54 



NATURE 



[May 9, 1878 



Verhandlungen der k.k. Zoologische botanischen Geselhchaft in 

 U'ien. {1867, vol. ii,) This volume, like its predecessors, con- 

 tains valuable additions to zoological and botanical literature. 

 By far the most important papers contained in it are Dr. L. 

 Koch's notes on Japanese Arachnida and Myriapoda, and Herr 

 H. B. Moschler's remarks on the Lepidoptera fauna of Surinam, 

 continued from a former volume. Of other interesting papers 

 we note :—Lichenological excursions in the Tyrol, by F. Arnold. 

 — On the spiders of Uruguay and other parts of America, by 

 E. ; Keyserling. — Introduction to the monography of Phanero- 

 pterida, by Brunner von Wattenwyl. — Hymenopterological notes, 

 by F. F. Kohl. — On the flora of the Ionian Islands of Corfu, 

 Cepbalonia and Ithaca, by G. C. Spreitzenhofer. — On a species 

 of Aphis, Pemphigus Zeae Mdidis, L. Duf, which attacks Indian 

 corn, by Dr. Franz Low. — Notes on the Aeolidiadae, by Dr. 

 Rudolph Bergh. — On the Brazilian ants collected by Prof. 

 Trail, by Dr. Gustav Mayr. — There are also in this volume some 

 smaller communications from the botanical laboratory of Dr. 

 H. W. Reichardt. 



SOCIETIES AND ACADEMIES 



London 



Royal Society, April ii. — "On Stresses in Rarefied Gases 

 arising from Inequalities of Temperature," by J. Clerk- 

 Maxwell, F.R.S., Professor of Experimental Physics in the 

 "University of Cambridge. 



1. In this paper I have followed the method given in my 

 paper "On the Dynamical Theory of Gases" (Phil. Trans. 

 1867, p. 49). I have shown that when inequalities of tempera- 

 ture exist in a gas, the pressiu-e at a given point is not the same 

 in all directions, and that the difference between the maximum 

 and the minimum pressure at a point may be of considerable 

 magnitude when the density of the gas is small enough, and 

 when (the inequalities of temperature are produced by small 

 solid bodies at a higher or lower temperature than the vessel 

 <!ontaining the gas. 



2. The nature of this stress may be thus defined ; let the 

 distance from the given point, measured in a given direction, be 

 denoted by h, and the absolute temperature by Q ; then the space- 

 variation of the temperature for a point moving along this line 



will be denoted by — -, and the space -variation of this quantity 



dh 

 along the same line by — - . 



There is in general a particular 



d^e 



direction of the line h, for which :— - is a maximum, 



dh^ 



another 



for which it is a minimum, and a third for which it is a maximum- 

 minimum. These three directions are at right angles to each 

 other, and are the axes of principal stress at the given point ; 

 and the part of the stress arising from inequalities of temperature 

 is in each of these principal axes a pressure equal to — 



^pO dh*' 

 where /* is the coefficient of viscosity, p the density, and the 

 absolute temperature. 



3. Now, for dry air at 15° C, ju = I'g x lO"* in centimetre- 



gramme-second measure, and ^i- = — o'3iS, where / is the 

 P9 P 



pressure, the unit of pressure being one dyne per square centi 

 metre, or nearly one-millionth part of an atmosphere. 



If a sphere of one centimetre in diameter is T degrees centi- 

 grade hotter than the air at a distance from it, then, when the 

 flow of heat has become steady, the temperature at a distance of 

 r centimetres will be 



e = To -f- — , and -~ =-.. 

 2,r dr^ r^ 



Hence, "at a distance of one centimetre from the centre of the 



sphere, the pressure in the direction of the radius arising from 



inequality of temperature will be — 



T 



— 0'3i5 dynes per square centimetre. 



4. In Mr. Crookes's experiments the pressure, /, was often so 

 small that this stress would be capable, if it existed alone, of 

 producing rapid motion in small masses. 



Indeed, if we were to consider only the normal part of the 

 .stress exerted on solid bodies immersed in the gas, most of 



the phenomena observed by Mr. Crookes could be readily 

 explained. 



5. Let us take the case of two small bodies symmetrical with 

 respect to the axis joining their centres of figure. If both 

 bodies are warmer than the air at a distance from them, then in 

 any section perpendicular to the axis joining their centres, the 

 point where it cuts this line will have the highest temperature, 

 and there will be a flow of heat outwards from this axis in all 

 directions. 



d^O 



Hence — „ will be positive for the axis, and it will be a line 

 dh^ 

 of maximum pressