +<i>Impressions de théâtre</i> did much to encourage discussion. W. Archer forwarded the cause in England from 1878 onwards. In Germany Ibsen began to be known in 1866, when John Grieg, P. F. Siebold and Adolf Strodtmann successively drew attention to his early @@ -23175,7 +23136,7 @@ Dorian, the poems breathe the spirit of Aeolian melic poetry.</p> <div class="condensed"> <p>The best editions of the fragments are by F. W. Schneidewin -(1833) and Bergk, <i>Potae lyrici Graeci</i>.</p> +(1833) and Bergk, <i>Poëtae lyrici Graeci</i>.</p> </div> @@ -23239,10 +23200,10 @@ permanency of the ice. The temperature at which water freezes, and also at which ice melts, is so readily determined that it is employed as one of the standard temperatures in the graduation of ordinary thermometer scales, this temperature -being the zero of the Centigrade and Raumur scales, and 32 +being the zero of the Centigrade and Réaumur scales, and 32° of the Fahrenheit (see <span class="sc"><a href="#artlinks">Thermometry</a></span>). In the act of freezing, water, though its temperature remains unchanged, undergoes -a remarkable expansion so that ice at 0 C. is less dense than +a remarkable expansion so that ice at 0° C. is less dense than water—a fact demonstrated by its power of floating. The sub-aqueous retention of “ground-ice” or “anchor-ice,” which forms in certain circumstances at the bottom of streams @@ -23252,21 +23213,21 @@ the streams or pools. As water expands on freezing, so conversely ice contracts on melting; and the ice-cold water thus formed continues to contract when heated until it has reached its point of maximum density, the temperature at which this -occurs being about 39 Fahr, or 4 C. Above this point water +occurs being about 39° Fahr, or 4° C. Above this point water continuously expands, and at no temperature is it less dense than ice as is shown by the following table:—</p> <table class="ws f90" summary="Contents"> -<tr><td class="tcl">Density of ice at</td> <td class="tcr">0C. =  .9175 </td></tr> -<tr><td class="tcl">  ”    water at</td> <td class="tcr">0C. =  .99988</td></tr> -<tr><td class="tcl">  ”     ”</td> <td class="tcr">4C. = 1.00000</td></tr> -<tr><td class="tcl">  ”     ”</td> <td class="tcr">10C. =  .99976</td></tr> -<tr><td class="tcl">  ”     ”</td> <td class="tcr">100C. =  .95866</td></tr> +<tr><td class="tcl">Density of ice at</td> <td class="tcr">0°C. =  .9175 </td></tr> +<tr><td class="tcl">  ”    water at</td> <td class="tcr">0°C. =  .99988</td></tr> +<tr><td class="tcl">  ”     ”</td> <td class="tcr">4°C. = 1.00000</td></tr> +<tr><td class="tcl">  ”     ”</td> <td class="tcr">10°C. =  .99976</td></tr> +<tr><td class="tcl">  ”     ”</td> <td class="tcr">100°C. =  .95866</td></tr> </table> <p>Under the influence of heat, ice itself behaves as most solids do, contracting when cooled, expanding when heated. According -to Plcker, the coefficient of cubical dilatation at moderately +to Plücker, the coefficient of cubical dilatation at moderately low temperatures is 0.0001585. From a series of elaborate experiments, Person deduced 0.505 as the specific heat of ice, or about half that of water.</p> @@ -23281,11 +23242,11 @@ in 1849. He showed that, since water expands on freezing, the laws of thermodynamics require that its freezing-point must be lowered by increase of pressure; and he calculated that for every additional atmosphere of pressure the freezing-point -of water was lowered by 0.0075. This result was verified +of water was lowered by 0.0075°. This result was verified by his brother, Sir William Thomson (Lord Kelvin), in 1850. The Thomsons and H. L. F. Helmholtz successfully applied this behaviour of ice under pressure to the explanation of many -properties of the substance. When two blocks of ice at 0 C. +properties of the substance. When two blocks of ice at 0° C. are pressed together or even simply laid in contact, they gradually unite along their touching surfaces till they form one block. This “regelation” is due to the increased pressure at the various @@ -23302,7 +23263,7 @@ not until the whole mass of water has been cooled down to its point of maximum density, so that the subsequent cooling of the surface can give rise to no convection currents, is freezing possible. Sea-water, in the most favourable circumstances, -does not freeze till its temperature is reduced to about −2 C.; +does not freeze till its temperature is reduced to about −2° C.; and the ice, when formed, is found to have rejected four-fifths of the salt which was originally present. In the upper provinces of India water is made to freeze during cold clear nights by @@ -23346,9 +23307,9 @@ as they set sail. If this does not happen at once it is likely to occur later as the result of the wave-cutting and melting which disturb their equilibrium” (T. C. Chamberlin and R. D. Salisbury, <i>Geology: Processes and their Results</i>, 1905). These bergs carry -a load of dbris from the glacier and gradually strew their load +a load of débris from the glacier and gradually strew their load upon the sea floor. They do not travel far before losing all -stony and earthy dbris, but glacial material found in dredgings +stony and earthy débris, but glacial material found in dredgings shows that icebergs occasionally carry their load far from land. The structure of the iceberg varies with its origin and is always that of the glacier or ice-sheet from which it was broken. The @@ -23365,8 +23326,8 @@ is a simpler matter, as the ice is already floating.</p> <hr class="art" /> <p><span class="bold">ICELAND<a name="ar100" id="ar100"></a></span> (Dan. <i>Island</i>), an island in the North Atlantic Ocean, belonging to Denmark. Its extreme northerly point -is touched by the Arctic Circle; it lies between 13 22′ and 24 -35′ W., and between 63 12′ and 66 33′ N., and has an area of +is touched by the Arctic Circle; it lies between 13° 22′ and 24° +35′ W., and between 63° 12′ and 66° 33′ N., and has an area of 40,437 sq. m. Its length is 298 m. and its breadth 194 m., the shape being a rough oval, broken at the north-west, where a peninsula, diversified by a great number of fjords, projects @@ -23383,9 +23344,9 @@ is absolutely uninhabitable. At the outside, not more than one-fourth of the area of Iceland is inhabited; the rest consists of elevated deserts, lava streams and glaciers. The north-west peninsula is separated from the main mass of the island by the -bays Hunafli and Breiifjrr, so that there are really two +bays Hunaflói and Breiðifjörðr, so that there are really two tablelands, a larger and a smaller. The isthmus which connects -the two is only 4 m. across, but has an altitude of 748 ft. The +the two is only 4¼ m. across, but has an altitude of 748 ft. The <span class="pagenum"><a name="page228" id="page228"></a>228</span> mean elevation of the north-west peninsula is 2000 ft. The fjords and glens which cut into it are shut in by precipitous walls @@ -23393,16 +23354,16 @@ of basalt, which plainly shows that they have been formed by erosion through the mass of the plateau. The surface of this tableland is also bare and desolate, being covered with gravel and fragments of rock. Here and there are large straggling -snowfields, the largest being Glmu and Drangajkull,<a name="fa1j" id="fa1j" href="#ft1j"><span class="sp">1</span></a> on the +snowfields, the largest being Glámu and Drangajökull,<a name="fa1j" id="fa1j" href="#ft1j"><span class="sp">1</span></a> on the culminating points of the plateau. The only inhabited districts are the shores of the fjords, where grass grows capable of supporting sheep; but a large proportion of the population gain their livelihood by fishing. The other and larger tableland, which constitutes the substantial part of Iceland, reaches its culminating -point in the south-east, in the gigantic snowfield of Vatnajkull, +point in the south-east, in the gigantic snowfield of Vatnajökull, which covers 3300 sq. m. The axis of highest elevation of Iceland stretches from north-west to south-east, from the head of -Hvammsfjrr to Hornafjrr, and from this water-parting the +Hvammsfjörðr to Hornafjörðr, and from this water-parting the rivers descend on both sides. The crest of the water-parting is crowned by a chain of snow-capped mountains, separated by broad patches of @@ -23410,15 +23371,15 @@ lower ground. They are really a chain of minor plateaus which rise 4500 to 6250 ft. above sea-level and 2000 to 3000 ft. above the tableland itself. In the extreme east is -Vatnajkull, which is separated from Tungnafellsjkull +Vatnajökull, which is separated from Tungnafellsjökull by Vonarskard (3300 ft.). Between -Tungnafellsjkull and Hofsjkull lies the broad +Tungnafellsjökull and Hofsjökull lies the broad depression of Sprengisandr (2130 ft.). Continuing -north-west, between Hofsjkull and the -next snow-capped mountain, Langjkull, lies -Kjlur (2000 ft.); and between Langjkull -and Eiriksjkull, Flosaskard (2630 ft.). To -the north of the <i>jklar</i> last mentioned there +north-west, between Hofsjökull and the +next snow-capped mountain, Langjökull, lies +Kjölur (2000 ft.); and between Langjökull +and Eiriksjökull, Flosaskard (2630 ft.). To +the north of the <i>jöklar</i> last mentioned there are a number of lakes, all well stocked with fish. Numerous valleys or glens penetrate into the tableland, especially on the north and east, @@ -23426,7 +23387,7 @@ and between them long mountain spurs, sections of the tableland which have resisted the action of erosion, thrust themselves towards the sea. Of these the most considerable is the mass -crowned by Mrdalsjkull, which stretches +crowned by Mýrdalsjökull, which stretches towards the south. The interior of the tableland consists for the most part of barren, grassless deserts, the surface being covered @@ -23435,10 +23396,10 @@ ashes and glacial detritus.</p> <p>Save the lower parts of the larger glens, there are no lowlands on the north and east. The south coast is flat next the sea; -but immediately underneath Vatnajkull there is a strip of +but immediately underneath Vatnajökull there is a strip of gravel and sand, brought down and deposited by the glacial streams. The largest low-lying plain of Iceland, lying between -Mrdalsjkull and Reykjanes, has an area of about 1550 sq. m. +Mýrdalsjökull and Reykjanes, has an area of about 1550 sq. m. In its lowest parts this plain barely keeps above sea-level, but it rises gradually towards the interior, terminating in a ramification of valleys. Its maximum altitude is attained @@ -23448,16 +23409,16 @@ great injury of its inhabited districts, which are thus exposed to the clouds of pumice dust and driftsand that cover large areas of the interior. Nevertheless the greater part of this lowland plain produces good grass, and is relatively well inhabited. The -plain is drained by three rivers—Markarfljt, Thjrs and -Oelfus—all of large volume, and numerous smaller streams. +plain is drained by three rivers—Markarfljót, Thjórsá and +Oelfusá—all of large volume, and numerous smaller streams. Towards the west there exist a number of warm springs. There -is another lowland plain around the head of Faxafli, nearly +is another lowland plain around the head of Faxaflói, nearly 400 sq. m. in extent. As a rule the surface of this second plain is very marshy. Several dales or glens penetrate the central -tableland; the eastern part of this lowland is called Borgarfjrr, -the western part Mrar.</p> +tableland; the eastern part of this lowland is called Borgarfjörðr, +the western part Mýrar.</p> -<p>The great bays on the west of the island (Faxafli and Breiifjrr),<a name="fa2j" id="fa2j" href="#ft2j"><span class="sp">2</span></a> +<p>The great bays on the west of the island (Faxaflói and Breiðifjörðr),<a name="fa2j" id="fa2j" href="#ft2j"><span class="sp">2</span></a> as well as the many bays on the north, which are separated from one another by rocky promontories, appear to owe their origin to subsidences of the surface; whereas the @@ -23471,41 +23432,41 @@ and glaciers. This extraordinary development of ice and snow is due to the raw, moist climate, the large rainfall and the low summer temperature. The snow-line varies greatly in different parts of the island, its range being from 1300 to 4250 ft. It is -highest on the tableland, on the north side of Vatnajkull, and +highest on the tableland, on the north side of Vatnajökull, and lowest on the north-west peninsula, to the south of North Cape. -Without exception the great <i>nvs</i> of Iceland belong to the interior +Without exception the great <i>névés</i> of Iceland belong to the interior tableland. They consist of slightly rounded domes or billowy snowfields of vast thickness. In external appearance they bear a closer resemblance to the glaciers of the Polar regions than -to those of the Alps. The largest snowfields are Vatnajkull -(3280 sq. m.), Hofsjkull (520) Langjkull (500) and Mrdalsjkull +to those of the Alps. The largest snowfields are Vatnajökull +(3280 sq. m.), Hofsjökull (520) Langjökull (500) and Mýrdalsjökull (390). The glaciers which stream off from these snowfields -are often of vast extent, <i>e.g.</i> the largest glacier of Vatnajkull +are often of vast extent, <i>e.g.</i> the largest glacier of Vatnajökull has an area of 150 to 200 sq. m., but the greater number are small. Altogether, more than 120 glaciers are known in Iceland. -It is on the south side of Vatnajkull that they descend lowest; -the lower end of Breidamerkurjkull was in the year 1894 only +It is on the south side of Vatnajökull that they descend lowest; +the lower end of Breidamerkurjökull was in the year 1894 only 30 ft. above sea-level. The glaciers of the north-west peninsula also descend nearly to sea-level. The great number of streams of large volume is due to the moist climate and the abundance of glaciers, and the milky white or yellowish-brown colour of -their waters (whence the common name Hvt, white) is due to +their waters (whence the common name Hvítá, white) is due to the glacial clays. The majority of them change their courses very often, and vary greatly in volume; frequently they are impetuous torrents, forming numerous waterfalls. Iceland also possesses a great number of lakes, the largest being Thingvallavatn<a name="fa3j" id="fa3j" href="#ft3j"><span class="sp">3</span></a> and Thorisvatn, each about 27 sq. m. in area. -Mvatn, in the north, is well known from the natural beauty of +Mývatn, in the north, is well known from the natural beauty of its surroundings. Above its surface tower a great number of volcanoes and several craters, and its waters are alive with water-fowl, a multitude of ducks of various species breeding on its islands. The lakes of Iceland owe their origin to different causes, some being due to glacial erosion, others to volcanic -subsidence. Mvatn fills a depression between lava streams, -and has a depth of not more than 8 ft. The group of lakes -called Fiskivtn (or Veidivtn), which lie in a desolate region -to the west of Vatnajkull, consist for the most part of crater -lakes. The groups of lakes which lie north-west from Langjkull +subsidence. Mývatn fills a depression between lava streams, +and has a depth of not more than 8¾ ft. The group of lakes +called Fiskivötn (or Veidivötn), which lie in a desolate region +to the west of Vatnajökull, consist for the most part of crater +lakes. The groups of lakes which lie north-west from Langjökull occupy basins formed between ridges of glacial gravel; and in <span class="pagenum"><a name="page229" id="page229"></a>229</span> the valleys numerous lakes are found at the backs of the old @@ -23524,11 +23485,11 @@ from which they have flowed, the bulk of the lava dating from outbreaks which occurred in prehistoric times. The largest volume of lava which has issued at one outflow within historic times is the stream which came from the craters of Laki at -Skapt. This belongs to the year 1783, and covers an area of +Skaptá. This belongs to the year 1783, and covers an area of 218 sq. m., and amounts to a volume represented by a cube each -of whose sides measures 7 m. The largest unbroken lava-field -in Iceland is Odaahraun (Lava of Evil Deeds), upon the tableland -north from Vatnajkull (2000 to 4000 ft. above sea-level). +of whose sides measures 7½ m. The largest unbroken lava-field +in Iceland is Odaðahraun (Lava of Evil Deeds), upon the tableland +north from Vatnajökull (2000 to 4000 ft. above sea-level). It is the accretion of countless eruptions from over twenty volcanoes, and covers an area of 1300 sq.m. (or, including all its ramifications and minor detached streams, 1700 sq. m.), and @@ -23543,7 +23504,7 @@ diversified by long twisted “ropes,” curving backwards and forwards up and down the undulations. Moreover, there are gigantic fissures, running for several miles, caused by subsidences of the underlying sections. The best-known fissure of this -character is Almannagj at Thingvellir. On the occasion of +character is Almannagjá at Thingvellir. On the occasion of outbreaks the fine ashes are scattered over a large portion of the island, and sometimes carried far across the Atlantic. After the eruption of Katla in 1625 the ashes were blown as far as @@ -23563,7 +23524,7 @@ After that the island was visited by a famine, which destroyed of ashes, scoriae and lava; (2) cupola-shaped, with an easy slope and a vast crater opening at the top—these shield-shaped cupolas are composed entirely of layers of lava, and their inclination -is seldom steeper than 7-8; (3) chains of craters running +is seldom steeper than 7°-8°; (3) chains of craters running close alongside a fissure in the ground. For the most part the individual craters are low, generally not exceeding 300 to 500 ft. These crater chains are both very common and often very long. @@ -23574,19 +23535,19 @@ fissures in the earth without any crater being formed. Many of the Icelandic volcanoes during their periods of quiescence are covered with snow and ice. Then when an outbreak occurs the snow and ice melt, and in that way they sometimes give -rise to serious catastrophes (<i>jkulhlaup</i>), through large areas +rise to serious catastrophes (<i>jökulhlaup</i>), through large areas being suddenly inundated by great floods of water, which bear masses of ice floating on their surface. Katla caused very serious destruction in this way by converting several cultivated districts into barren wastes. In the same way in the year -1362 Oerfajkull, the loftiest mountain in Iceland (6424 ft.), +1362 Oeræfajökull, the loftiest mountain in Iceland (6424 ft.), swept forty farms, together with their inhabitants and live stock, bodily into the ocean. The best-known volcano is Hekla (5108 ft.), which was in eruption eighteen times within the historic period down to 1845. Katla during the same period was active thirteen times down to 1860. The largest volcano -is Askja, situated in the middle of the lava-field of Odaahraun. -Its crater measures 34 sq. m. in area. At Mvatn there are +is Askja, situated in the middle of the lava-field of Odaðahraun. +Its crater measures 34 sq. m. in area. At Mývatn there are several volcanoes, which were particularly active in the years 1724-1730. On several occasions there have been volcanic outbreaks under the sea outside the peninsula of Reykjanes, islands @@ -23601,10 +23562,10 @@ craters) have only vented themselves in a solitary outburst.</p> <p>Earthquakes are frequent, especially in the districts which are peculiarly volcanic. Historical evidence goes to show that they are closely associated with three naturally defined -regions: (1) the region between Skjlfandi and Axarfjrr +regions: (1) the region between Skjálfandi and Axarfjörðr in the north, where violent earth tremblings are extremely -common; (2) at Faxafli, where minor vibrations are frequent; -(3) the southern lowlands, between Reykjanes and Mrdalsjkull, +common; (2) at Faxaflói, where minor vibrations are frequent; +(3) the southern lowlands, between Reykjanes and Mýrdalsjökull, have frequently been devastated by violent earthquake shocks, with great loss of property and life, <i>e.g.</i> on the 14th-16th of August 1784, when 92 farmsteads were totally destroyed, @@ -23617,13 +23578,13 @@ portion of the southern lowlands, where amongst others is the famous Geyser (<i>q.v.</i>). Sulphur springs and boiling mud lakes are also general in the volcanic districts; and in places there are carbonic acid springs, these more especially on the peninsula -of Snfellsnes, north of Faxafli.</p> +of Snæfellsnes, north of Faxaflói.</p> <div class="condensed"> <p><i>Geology</i>.—Iceland is built up almost entirely of volcanic rocks, none of them older, however, than the middle of the Tertiary period. The earlier flows were probably contemporaneous with those of Greenland, -the Froes, the western islands of Scotland and the north-east +the Færoes, the western islands of Scotland and the north-east of Ireland. The principal varieties are basalt and palagonitic breccias, the former covering two-thirds of the entire area, the latter the remaining one-third. Compared with these two systems, all @@ -23639,7 +23600,7 @@ developed in greatest thickness in the north-west peninsula. Indeed, in some few places well-marked impressions of leaves and fruit have been discovered, proving that in Tertiary times Iceland possessed extensive forests, and its annual mean temperature must have been -at least 48 Fahr., whereas the present mean is 35.6. The palagonitic +at least 48° Fahr., whereas the present mean is 35.6°. The palagonitic breccias, which attain their greatest development in the south of the island and on the tableland, consist of reddish, brown or yellowish rocks, tuffs and breccias, belonging to several different groups or @@ -23648,8 +23609,8 @@ to the Glacial epoch. All over Iceland, in both the basalt and breccia formations, there occur small intrusive beds and dikes of liparite, and as this rock is of a lighter colour than the basalt, it is visible from a distance. In the south-east of the island, in the parish of -Ln, there exist a few mountains of gabbro, a rock which does not -occur in any other part of Iceland. Near Hsavik in the north there +Lón, there exist a few mountains of gabbro, a rock which does not +occur in any other part of Iceland. Near Húsavik in the north there have been found marine deposits containing a number of marine shells; they belong to the Red Crag division of the Pliocene. In the middle of Iceland, where the geological foundation is tuff and @@ -23692,30 +23653,30 @@ south and east the weather is generally changeable, stormy and moist; whilst on the north the rainfall is less. The climate of the interior tableland approximates to the continental type and is often extremely cold. The mean annual temperature is -37.2 F. in Stykkishlmr on Breiifjrr, 38.5 at Eyrārbakki in -the south of Iceland, 41 at Vestmannyjar, 36 at Akureyri in -the north, 36.7 on Berufjrr in the east, and 30.6 at Mdrudalr +37.2° F. in Stykkishólmr on Breiðifjörðr, 38.5° at Eyrārbakki in +the south of Iceland, 41° at Vestmannæyjar, 36° at Akureyri in +the north, 36.7° on Berufjörðr in the east, and 30.6° at Mödrudalr on the central tableland. The range is great not only from year to year, but also from month to month. For instance, at -Stykkishlmr the highest annual mean for March was 39.7, -and the lowest 8, during a period of thirty-eight years. Iceland +Stykkishólmr the highest annual mean for March was 39.7°, +and the lowest 8°, during a period of thirty-eight years. Iceland lies contiguous to that part of the north Atlantic in which the shifting areas of low pressure prevail, so that storms are frequent and the barometer is seldom firm. The barometric pressure at sea-level in the south-west of Iceland during the period 1878-1900 varied between 30.8 and 27.1 in. The climate of the coasts is relatively mild in summer, but tolerably cold in winter. The -winter means of the north and east coasts average 31.7 and -31.3 F. respectively; the summer means, 42.8 and 44.6; -and the means of the year, 33.1 and 35.6. The winter means -of the south and west coasts average 32 and 31.7 respectively; -the summer means, 48.2 and 50; the annual means, 37.4 and -39.2. The rainfall on the south and east coasts is considerable, -<i>e.g.</i> at Vestmannyjar, 49.4 in. in the year; at Berufjrr, -43.6 in. On the west coast it is less, <i>e.g.</i> 24.3 in. at Stykkishlmr; +winter means of the north and east coasts average 31.7° and +31.3° F. respectively; the summer means, 42.8° and 44.6°; +and the means of the year, 33.1° and 35.6°. The winter means +of the south and west coasts average 32° and 31.7° respectively; +the summer means, 48.2° and 50°; the annual means, 37.4° and +39.2°. The rainfall on the south and east coasts is considerable, +<i>e.g.</i> at Vestmannæyjar, 49.4 in. in the year; at Berufjörðr, +43.6 in. On the west coast it is less, <i>e.g.</i> 24.3 in. at Stykkishólmr; but least of all on the north coast, being only 14.6 in. on the island of Grimsey, which lies off that coast. Mist is commonly -prevalent on the east coast; at Berufjrr there is mist on +prevalent on the east coast; at Berufjörðr there is mist on no fewer than 212 days in the year. The south and west coasts are washed by the Gulf Stream, and the north coast by an Arctic current, which frequently brings with it a quantity of drift-ice, @@ -23759,7 +23720,7 @@ in prehistoric times it was common. There are numerous species of seals; and the seas abound in whales. Of birds there are over 100 species, more than one-half being aquatic. In the interior the whistling swan is common, and numerous varieties of ducks are found -in the lakes. The eider duck, which breeds on the islands of Breiifjrr, +in the lakes. The eider duck, which breeds on the islands of Breiðifjörðr, is a source of livelihood to the inhabitants, as are also the many kinds of sea-fowl which breed on the sea-cliffs. Iceland possesses neither reptiles nor batrachians. The fish fauna is abundant @@ -23775,14 +23736,14 @@ population of 70,927, and this number had increased by 1901 to 78,489. The increase during the 19th century was 27,000, while at least 15,600 Icelanders emigrated to America, chiefly to Manitoba, from 1872 to the close of the century. The largest -town is Reykjavik on Faxafli, with 6700 inhabitants, the +town is Reykjavik on Faxaflói, with 6700 inhabitants, the capital of the island, and the place of residence of the governor-general and the bishop. Here the Althing meets; and here, further, are the principal public institutions of the island (library, schools, &c.). The town possesses a statue to Thorvaldsen, the famous sculptor, who was of Icelandic descent. The remaining -towns include Isafjrr (pop. 1000) on the north-west -peninsula, Akureyri (1000) on the north and Seydisfjrr (800) +towns include Isafjörðr (pop. 1000) on the north-west +peninsula, Akureyri (1000) on the north and Seydisfjörðr (800) in the east.</p> <p><i>Industries</i>.—The principal occupation of the Icelanders is @@ -23807,7 +23768,7 @@ boats, notwithstanding the dangers of so stormy a coast. But larger decked vessels have come into increasing use. In summer the waters are visited by a great number of foreign fishermen, inclusive of about 300 fishing-boats from French ports, as well -as by fishing-boats from the Froes and Norway, and steam +as by fishing-boats from the Færoes and Norway, and steam trawlers from England. Excellent profit is made in certain parts of the island from the herring fishery; this is especially the case on the east coast. There are marine insurance societies @@ -23815,7 +23776,7 @@ and a school of navigation at Reykjavik. The export of fish and fish products has greatly increased. In 1849 to 1855 the annual average exported was 1480 tons; whereas at the close of the century (in 1899) it amounted to 11,339 tons and 68,079 barrels -of oil, valued at 276,596.</p> +of oil, valued at £276,596.</p> <p><i>Commerce</i>.—From the first colonization of the island down to the 14th century the trade was in the hands of native Icelanders @@ -23826,23 +23787,23 @@ government; in the latter year it was declared free to all Danish subjects and in 1854 free to all nations. Since 1874, when Iceland obtained her own administration, commerce has increased considerably. Thus the total value of the imports and exports -together in 1849 did not exceed 170,000; while in 1891-1895 -the imports averaged 356,000 and the exports 340,000. In +together in 1849 did not exceed £170,000; while in 1891-1895 +the imports averaged £356,000 and the exports £340,000. In <span class="pagenum"><a name="page231" id="page231"></a>231</span> -1902 imports were valued at 596,193 and exports at 511,083. +1902 imports were valued at £596,193 and exports at £511,083. Trade is almost entirely with Denmark, the United Kingdom, and Norway and Sweden, in this order according to value. The principal native products exported are live sheep, horses, salt meat, wool and hides, to which must be added the fish products—cod, train-oil, herring and salmon—eiderdown and woollen wares. The spinning, weaving and knitting of wool is a widespread -industry, and the native tweed (<i>vamal</i>) is the principal +industry, and the native tweed (<i>vaðmal</i>) is the principal material for the clothing of the inhabitants. The imports consist principally of cereals and flour, coffee, sugar, ale, wines and spirits, tobacco, manufactured wares, iron and metal wares, timber, salt, coal, &c. The money, weights and measures in use are the same as in Denmark. The Islands Bank in Reykjavik -(1904) is authorized to issue bank-notes up to 133,900 +(1904) is authorized to issue bank-notes up to £133,900 in total value.</p> <p><i>Communications</i>.—All land journeys are made on horseback, @@ -23863,7 +23824,7 @@ at nearly every port.</p> <p><i>Religion</i>.—The Icelanders are Lutherans. For ecclesiastical purposes the island is divided into 20 deaneries and 142 parishes, and the affairs of each ecclesiastical parish are administered -by a parish council, and in each deanery by a district (<i>hjera</i>) +by a parish council, and in each deanery by a district (<i>hjerað</i>) council. When a living falls vacant, the governor-general of the island, after consultation with the bishop, selects three candidates, and from these the congregation chooses one, the @@ -23900,21 +23861,21 @@ The minister for Iceland, who resided in Copenhagen until to the king and the Althing for the maintenance of the constitution, and he submits to the king for confirmation the legislative measures proposed by the Althing. The king appoints a governor-general -(<i>landshfingi</i>) who is resident in the island and +(<i>landshöfðingi</i>) who is resident in the island and carries on the government on the responsibility of the minister. Formerly Iceland was divided into four quarters, the east, the south, the west and north. Now the north and the east are united under one governor, and the south and the west under -another. The island is further divided into 18 <i>sslur</i> (counties), +another. The island is further divided into 18 <i>sýslur</i> (counties), and these again into 169 hreppur (rapes) or poor-law districts. -Responsible to the governors are the sheriffs (<i>sslumenn</i>), who +Responsible to the governors are the sheriffs (<i>sýslumenn</i>), who act as tax gatherers, notaries public and judges of first instance; -the sheriff has in every <i>hreppur</i> an assistant, called <i>hreppstjri</i>. +the sheriff has in every <i>hreppur</i> an assistant, called <i>hreppstjóri</i>. In every <i>hreppur</i> there is also a representative committee, who administer the poor laws, and look after the general concerns of the <i>hreppur</i>. These committees are controlled by the committees -of the <i>sslur</i> (county boards), and these again are under -the control of the <i>amtsr</i> (quarter board), consisting of three +of the <i>sýslur</i> (county boards), and these again are under +the control of the <i>amtsráð</i> (quarter board), consisting of three members. From the sheriff courts appeals lie to the superior court at Reykjavik, consisting of three judges. Appeals may be taken in all criminal cases and most civil cases to the supreme @@ -23924,8 +23885,8 @@ court at Copenhagen.</p> of 1874, the right to vote its own supplies. As the Althing only meets every other year, the budget is passed for two years at once. The total income and expenditure are each about -70,000 per financial period. There is a national reserve fund -of about 60,000, but no public debt; nor is there any contribution +£70,000 per financial period. There is a national reserve fund +of about £60,000, but no public debt; nor is there any contribution for either military or naval purposes. Iceland has her own customs service, but the only import duties levied are upon spirits, tobacco, coffee and sugar, and in each case the duties @@ -23942,7 +23903,7 @@ extensive circulation. Eighteen newspapers are issued (once and twice a week), besides several journals, and Iceland has always been distinguished for her native literature. At Reykjavik there are a Latin school, a medical school and a theological -school; at Mdruvellir and Hafnarfjrr, modern high schools +school; at Mödruvellir and Hafnarfjörðr, modern high schools (<i>Realschulen</i>); and in addition to these there are four agricultural schools, a school of navigation, and three girls’ schools. The national library at Reykjavik contains some 40,000 volumes @@ -23956,10 +23917,10 @@ Reykjavik.</p> <p><span class="sc">Authorities</span>.—Among numerous works of Dr Thorvald Thoroddsen, see <i>Geschichte der Islands Geographie</i> (Leipzig, 1898); and the following articles in <i>Geografisk Tidskrift</i> (Copenhagen): -“Om Islands geografiske og geologiske Undersgelse” (1893); +“Om Islands geografiske og geologiske Undersögelse” (1893); “Islandske Fjorde og Bugter” (1901); “Geog. og geol. Unders. -ved den sydlige Del af Faxafli paa Island” (1903); “Lavarkener -og Vulkaner paa Islands Hjland” (1905). See also C. S. Forbes, +ved den sydlige Del af Faxaflói paa Island” (1903); “Lavaörkener +og Vulkaner paa Islands Höjland” (1905). See also C. S. Forbes, <i>Iceland</i> (London, 1860); S. Baring-Gould, <i>Iceland, its Scenes and Sagas</i> (London, 1863); Sir R. F. Burton, <i>Ultima Thule</i> (Edinburgh, 1875); W. T. McCormick, <i>A Ride across Iceland</i> (London, 1892); @@ -23981,7 +23942,7 @@ Culdees), a stream of immigration set in towards it, which lasted for sixty years, and resulted in the establishment of some 4000 homesteads. In this immigration three distinct streams can be traced. (1) About 870-890 four great noblemen from Norway, -Ingolf, Ketil Hng, Skalla-Grim and Thorolf, settled with their +Ingolf, Ketil Hæng, Skalla-Grim and Thorolf, settled with their dependants in the south-west of the new found land. (2) In 890-900 there came from the western Islands Queen Aud, widow of Olaf the White, king of Dublin, preceded and followed by a @@ -24062,7 +24023,7 @@ of Irish blood. In 1100 there were 4500 franklins, <i>i.e.</i> about <p class="pt2">The unit of Icelandic politics was the homestead with its franklin-owner (<i>buendi</i>), its primal organization the hundred-moot -(<i>thing</i>), its tie the goor (godar) or chieftainship. +(<i>thing</i>), its tie the goðorð (godar) or chieftainship. The chief who had led a band of kinsmen and dependants <span class="sidenote">Organization.</span> to the new land, taken a “claim” there, and @@ -24070,10 +24031,10 @@ parcelled it out among them, naturally became their leader, presiding as priest at the temple feasts and sacrifices of heathen times, acting as speaker of their moot, and as their representative towards the neighbouring chiefs. He was not a feudal lord nor -a local sheriff, for any franklin could change his goor when +a local sheriff, for any franklin could change his goðorð when he would, and the rights of “judgment by peers” were in full use; moreover, the office could be bequeathed, sold, divided -or pledged by the possessor; still the goi had considerable +or pledged by the possessor; still the goði had considerable power as long as the commonwealth lasted.</p> <p>Disputes between neighbouring chiefs and their clients, @@ -24119,11 +24080,11 @@ old Common Law was replaced by the New Norse Code “Ironside” in <p>The political life and law of the old days is abundantly illustrated in the sagas (especially Eyrbyggia, Hamsa-Thori, -Reykdla, Hrafnkell, and Niala), the two collections of +Reykdæla, Hrafnkell, and Niala), the two collections of law-scrolls (<i>Codex Regius</i>, <i>c.</i> 1235, and <i>Stadarhol’s Book</i>, c. -1271), the Libellus, the Liberfragments, and the Landnamabk of +1271), the Libellus, the Liberfragments, and the Landnamabók of Ari, and the Diplomatarium. K. Maurer has made the subject his -own in his <i>Beitrge, Island, Grgs</i>, &c.</p> +own in his <i>Beiträge, Island, Grágás</i>, &c.</p> <p>The medieval Icelandic church had two bishoprics, Skalholt (S., W., and E.) 1056, and Holar (N.) 1106, and about 175 parishes @@ -24139,7 +24100,7 @@ the Althing till 1237, enjoyed considerable power; two, Thorlak of Skalholt and John of Holar, were publicly voted saints at the Althing, and one, Gudmund, received the title of “Good” by decree of the bishop and chapter. Full details as to ecclesiastical -history will be found in the <i>Biskupasgur</i> (edited by Dr +history will be found in the <i>Biskupasögur</i> (edited by Dr Vigfusson).</p> <p>Iceland was not agricultural but pastoral, depending upon flocks @@ -24160,7 +24121,7 @@ after the summer, and the long yule feasts at midwinter. There were but two degrees of men, free and unfree, though only the franklins had any political power; and, from the nature of the life, social intercourse was unrestrained and unfettered; -goi and thrall lived the same lives, ate the same food, spoke +goði and thrall lived the same lives, ate the same food, spoke the same tongue, and differed little in clothing or habits. The thrall had a house of his own and was rather villein or serf than slave, having rights and a legal price by law. During the @@ -24187,10 +24148,10 @@ save how to live by as little labour as possible, and pay as few taxes as they could to their foreign rulers. The island received a foreign governor (<i>Earl</i>, <i>Hirdstjori</i> or <i>Stiptamtsmadr</i> as he was successively called), and was parcelled out into -counties (<i>sslur</i>), administered by sheriffs (<i>sslumadr</i>) appointed +counties (<i>sýslur</i>), administered by sheriffs (<i>sýslumadr</i>) appointed by the king. A royal court took the place of the Althing courts; the local business of the local things was carried out by the -(<i>hreppstjri</i>) bailiff, a subordinate of the sheriff; and the goor, +(<i>hreppstjóri</i>) bailiff, a subordinate of the sheriff; and the goðorð, things, quarter-courts, trial by jury, &c., were swept away by these innovations. The power of the crown was increased by the confiscation of the great Sturlung estates, which were underleased @@ -24317,27 +24278,27 @@ groups:—</p> <p>(<i>a</i>) The <i>Helgi</i> trilogy (last third lost save a few verses, but preserved in prose in <i>Hromund Gripsson’s Saga</i>), the <i>Raising of Anganty</i> and <i>Death of Hialmar</i> (in <i>Hervarar Saga</i>), the fragments of a <i>Volsung -Lay</i> (<i>Volsungakiraa</i>) (part interpolated in earlier poems, part underlying +Lay</i> (<i>Volsungakiraða</i>) (part interpolated in earlier poems, part underlying the prose in <i>Volsunga Saga</i>), all by one poet, to whom Dr -Vigfusson would also ascribe <i>Vlusp</i>, <i>Vegtamskvia</i>, <i>rymskvia</i>, -<i>Grtta Song</i> and <i>Vlundarkvia</i>.</p> +Vigfusson would also ascribe <i>Völuspá</i>, <i>Vegtamskviða</i>, <i>Þrymskviða</i>, +<i>Grötta Song</i> and <i>Völundarkviða</i>.</p> -<p>(<i>b</i>) The Dramatic Poems:—<i>Flyting of Loki</i>, the <i>Fr Skirnis</i>, the -<i>Harbarslio</i> and several fragments, all one man’s work, to whose +<p>(<i>b</i>) The Dramatic Poems:—<i>Flyting of Loki</i>, the <i>För Skirnis</i>, the +<i>Harbarðslioð</i> and several fragments, all one man’s work, to whose school belong, probably, the <i>Lay</i> underlying the story of Ivar’s death in <i>Skioldunga Saga</i>.</p> -<p>(<i>c</i>) The Didactic Poetry:—<i>Grmnisml</i>, <i>Vafprunisml</i>, <i>Alvssmal</i>, +<p>(<i>c</i>) The Didactic Poetry:—<i>Grímnismál</i>, <i>Vafpruðnismál</i>, <i>Alvíssmal</i>, &c.</p> -<p>(<i>d</i>) The Genealogical and Mythological Poems:—<i>Hyndluljo</i> +<p>(<i>d</i>) The Genealogical and Mythological Poems:—<i>Hyndluljoð</i> written for one of the Haurda-Kari family, so famous in the Orkneys; <i>Ynglingatal</i> and <i>Haustlong</i>, by Thiodolf of Hvin; <i>Rig’s Thul</i>, &c.</p> <p>(<i>e</i>) The Dirges and Battle Songs—such as that on Hafur-firth -Battle <i>Hrafnsmal</i>, by Thiodolf of Hvin or Thorbjrn Hornklofi, shortly -after 870; Eirik’s Dirge (<i>Erksml</i>) between 950 and 969; the <i>Dart-Lay -on Clontarf Battle</i> (1014); <i>Barka-mal</i> (fragments of which we +Battle <i>Hrafnsmal</i>, by Thiodolf of Hvin or Thorbjörn Hornklofi, shortly +after 870; Eirik’s Dirge (<i>Eíríksmál</i>) between 950 and 969; the <i>Dart-Lay +on Clontarf Battle</i> (1014); <i>Bíarka-mal</i> (fragments of which we have, and paraphrase of more is found in <i>Hrolf Kraki’s Saga</i> and in Saxo).</p> @@ -24348,19 +24309,19 @@ Saga</i>, in the Latin verses of Saxo, and the Shield Lays the early compositions of the Irish Church, and with the 12th-century <i>Lay of Ragnar</i>, <i>Lay of Starkad</i>, <i>The Proverb Song</i> (<i>Havamal</i>) and <i>Krakumal</i>, to which we may add those singular Gloss-poems, the -<i>ulur</i>, which also belong to the Western Isles.</p> +<i>Þulur</i>, which also belong to the Western Isles.</p> <p>To Greenland, Iceland’s farthest colony, founded in the 10th -century, we owe the two <i>Lays of Atli</i>, and probably <i>Hymiskvtia</i>, +century, we owe the two <i>Lays of Atli</i>, and probably <i>Hymiskvtiða</i>, which, though of a weirder, harsher cast, yet belong to the Western Isles school and not to Iceland.</p> </div> -<p>In form all these poems belong to two or three classes:—<i>kvia</i>, -an epic “cantilena”; <i>tl</i>, a genealogical poem; <i>drapa</i>, songs +<p>In form all these poems belong to two or three classes:—<i>kviða</i>, +an epic “cantilena”; <i>tál</i>, a genealogical poem; <i>drapa</i>, songs of praise, &c., written in modifications of the old Teutonic metre which we know in Beowulf; <i>galdr</i> and <i>lokkr</i>, spell and -charm songs in a more lyric measure; and <i>ml</i>, a dialogue +charm songs in a more lyric measure; and <i>mál</i>, a dialogue poem, and <i>liod</i>, a lay, in elegiac measure suited to the subject.</p> <p>The characteristics of this Western school are no doubt the @@ -24405,10 +24366,10 @@ satire or with a sword-thrust, but clinging through all to their art, in which they attained most marvellous skill.</p> <p>Such men were Egil, the foe of Eirik Bloodaxe and the -friend of thelstan; Kormak, the hot-headed champion; +friend of Æthelstan; Kormak, the hot-headed champion; Eyvind, King Haakon’s poet, called Skaldaspillir, because -he copied in his dirge over that king the older and finer <i>Erksml</i>; -Gunnlaug, who sang at thelred’s court, and fell at the +he copied in his dirge over that king the older and finer <i>Eíríksmál</i>; +Gunnlaug, who sang at Æthelred’s court, and fell at the hands of a brother bard, Hrafn; Hallfred, Olaf Tryggvason’s poet, who lies in Iona by the side of Macbeth; Sighvat, Saint Olafs henchman, most prolific of all his comrades; Thormod, @@ -24455,16 +24416,16 @@ and his poet visitors and henchmen. The Icelandic sagas also comprise much verse which is partly genuine, partly the work of the 12th and 13th century editors. Thus there are genuine pieces in <i>Nial’s Saga</i> (chaps. 34, 78, 103, 126, 146), in <i>Eyrbyggia</i>, -<i>Laxdla</i>, <i>Egil’s Saga</i> (part only), <i>Grettla</i> (two and a half stanzas, -cf. <i>Landnamabk</i>), <i>Biorn’s Saga</i>, <i>Gunnlaug’s Saga</i>, <i>Havard’s +<i>Laxdæla</i>, <i>Egil’s Saga</i> (part only), <i>Grettla</i> (two and a half stanzas, +cf. <i>Landnamabók</i>), <i>Biorn’s Saga</i>, <i>Gunnlaug’s Saga</i>, <i>Havard’s Saga</i>, <i>Kormak’s Saga</i>, <i>Viga-Glum’s Saga</i>, <i>Erik the Red’s Saga</i> -and <i>Fostbrdra Saga</i>. In <i>Nial’s</i>, <i>Gisli’s</i> and <i>Droplaug’s Sons’ +and <i>Fostbrædra Saga</i>. In <i>Nial’s</i>, <i>Gisli’s</i> and <i>Droplaug’s Sons’ Sagas</i> there is good verse of a later poet, and in many sagas worthless rubbish foisted in as ornamental.</p> <p>To these may be added two or three works of a semi-literary kind, composed by learned men, not by heroes and warriors. -Such are <i>Konunga-tl</i>, <i>Hugsvinnsml</i> (a paraphrase of Cato’s +Such are <i>Konunga-tál</i>, <i>Hugsvinnsmál</i> (a paraphrase of Cato’s <span class="pagenum"><a name="page235" id="page235"></a>235</span> Distichs), <i>Merlin’s Prophecy</i> (paraphrased from Geoffrey of Monmouth by Gunnlaug the monk), <i>Jomsvikinga-drapa</i> (by @@ -24479,7 +24440,7 @@ which followed the union with Norway, completed a process which had been in force since the end of the 11th century, when it overthrew the old Icelandic poetry in favour of the rimur.</p> -<p>The introduction of the <i>danz</i>, ballads (or <i>fornkvdi</i>, as they +<p>The introduction of the <i>danz</i>, ballads (or <i>fornkvædi</i>, as they are now called) for singing, with a burden, usually relating to a love-tale, which were immensely popular with the people and performed by whole companies at weddings, yule feasts @@ -24494,7 +24455,7 @@ century. These were rhymed but also alliterative, in regular form, with prologue or <i>mansong</i> (often the prettiest part of the whole), main portion telling the tale (mostly derived in early days from the French romances of the Carlovingian, Arthurian -or Alexandrian cycles, or from the mythic or skrk-sgur), and +or Alexandrian cycles, or from the mythic or skrök-sögur), and epilogue. Their chief value to us lies in their having preserved versions of several French poems now lost, and in their evidence as to the feelings and bent of Icelanders in the “Dark Age” @@ -24502,14 +24463,14 @@ of the island’s history. The ring and melody which they all possess is their chief beauty.</p> <p>Of the earliest, <i>Olafsrima</i>, by Einar Gilsson (<i>c.</i> 1350), and the -best, the Aristophanic <i>Skda-rima</i> (<i>c.</i> 1430), by Einar Fostri, +best, the Aristophanic <i>Skída-rima</i> (<i>c.</i> 1430), by Einar Fostri, the names may be given. Rimur on sacred subjects was called “diktur”; of these, on the legends of the saints’ lives, many remain. The most notable of its class is the <i>Lilia</i> of Eystein Asgrimsson, a monk of Holyfell (<i>c.</i> 1350), a most “sweet sounding song.” Later the poems of the famous Jon Arason (b. 1484), last Catholic bishop of Holar (<i>c.</i> 1530), <i>Liomr</i> (“gleam”) -and <i>Pslargrtr</i> (“passion-tears”), deserve mention. Arason +and <i>Píslargrátr</i> (“passion-tears”), deserve mention. Arason is also celebrated as having introduced printing into Iceland.</p> <p>Taste has sunk since the old days; but still this rimur poetry @@ -24521,9 +24482,9 @@ a certain number of <i>kenningar</i> (poetical paraphrases) have survived from the old school even to the present day, though the mass of them have happily perished. The change in the <i>phonesis</i> of the language is well illustrated by the new metres -as compared with the old Icelandic <i>drott-kvdi</i> in its varied +as compared with the old Icelandic <i>drott-kvædi</i> in its varied forms. Most of the older rimur and diktur are as yet unprinted. -Many of the <i>fornkvdi</i> are printed in a volume of the old <i>Nordiske +Many of the <i>fornkvædi</i> are printed in a volume of the old <i>Nordiske Litteralur-Samfund</i>.</p> <p>The effects of the Reformation was deeply felt in Icelandic @@ -24539,21 +24500,21 @@ Reformation hymns, adapted, many of them, from the German, the <i>Holar-book</i>, had preceded them in 1619. There was a good deal of verse-writing of a secular kind, far inferior in every way, during this period. In spite of the many physical distresses -that weighed upon the island, ballads (<i>fornkvdi</i>) were still +that weighed upon the island, ballads (<i>fornkvædi</i>) were still written, ceasing about 1750, rimur composed, and more elaborate compositions published.</p> <p>The most notable names are those of the improvisatore -Stephen the Blind; Thorlak Gudbrandsson, author of <i>Ulfar-Rmur</i>, +Stephen the Blind; Thorlak Gudbrandsson, author of <i>Ulfar-Rímur</i>, d. 1707; John Magnusson, who wrote <i>Hristafla</i>, a didactic poem; Stefan Olafsson, composer of psalms, rimur, -&c., d. 1688; Gunnar Plsson, the author of <i>Gunnarslag</i>, often +&c., d. 1688; Gunnar Pálsson, the author of <i>Gunnarslag</i>, often printed with the Eddic poems, <i>c.</i> 1791; and Eggert Olafsson, traveller, naturalist and patriot, whose untimely death in 1768 was a great loss to his country. His <i>Bunadar-balkr</i>, a Georgic written, like Tusser’s <i>Points</i>, with a practical view of raising the state of agriculture, has always been much prized. -Paul Vidalin’s ditties are very nave and clever.</p> +Paul Vidalin’s ditties are very naïve and clever.</p> <p>Of later poets, down to more recent times, perhaps the best was Sigurd of Broadfirth, many of whose prettiest poems were @@ -24562,9 +24523,9 @@ him, <i>c.</i> 1750; John Thorlaksson’s translation of Milton’s grea epic into Eddic verse is praiseworthy in intention, but, as may be imagined, falls far short of its aim. He also turned Pope’s <i>Essay on Man</i> and Klopstock’s <i>Messiah</i> into Icelandic. -Benedikt Grndal tried the same experiment with Homer in -his <i>Ilion’s Kvdi</i>, <i>c.</i> 1825. There is a fine prose translation -of the <i>Odyssey</i> by Sweinbjrn Egillson, the lexicographer, both +Benedikt Gröndal tried the same experiment with Homer in +his <i>Ilion’s Kvædi</i>, <i>c.</i> 1825. There is a fine prose translation +of the <i>Odyssey</i> by Sweinbjörn Egillson, the lexicographer, both faithful and poetic in high degree.</p> <p><i>Sagas.</i>—The real strength of ancient Icelandic literature is @@ -24625,7 +24586,7 @@ have been faithful, artistic or foolish; for the first generation of MSS. have all perished. We have also complex sagas put together in the 13th century out of the scrolls relating to a given locality, such a group as still exists untouched in <i>Vapnfirdinga</i> -being fused into such a saga as <i>Niala</i> or <i>Laxdla</i>. Of the authors +being fused into such a saga as <i>Niala</i> or <i>Laxdæla</i>. Of the authors nothing is known; we can only guess that some belong to the Sturlung school. According to subject they fall into two classes, those relating to the older generation before Christianity and @@ -24634,7 +24595,7 @@ third generation.</p> <p>Beginning with the sagas of the west, most perfect in style and form, the earliest in subject is that of <i>Gold-Thori</i> (<i>c.</i> 930), -whose adventurous career it relates; <i>Hensa-orissaga</i> tells of +whose adventurous career it relates; <i>Hensa-Þorissaga</i> tells of the burning of Blund-Ketil, a noble chief, an event which led to Thord Gelli’s reforms next year (<i>c.</i> 964); <i>Gislasaga</i> (960-980) tells of the career and death of that ill-fated outlaw; it is beautifully @@ -24643,16 +24604,16 @@ good and appropriate; <i>Hord’s Saga</i> (980) is the life of a band of outlaws on Whalesfirth, and especially of their leader Hord. Of later subject are the sagas of <i>Havard</i> and his revenge for his son, murdered by a neighbouring chief (997-1002); of the -<i>Heiarirgasaga</i> (990-1014), a typical tale of a great blood feud, +<i>Heiðarirgasaga</i> (990-1014), a typical tale of a great blood feud, written in the most primitive prose; of Gunnlaug and Hrafn (<i>Gunnlaugssaga Ormstungu</i>, 980-1008), the rival poets and their ill-starred love. The verse in this saga is important and interesting. To the west also belong the three great complex sagas -<i>Egla</i>, <i>Eyrbyggia</i> and <i>Laxdla</i>. The first (870-980), after +<i>Egla</i>, <i>Eyrbyggia</i> and <i>Laxdæla</i>. The first (870-980), after noticing the migration of the father and grandfather of the hero poet Egil, and the origin of the feud between them and the kings of Norway, treats fully of Egil’s career, his enmity with Eirik -Bloodaxe, his service with thelstan, and finally, after many +Bloodaxe, his service with Æthelstan, and finally, after many adventures abroad, of his latter days in Iceland at Borg, illustrating very clearly what manner of men those great settlers and their descendants were, and the feelings of pride and freedom @@ -24664,7 +24625,7 @@ It includes a mass of information on the law, religion, traditions, real discoverer of Greenland, Biorn of Broadwick, a famous chief, and Snorri, the greatest statesman of his day. Dr Vigfusson would ascribe its editing and completion to Sturla the Lawman, -<i>c.</i> 1250. <i>Laxdla</i> (910-1026) is the saga of Romance. Its +<i>c.</i> 1250. <i>Laxdæla</i> (910-1026) is the saga of Romance. Its heroine Gudrun is the most famous of all Icelandic ladies. Her love for Kiartan the poet, and his career abroad, his betrayal by his friend Bolli, the sad death of Kiartan at his hands, the @@ -24677,12 +24638,12 @@ common with the best works of the Sturlung school.</p> <p>Of the north there are the sagas of <i>Kormak</i> (930-960), most primitive of all, a tale of a wild poet’s love and feuds, containing -many notices of the heathen times; of <i>Vatzdlasaga</i> (890-980), +many notices of the heathen times; of <i>Vatzdælasaga</i> (890-980), relating to the settlement and the chief family in Waterdale; of <i>Hallfred</i> the poet (996-1014), narrating his fortune at King Olafs court, his love affairs in Iceland, and finally his death -and burial at Iona; of <i>Reyk-dla</i> (990), which preserves the -lives of Askell and his son Viga-Skuti; of <i>Svarf-dla</i> (980-990), +and burial at Iona; of <i>Reyk-dæla</i> (990), which preserves the +lives of Askell and his son Viga-Skuti; of <i>Svarf-dæla</i> (980-990), a cruel, coarse story of the old days, with some good scenes in it, unfortunately imperfect, chapters 1-10 being forged; of <i>Viga-Glum</i> (970-990), a fine story of a heathen hero, brave, crafty @@ -24699,8 +24660,8 @@ neighbours are the heroes of these tales, which form a little cycle. The <i>Banda-manna saga</i> (1050-1060), the only comedy among the sagas, is also a northern tale; it relates the struggles of a plebeian who gets a chieftancy against the old families of -the neighbourhood, whom he successfully outwits; <i>l-kofra -attr</i> is a later imitation of it in the same humorous strain. The +the neighbourhood, whom he successfully outwits; <i>Öl-kofra +þattr</i> is a later imitation of it in the same humorous strain. The sagas of the north are rougher and coarser than those of the west, but have a good deal of individual character.</p> @@ -24714,7 +24675,7 @@ of sagas and best of the eastern tales. Of later times there are <i>Droplaug’s Sons’ Saga</i> (997-1007), written probably about 1110, and preserved in the uncouth style of the original (a brother’s revenge for his brother’s death is the substance of it; <i>Brandkrossa -attr</i> is an appendix to it), and the tales of <i>Thorstein +Þattr</i> is an appendix to it), and the tales of <i>Thorstein Hall of Side’s Son</i> (<i>c.</i> 1014) and his brother <i>Thidrandi</i> (<i>c.</i> 996), which belong to the cycle of <i>Hall o’ Side’s Saga</i>, unhappily lost; they are weird tales of bloodshed and magic, with idyllic and @@ -24752,11 +24713,11 @@ Vinland (N. America), are the <i>Floamannasaga</i> (985-990), a good story of the adventures of Thorgils and of the struggles of shipwrecked colonists in Greenland, a <span class="sidenote">Of Greenland and North America.</span> -graphic and terrible picture; and <i>Eirikssaga raua</i> +graphic and terrible picture; and <i>Eirikssaga rauða</i> (990-1000), two versions, one northern (Flatey-book), one western, the better (in <i>Hawk’s Book</i>, and AM. 557), the story of the discovery of Greenland and Vinland (America) by the -Icelanders at the end of the 9th century. Later is the <i>Fostbrdrasaga</i> +Icelanders at the end of the 9th century. Later is the <i>Fostbrædrasaga</i> (1015-1030), a very interesting story, told in a quaint romantic style, of Thorgeir, the reckless henchman of King Olaf, and how his death was revenged in Greenland by his sworn @@ -24766,7 +24727,7 @@ may also be noticed. The lost saga of <i>Poet Helgi</i>, of which only fragments remain, was also laid in Greenland.</p> <p>Besides complete sagas there are embedded in the <i>Heimskringla</i> -numerous small <i>ttir</i> or episodes, small tales of Icelanders’ +numerous small <i>Þættir</i> or episodes, small tales of Icelanders’ adventures, often relating to poets and their lives at the kings’ courts; one or two of these seem to be fragments of sagas now lost. Among the more notable are those of <i>Orm @@ -24774,7 +24735,7 @@ Storolfsson</i>, <i>Ogmund Dijtt</i>, <i>Halldor Snorrason</i>, <i>Thorstein Oxf <i>Hromund Halt</i>, <i>Thorwald Tasaldi</i>, <i>Svadi</i> and <i>Arnor Herlingar-nef</i>, <i>Audunn of Westfirth</i>, <i>Sneglu-Halli</i>, <i>Hrafn of Hrutfiord</i>, <i>Hreidar</i> <span class="pagenum"><a name="page237" id="page237"></a>237</span> -<i>Heimski</i>, <i>Gisli Illugison</i>, <i>Ivar</i> the poet, <i>Gull-su Thord</i>, <i>Einar +<i>Heimski</i>, <i>Gisli Illugison</i>, <i>Ivar</i> the poet, <i>Gull-Æsu Thord</i>, <i>Einar Skulason</i> the poet, <i>Mani</i> the poet, &c.</p> <p>The forged Icelandic sagas appear as early as the 13th century. @@ -24782,7 +24743,7 @@ They are very poor, and either worked up on hints given in genuine stories or altogether apocryphal.</p> <p><i>History.</i>—About the year of the battle of Hastings was born -Ari Froi Thorgilsson (1067-1148), one of the blood of Queen +Ari Froði Thorgilsson (1067-1148), one of the blood of Queen Aud, who founded the famous historical school of Iceland, and himself produced its greatest monument in a work which can be compared for value with the English Domesday Book. @@ -24794,25 +24755,25 @@ tradition that was already dying out in his day. And perhaps it is the highest praise of all to him that he wrote in his own “Danish tongue,” and so ensured the use of that tongue by the cultured of after generations. Ari’s great works are -<i>Konungabk</i>, or <i>The Book of Kings</i>, relating the history of the +<i>Konungabók</i>, or <i>The Book of Kings</i>, relating the history of the kings of Norway from the rise of the Yngling dynasty down to the death of Harald Sigurdsson in the year of his own birth. This book he composed from the dictation of old men such as Odd Kolsson, from the genealogical poems, and from the various dirges, battle-songs and eulogia of the poets. It is most probable that he also compiled shorter <i>Kings’ Books</i> -relating to Denmark and perhaps to England. The <i>Konungabk</i> +relating to Denmark and perhaps to England. The <i>Konungabók</i> is preserved under the <i>Heimskringla</i> of Snorri Sturloson, parts of it almost as they came from Ari’s hands, for example <i>Ynglinga</i> and <i>Harald Fairhair’s Saga</i>, and the prefaces stating the plan and critical foundations of the work, parts of it only used as a framework for the magnificent superstructure of the lives of the two Olafs, and of Harald Hardrada and his nephew Magnus -the Good. The best text of Ari’s <i>Konungabk</i> (<i>Ynglinga</i>, and +the Good. The best text of Ari’s <i>Konungabók</i> (<i>Ynglinga</i>, and the sagas down to but not including Olaf Tryggvason’s) is that -of <i>Frisbk</i>.</p> +of <i>Frisbók</i>.</p> -<p>The <i>Book of Settlements</i> (<i>Landnamabk</i>) is a wonderful performance, +<p>The <i>Book of Settlements</i> (<i>Landnamabók</i>) is a wonderful performance, both in its scheme and carrying out. It is divided into five parts, the first of which contains a brief account of the discovery of the island; the other four, one by one taking @@ -24827,19 +24788,19 @@ is breathed into the whole, astonish the reader, when he reflects that this colossal task was accomplished by one man, for his collaborator Kolsegg merely filled up his plan with regard to part of the east coast, a district with which Ari in his western -home at Stad was little familiar. <i>Landnamabk</i> has reached us +home at Stad was little familiar. <i>Landnamabók</i> has reached us in two complete editions, one edited by Sturla, who brought down the genealogies to his own grandfather and grandmother, Sturla and Gudny, and one by Hawk, who traces the pedigrees still later to himself.</p> -<p>Ari also wrote a <i>Book of Icelanders</i> (<i>Islendingabk</i>, <i>c.</i> 1127), +<p>Ari also wrote a <i>Book of Icelanders</i> (<i>Islendingabók</i>, <i>c.</i> 1127), which has perished as a whole, but fragments of it are embedded in many sagas and <i>Kings’ Lives</i>; it seems to have been a complete epitome of his earlier works, together with an account of the constitutional history, ecclesiastical and civil, of Iceland. An abridgment of the latter part of it, the little <i>Libellus Islandorum</i> -(to which the title of the bigger <i>Liber—Islendingabk</i>—is +(to which the title of the bigger <i>Liber—Islendingabók</i>—is often given), was made by the historian for his friends Bishops Ketil and Thorlak, for whom he wrote the <i>Liber</i> (<i>c.</i> 1137). This charming little book is, with the much later collections of laws, @@ -24857,7 +24818,7 @@ of good memory and a speaker of the truth.” If Thucydides is justly accounted the first political historian, Ari may be fitly styled the first of scientific historians.</p> -<p>A famous contemporary and friend of Ari is Smund (1056-1131), +<p>A famous contemporary and friend of Ari is Sæmund (1056-1131), a great churchman, whose learning so impressed his age that he got the reputation of a magician. He was the friend of Bishop John, the founder of the great Odd-Verjar family, and @@ -24874,14 +24835,14 @@ of Sigurd Evil-deacon and the sons of Harold Gille, in his collections of <i>Kings’ Lives</i>, <i>Morkin-skinna</i>, &c. Karl Jonsson, abbot of Thingore, the Benedictine minister, wrote (<i>c.</i> 1184) <i>Sverrissaga</i> from the lips of that great king, a fine racy biography, -with a style and spirit of its own. <i>Bglunga-Sgur</i> tell the +with a style and spirit of its own. <i>Böglunga-Sögur</i> tell the story of the civil wars which followed Sverri’s death. They are probably by a contemporary.</p> <p>The Latin <i>Lives of St Olaf</i>, Odd’s in Latin (<i>c.</i> 1175), compiled from original authorities, and the <i>Legendary Life</i>, by another monk whose name is lost, are of the medieval Latin school of -Smund to which Gunnlaug belonged.</p> +Sæmund to which Gunnlaug belonged.</p> <p>Snorri Sturlason (<i>q.v.</i>) was known to his contemporaries as a statesman and poet; to us he is above all an historian. Snorri @@ -24913,7 +24874,7 @@ of Snorri’s style.</p> <p><i>Agrip</i> is a 12th-century compendium of the <i>Kings’ Lives</i> from Harald Fairhair to Sverri, by a scholastic writer of the school of -Smund. As the only Icelandic abridgment of Norwegian +Sæmund. As the only Icelandic abridgment of Norwegian history taken not from Snorri but sources now lost, it is of worth. Its real title is <i>Konunga-tal</i>.</p> @@ -24927,7 +24888,7 @@ here for completeness.</p> <p>Styrmi Karason, a contemporary of Snorri’s, dying in 1245, was a distinguished churchman (lawman twice) and scholar. He wrote a <i>Life of St Olaf</i>, now lost; his authority is cited. -He also copied out <i>Landnamabk</i> and <i>Sverri’s Life</i> from his +He also copied out <i>Landnamabók</i> and <i>Sverri’s Life</i> from his MSS., of which surviving copies were taken.</p> <p>Sturla, Snorri’s nephew, wrote the <i>Hakonssaga</i> and <i>Magnussaga</i> @@ -24968,7 +24929,7 @@ and a few episodes such as the <i>Burning of Bishop Adam</i>. A scholastic sketch of the rise of the Scandinavian empire, the <i>Foundation of Norway</i>, dating <i>c.</i> 1120, is prefixed to the whole.</p> -<p><i>Freyinga</i> tells the tale of the conversion of the Freys +<p><i>Færeyinga</i> tells the tale of the conversion of the Færeys or Faroes, and the lives of its chiefs Sigmund and Leif, composed in the 13th century from their separate sagas by an Icelander of the Sturlung school.</p> @@ -24995,7 +24956,7 @@ of the great Sturlung family, down to the settlement of his great lawsuit by Jon Loptsson, who thereupon took his son Snorri the historian to fosterage,—a humorous story but with traces of the decadence about it, and glimpses of the evil days -that were to come; of the <i>nundar-brennusaga</i> (1185-1200), a +that were to come; of the <i>Önundar-brennusaga</i> (1185-1200), a tale of feud and fire-raising in the north of the island, the hero of which, Gudmund Dyri, goes at last into a cloister; of <i>Hrafn Sveinbiornsson</i> (1190-1213), the noblest Icelander of his day, @@ -25003,7 +24964,7 @@ warrior, leech, seaman, craftsman, poet and chief, whose life at home, travels and pilgrimages abroad (Hrafn was one of the first to visit Becket’s shrine), and death at the hands of a foe whom he had twice spared, are recounted by a loving friend -in pious memory of his virtues, <i>c.</i> 1220; of <i>ron Hiorleifsson</i> +in pious memory of his virtues, <i>c.</i> 1220; of <i>Áron Hiorleifsson</i> (1200-1255), a man whose strength, courage and adventures befit rather a henchman of Olaf Tryggvason than one of King Haakon’s thanes (the beginning of the feuds that rise round @@ -25050,7 +25011,7 @@ his place in the first rank of Icelandic writers.</p> <p>Of the ecclesiastical biographers, an anonymous Skalholt clerk is the best. He wrote <i>Hungrvaka</i>, lives of the first five bishops of Skalholt, and biographies of his patron Bishop Paul -(<i>Plssaga</i>) and also of St Thorlak (<i>Thorlakssaga</i>). They are +(<i>Pálssaga</i>) and also of St Thorlak (<i>Thorlakssaga</i>). They are full of interesting notices of social and church life. Thorlak was a learned man, and had studied at Paris and Lincoln, which he left in 1161. These lives cover the years 1056-1193. The @@ -25100,7 +25061,7 @@ like Lawman Hauk they would have perished entirely.</p> <p>The Norwegian kings, Haakon Haakonson (<i>c.</i> 1225), and Haakon V. (<i>c.</i> 1305), employed Icelanders at their courts in translating the French romances of the Alexander, Arthur and Charlemagne -cycles. Some forty or fifty of these <i>Riddara-Sgur</i> (Romances +cycles. Some forty or fifty of these <i>Riddara-Sögur</i> (Romances of Chivalry) remain. They reached Iceland and were eagerly read, many Rimur being founded on them. Norse versions of <i>Mary of Brittany’s Lays</i>, the stories of <i>Brutus</i> and of <i>Troy</i>, and @@ -25117,17 +25078,17 @@ abbot of Thwera (d. 1158), complete the list of scientific works.</p> <p>The stories which contain the last lees of the old mythology and pre-history seem to be also non-Icelandic, but amplified by Icelandic editors, who probably got the plots from the Western -Islands. <i>Vlsunga Saga</i> and <i>Hervarar Saga</i> contain quotations +Islands. <i>Völsunga Saga</i> and <i>Hervarar Saga</i> contain quotations and paraphrases of lays by the Helgi poet, and <i>Half’s</i>, <i>Ragnar’s</i> and <i>Asmund Kappabana’s Sagas</i> all have bits of Western poetry in them. <i>Hrolf Kraki’s Saga</i> paraphrases part of <i>Biarkamal</i>; <i>Hromund Gripsson’s</i> gives the story of Helgi and Kara (the lost third of the Helgi trilogy); <i>Gautrek’s Arrow Odd’s</i>, <i>Frithiof’s Sagas</i>, &c., contain shreds of true tradition amidst a mass of -later fictitious matter of no worth. With the <i>Riddara-Sgur</i> +later fictitious matter of no worth. With the <i>Riddara-Sögur</i> they enjoyed great popularity in the 15th century, and gave matter for many Rimur. <i>Thidrek’s Saga</i>, a late version of the -Vlsung story, is of Norse composition (<i>c.</i> 1230), from North +Völsung story, is of Norse composition (<i>c.</i> 1230), from North German sources.</p> <p>The medieval religious literature of Western Europe also @@ -25143,7 +25104,7 @@ Priest Berg Gunsteinsson (d. 1211); Kygri-Biorn, bishop-elect (d. 1237); Bishop Brand (d. 1264); Abbot Runolf (d. 1307); Bishop Lawrence’s son Arni (<i>c.</i> 1330); Abbot Berg (<i>c.</i> 1340), &c. A paraphrase of the historical books of the Bible was made by -Bishop Brand (d. 1264), called <i>Gydinga Sgur</i>. About 1310 +Bishop Brand (d. 1264), called <i>Gydinga Sögur</i>. About 1310 King Haakon V. ordered a commentary on the Bible to be made, which was completed down to Exodus xix. To this Brand’s work was afterwards affixed, and the whole is known as <i>Stiorn</i>. @@ -25153,7 +25114,7 @@ for Prince Haakon (<i>c.</i> 1240), must not be forgotten.</p> <p><i>Post-classical Literature.</i>—The post-classical literature falls chiefly under three heads—religious, literary and scientific. Under the first comes foremost the noble translation of the New -Testament by Odd Gottskalksson, son of the bishop of Hlar. +Testament by Odd Gottskalksson, son of the bishop of Hólar. Brought up in Norway, he travelled in Denmark and Germany, and took upon him the new faith before he returned to Iceland, where he became secretary to Bishop Ogmund of Skalholt. Here @@ -25170,7 +25131,7 @@ by John Matthewson, at Breidabolstad, in Hunafloe, and a it in 1562. In 1584 Bishop Gudbrand, who had brought over a splendid fount of type from Denmark in 1575 (which he completed with his own hands), printed a translation of the whole -Bible at Hlar, incorporating Odd’s versions and some books +Bible at Hólar, incorporating Odd’s versions and some books (Proverbs and the Son of Sirach, 1580) translated by Bishop Gizar, but supplying most of the Old Testament himself. This fine volume was the basis of every Bible issued for Iceland till @@ -25255,22 +25216,22 @@ mass of documents, 870-1740. It has been continued by Bishop P. Peterson to modern times, 1740-1840. The results, however, of modern observers and scholars must be sought for in the periodicals, <i>Safn</i>, <i>Felagsrit</i>, <i>Ny Felagsrit</i> and others. John -Espolin’s <i>Arbkr</i> is very good up to its date, 1821.</p> +Espolin’s <i>Arbækr</i> is very good up to its date, 1821.</p> <div class="condensed"> <p>A brilliant sketch of Icelandic classic literature is given by Dr Gudbrandr Vigfusson in the Prolegomena to <i>Sturlunga Saga</i> (Oxford, 1879). It replaces much earlier work, especially the <i>Sciagraphia</i> -of Halfdan Einarsson (1777), and the <i>Saga-Bibliotek</i> of Mller. +of Halfdan Einarsson (1777), and the <i>Saga-Bibliotek</i> of Müller. The numerous editions of the classics by the Icelandic societies, -the Danish Socit des Antiquits, Nordiske Litteratur Samfund, +the Danish Société des Antiquités, Nordiske Litteratur Samfund, and the new Gammel Nordisk Litteratur Samfund, the splendid Norwegian editions of Unger, the labours of the Icelanders Sigurdsson and Gislason, and of those foreign scholars in Scandinavia and Germany who have thrown themselves into the work of illustrating, publishing and editing the sagas and poems (men like P. A. Munch, -S. Bugge, F. W. Bergmann, Th. Mbius and K. von Maurer, to name -only a few), can only be referred to here. See also Finnur Jnsson, +S. Bugge, F. W. Bergmann, Th. Möbius and K. von Maurer, to name +only a few), can only be referred to here. See also Finnur Jónsson, <i>Den Oldnorske og Oldislanske Litteraturs Historie</i> (Copenhagen, 1893-1900); R. B. Anderson’s translation (Chicago, 1884) of Winkel Horn’s <i>History of the Literature of the Scandinavian North</i>; and W. @@ -25283,68 +25244,68 @@ Morris and E. Magnusson’s <i>Saga Library</i>.</p> <p>The recent literature of Iceland has been in a more flourishing state than ever before since the 13th century. Lyrical poetry is by far the largest and the most interesting portion of it. The -great influence of Jnas Hallgrmsson (1807-1845) is still felt, +great influence of Jónas Hallgrímsson (1807-1845) is still felt, and his school was the reigning one up to the end of the 19th century, although then a change seemed to be in sight. The -most successful poet of this school is Steingrmr Thorsteinsson +most successful poet of this school is Steingrímr Thorsteinsson (b. 1830). He is specially famous for his splendid descriptions of scenery (<i>The Song of Gilsbakki</i>), his love-songs and his sarcastic epigrams. As a translator he has enriched the literature with <i>The Arabian Nights</i>, <i>Sakuntala</i>, <i>King Lear</i> and several other masterpieces of foreign literature. Equal in fame is -Matthas Jochumsson (b. 1835), who, following another of -Jnas Hallgrmsson’s many ways, has successfully revived the +Matthías Jochumsson (b. 1835), who, following another of +Jónas Hallgrímsson’s many ways, has successfully revived the old metres of the classical Icelandic poets, whom he resembles in his majestic, but sometimes too gorgeous, language. He is -as an artist inferior to Steingrmr Thorsteinsson, but surpasses +as an artist inferior to Steingrímr Thorsteinsson, but surpasses him in bold flight of imagination. He has successfully treated -subjects from Icelandic history <i>Grettislj</i>, a series of poems +subjects from Icelandic history <i>Grettisljóð</i>, a series of poems about the famous outlaw Grettir. His chief fault is a certain carelessness in writing; he can never write a bad poem, but -rarely a poem absolutely flawless. He has translated Tegnr’s +rarely a poem absolutely flawless. He has translated Tegnér’s <i>Frithiofs Saga</i>, several plays of Shakespeare and some other foreign masterpieces. The great religious poet of Iceland, -Hallgrmr Ptursson, has found a worthy successor in Valdemar +Hallgrímr Pétursson, has found a worthy successor in Valdemar Briem (b. 1848), whose <i>Songs of the Bible</i> are deservedly -popular. He is like Matthas Jochumsson in the copious flow +popular. He is like Matthías Jochumsson in the copious flow of his rhetoric; some of his poems are perfect both as regards form and contents, but he sometimes neglects the latter while polishing the former. An interesting position is occupied by -Benedict Grndal (b. 1826), whose travesties of the old -romantic stories,<a name="fa7j" id="fa7j" href="#ft7j"><span class="sp">7</span></a> and his Aristophanic drama <i>Gandreiin</i> +Benedict Gröndal (b. 1826), whose travesties of the old +romantic stories,<a name="fa7j" id="fa7j" href="#ft7j"><span class="sp">7</span></a> and his Aristophanic drama <i>Gandreiðin</i> (“The Magic Ride”) about contemporary events, are among the best satirical and humorous productions of Icelandic literature.</p> -<p>Influenced by Jnas Hallgrmsson with regard to language +<p>Influenced by Jónas Hallgrímsson with regard to language and poetic diction, but keeping unbroken the traditions of -Icelandic medieval poetry maintained by Sigurr Breifjr +Icelandic medieval poetry maintained by Sigurðr Breiðfjörð (1798-1846), is another school of poets, very unlike the first. In the middle of the 19th century this school was best represented -by Hjlmar Jnsson from Bla (1796-1875), a poor farmer +by Hjálmar Jónsson from Bóla (1796-1875), a poor farmer with little education, but endowed with great poetical talents, and the author of satirical verses not inferior to those of Juvenal both in force and coarseness. In the last decades of the 19th century this school produced two poets of a very high order, -both distinctly original and Icelandic. One is Pll Olafsson +both distinctly original and Icelandic. One is Páll Olafsson (b. 1827). His songs are mostly written in the medieval quatrains (<i>ferskeytla</i>), and are generally of a humorous and satirical character; his convivial songs are known by heart by every modern Icelander; and although some of the poets of the present day are more admired, there is none who is -more loved by the people. The other is orsteinn Erlingsson +more loved by the people. The other is Þorsteinn Erlingsson (b. 1858). His exquisite satirical songs, in an easy and elegant but still manly and splendid language, have raised much discussion. Of his poems may be mentioned <i>The Oath</i>, a series of most beautiful ballads, with a tragical love-story of the 17th century as their base, but with many and happy satirical allusions -to modern life; <i>Jrundr</i>, a long poem about the convict king, -the Danish pirate Jrgensen, who nearly succeeded in making +to modern life; <i>Jörundr</i>, a long poem about the convict king, +the Danish pirate Jörgensen, who nearly succeeded in making himself the master of Iceland, and <i>The Fate of the Gods</i> and <i>The Men of the West</i> (the Americans), two poems which, with their anti-clerical and half-socialistic tendencies, have caused strong protests from orthodox Lutheran clergy. Near to this school, -but still standing apart, is Grmur Thomsen (b. 1820).</p> +but still standing apart, is Grímur Thomsen (b. 1820).</p> <p>In the beginning of the ’eighties a new school arose—having its origin in the colony of Icelandic students at the University @@ -25352,9 +25313,9 @@ of Copenhagen. They had all attended the lectures of Georg Brandes, the great reformer of Scandinavian literature, and, influenced by his literary theories, they chose their models in the realistic school. This school is very dissimilar from the -half-romantic school of Jnas Hallgrmsson; it is nearer the -national Icelandic school represented by Pll Olafsson and -orsteinn Erlingsson, but differs from those writers by introducing +half-romantic school of Jónas Hallgrímsson; it is nearer the +national Icelandic school represented by Páll Olafsson and +Þorsteinn Erlingsson, but differs from those writers by introducing foreign elements hitherto unknown in Icelandic literature, and—especially in the case of the prose-writers—by imitating closely the style and manner of some of the great Norwegian @@ -25372,63 +25333,63 @@ adopted from foreign languages, sometimes invented by himself, a thing practised rarely and generally with small success by the Icelandic poets.</p> -<p>No Icelandic novelist has as yet equalled Jn Throddsen +<p>No Icelandic novelist has as yet equalled Jón Thóroddsen (1819-1868). The influence of the realistic school has of late been predominant. The most distinguished writer of that -school has been Gestur Plsson (1852-1891), whose short stories +school has been Gestur Pálsson (1852-1891), whose short stories with their sharp and biting satire have produced many imitations in Iceland. The best are <i>A Home of Love</i> and <i>Captain Sigurd</i>. -Jnas Jnasson (b. 1856), a clergyman of northern Iceland, +Jónas Jónasson (b. 1856), a clergyman of northern Iceland, has, in a series of novels and short stories, given accurate, but somewhat dry, descriptions of the more gloomy sides of Icelandic -country life. His best novel is <i>Randir from Hvassafell</i>, an +country life. His best novel is <i>Randiðr from Hvassafell</i>, an historical novel of the middle ages. Besides these we may -mention Torfhildur Hlm, one of the few women who have +mention Torfhildur Hólm, one of the few women who have distinguished themselves in Icelandic literature. Her novels are mostly historical. The last decade of the 19th century saw the establishment of a permanent theatre at Reykjavik. -The poet Matthas Jochumsson has written several dramas, +The poet Matthías Jochumsson has written several dramas, but their chief merits are lyrical. The most successful of Icelandic -dramatists as yet is Indri Einarsson, whose plays, chiefly +dramatists as yet is Indrði Einarsson, whose plays, chiefly historical, in spite of excessive rhetoric, are very interesting and possess a true dramatic spirit.</p> -<p>In geography and geology orvaldr Thoroddsen has acquired +<p>In geography and geology Þorvaldr Thoroddsen has acquired a European fame for his researches and travels in Iceland, especially in the rarely-visited interior. Of his numerous writings in Icelandic, Danish and German, the <i>History of</i> <span class="pagenum"><a name="page241" id="page241"></a>241</span> -<i>Icelandic Geography</i> is a monumental work. In history Pll -Melste’s (b. 1812) chief work, the large <i>History of the World</i>, +<i>Icelandic Geography</i> is a monumental work. In history Páll +Melsteð’s (b. 1812) chief work, the large <i>History of the World</i>, belongs to this period, and its pure style has had a beneficial influence upon modern Icelandic prose.</p> -<p>Of the younger historians we may mention orkell Bjarnason -(<i>History of the Reformation in Iceland</i>). Jn orkelsson (b. +<p>Of the younger historians we may mention Þorkell Bjarnason +(<i>History of the Reformation in Iceland</i>). Jón Þorkelsson (b. 1822), inspector of the archives of Iceland, has rendered great services to the study of Icelandic history and literature by his editions of the <i>Diplomatarium Islandicum</i> and <i>Obituarium Islandicum</i>, and by his <i>Icelandic Poetry in the 15th and 16th Century</i>, written in Danish, an indispensable work for any student of that period. A leading position among Icelandic lexicographers -is occupied by Jn orkelsson, formerly head of the Latin school -at Reykjavik, whose <i>Supplement til islandske Ordbger</i>, an +is occupied by Jón Þorkelsson, formerly head of the Latin school +at Reykjavik, whose <i>Supplement til islandske Ordbøger</i>, an Icelandic-Danish vocabulary (three separate collections), has hardly been equalled in learning and accuracy. Other distinguished philologists are his successor as head of the Latin -school, Bjrn Magnsson Olsen (<i>Researches on Sturlunga</i>, <i>Ari +school, Bjôrn Magnússon Olsen (<i>Researches on Sturlunga</i>, <i>Ari the Wise</i>, <i>The Runes in the Old Icelandic Literature</i>—the last -two works in Danish); Finnur Jnsson, professor at the University +two works in Danish); Finnur Jónsson, professor at the University of Copenhagen (<i>History of the Old Norwegian and Icelandic Literature</i>, in Danish, and excellent editions of many old -Icelandic classical works); and Valtr Gumundsson, lecturer +Icelandic classical works); and Valtýr Guðmundsson, lecturer at the University of Copenhagen (several works on the old architecture of Scandinavia) and editor of the influential Icelandic -literary and political review, <i>Eimreiin</i> (“The Locomotive”).</p> +literary and political review, <i>Eimreiðin</i> (“The Locomotive”).</p> <div class="condensed"> <p>See J. C. Poestion, <i>Islandische Dichter der Neuzeit</i> (Leipzig, 1897); -C. Kchler, <i>Geschichte der islndischen Dichtung der Neuzeit</i> (Leipzig, +C. Küchler, <i>Geschichte der isländischen Dichtung der Neuzeit</i> (Leipzig, 1896); Ph. Schweitzer, <i>Island; Land und Leute</i> (Leipzig, 1885); Alexander Baumgartner, <i>Island und die Faroer</i> (Freiburg im Breisgau, 1889).</p> @@ -25437,9 +25398,9 @@ Alexander Baumgartner, <i>Island und die Faroer</i> (Freiburg im Breisgau, <hr class="foot" /> <div class="note"> -<p><a name="ft1j" id="ft1j" href="#fa1j"><span class="fn">1</span></a> <i>Jkull</i>, plural <i>jklar</i>, Icel. snowfield, glacier.</p> +<p><a name="ft1j" id="ft1j" href="#fa1j"><span class="fn">1</span></a> <i>Jökull</i>, plural <i>jöklar</i>, Icel. snowfield, glacier.</p> -<p><a name="ft2j" id="ft2j" href="#fa2j"><span class="fn">2</span></a> <i>Fli</i>, bay; <i>fjrr</i>, fjord.</p> +<p><a name="ft2j" id="ft2j" href="#fa2j"><span class="fn">2</span></a> <i>Flói</i>, bay; <i>fjörðr</i>, fjord.</p> <p><a name="ft3j" id="ft3j" href="#fa3j"><span class="fn">3</span></a> <i>Vatn</i>, lake.</p> @@ -25451,12 +25412,12 @@ Alexander Baumgartner, <i>Island und die Faroer</i> (Freiburg im Breisgau, the <i>History</i> of Finn Jonsson are the best authority.</p> <p><a name="ft6j" id="ft6j" href="#fa6j"><span class="fn">6</span></a> Many of these poems were Englished in prose by the translator -of Mallet, by B. Thorpe in his <i>Smund’s Edda</i>, and two or three +of Mallet, by B. Thorpe in his <i>Sæmund’s Edda</i>, and two or three by Messrs Morris and Magnussen, as appendices to their translation of <i>Volsunga Saga</i>. Earlier translations in verse are those in Dryden’s <i>Miscellany</i> (vol. vi), A. Cottle’s <i>Edda</i>, Mathias’s <i>Translations</i>, and W. Herbert’s <i>Old Icelandic Poetry</i>. Gray’s versions of <i>Darradar-liod</i> -and <i>Vegtamskvia</i> are well known.</p> +and <i>Vegtamskviða</i> are well known.</p> <p><a name="ft7j" id="ft7j" href="#fa7j"><span class="fn">7</span></a> E.g. “The Battle of the Plains of Death,” a burlesque on the battle of Solferino.</p> @@ -25578,12 +25539,12 @@ The best woods for these pieces are basswood, butternut and pine. They are cut from the log in such a way that the heart of the timber expands, giving the planks a permanent curve, which, in the finished boat, is turned upward. The two forward runners, -usually made of soft cast iron and about 2 ft. 7 in. long and 2 +usually made of soft cast iron and about 2 ft. 7 in. long and 2½ in. high, are set into oak frames a little over 5 ft. long and 5 in. high. The runners have a cutting edge of 90%, though a <b>V</b>-shaped edge is often preferred for racing. The rudder is a runner about 3 ft. 7 in. long, worked by a tiller, sometimes made -very long, 7 ft. not being uncommon. This enables the helmsman +very long, 7½ ft. not being uncommon. This enables the helmsman to lie in the box at full length and steer with his feet, leaving his hands free to tend the sheet. Masts and spars are <span class="pagenum"><a name="page242" id="page242"></a>242</span> @@ -25658,8 +25619,8 @@ Tobogganing, &c.</i> in the “Badminton Library.”</p> <hr class="art" /> <p><span class="bold">I-CH‘ANG<a name="ar104" id="ar104"></a></span> (<span class="sc">Yi-ch‘ang</span>, anciently known as <i>Yi-ling</i>), a town of China in the province of Hu-peh, one of the four ports opened -to foreign trade by treaty in 1877. It is situated in 30 42′ N. -and (approximately) 111 20′ E., on the Yangtsze-Kiang, 1000 m. +to foreign trade by treaty in 1877. It is situated in 30° 42′ N. +and (approximately) 111° 20′ E., on the Yangtsze-Kiang, 1000 m. from Shanghai. Built on the left bank of the river where it escapes from the ravines and gorges which for 350 m. have imprisoned its channel, I-ch’ang is exposed to considerable @@ -25668,7 +25629,7 @@ the town had many of its houses and about half of its wall swept away. The first English vessels to ascend the river as far as I-ch’ang were those of Admiral Sir James Hope’s expedition in 1861. All cargo to or from Szech’uen is here transhipped -from steamer to junk, or <i>vice vers</i>. About 10 m. above I-ch’ang +from steamer to junk, or <i>vice versâ</i>. About 10 m. above I-ch’ang the famed scenery of the Yangtsze gorges begins. Through these the great river runs in a series of rapids, which make navigation by vessels of any size extremely difficult. A very @@ -25679,8 +25640,8 @@ Szech’uen being almost its sole business. The population is estimated at 35,000. The number of foreign residents is very small, trade being carried on by Chinese agents. Before the anti-opium campaign of 1906 (see <span class="sc"><a href="#artlinks">China</a></span>) opium was much -grown. The trade of the port amounted in 1899 to 531,229, -and in 1904 to 424,442, the principal import being cotton +grown. The trade of the port amounted in 1899 to £531,229, +and in 1904 to £424,442, the principal import being cotton yarn and the principal export opium.</p> @@ -25690,7 +25651,7 @@ yarn and the principal export opium.</p> <tr><td class="figright1"><img style="width:341px; height:115px" src="images/img242.jpg" alt="" /></td></tr> <tr><td class="caption1">Egyptian Ichneumon (<i>Herpestes ichneumon</i>).</td></tr></table> -<p><span class="bold">ICHNEUMON<a name="ar105" id="ar105"></a></span> (Gr. <span class="grk" title="ichneumn">ἰχνεύμων</span>, from <span class="grk" title="ichneuein">ἰχνεύειν</span>, to track out), +<p><span class="bold">ICHNEUMON<a name="ar105" id="ar105"></a></span> (Gr. <span class="grk" title="ichneumôn">ἰχνεύμων</span>, from <span class="grk" title="ichneuein">ἰχνεύειν</span>, to track out), the common name of the North African representative of a number of small weasel-shaped mammals belonging to the carnivorous family <i>Viverridae</i>; the Indian representatives @@ -25833,7 +25794,7 @@ and sometimes in layers of different colours and texture.</p> <p><span class="sc">Authorities.</span>—Among the older works on Ichneumonoidea may be specially mentioned J. L. K. Gravenhorst, <i>Ichneumonologia Europaea</i> (Breslau, 1829); A. H. Haliday (<i>Entom. Mag.</i> i.-v., 1833-1838), -and A. Frster (<i>Verhandl. Naturhist. Ver. Rheinl. u. Westph.</i> +and A. Förster (<i>Verhandl. Naturhist. Ver. Rheinl. u. Westph.</i> xix., xxv., 1862, 1868). Full reference to the systematic literature of the group will be found in C. G. de Dalla Torre’s <i>Catalogus hymenopterorum</i>, vols, iii., iv. (Leipzig, 1898-1902), and a comprehensive @@ -25846,7 +25807,7 @@ Nat. Mus.</i> xxiii., 1901). For the British species consult C. Morley, <hr class="art" /> -<p><span class="bold">ICHNOGRAPHY<a name="ar107" id="ar107"></a></span> (Gr. <span class="grk" title="ichnos">ἴχνος</span>, a trace, and <span class="grk" title="graph">γραφή</span>, description), +<p><span class="bold">ICHNOGRAPHY<a name="ar107" id="ar107"></a></span> (Gr. <span class="grk" title="ichnos">ἴχνος</span>, a trace, and <span class="grk" title="graphê">γραφή</span>, description), in architecture, a term defined by Vitruvius (i.2) as “the ground-plan of the work,” <i>i.e.</i> the geometrical projection or horizontal section representing the plan of any building, taken at such a @@ -25857,384 +25818,7 @@ features which constitute the design.</p> <hr class="art" /> - - - - - - - - -<pre> - - - - - -End of the Project Gutenberg EBook of Encyclopaedia Britannica, 11th -Edition, Volume 14, Slice 2, by Various - -*** END OF THIS PROJECT GUTENBERG EBOOK ENCYCLOPAEDIA BRITANNICA *** - -***** This file should be named 40370-h.htm or 40370-h.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/4/0/3/7/40370/ - -Produced by Marius Masi, Don Kretz and the Online -Distributed Proofreading Team at http://www.pgdp.net - - -Updated editions will replace the previous one--the old editions -will be renamed. - -Creating the works from public domain print editions means that no -one owns a United States copyright in these works, so the Foundation -(and you!) can copy and distribute it in the United States without -permission and without paying copyright royalties. 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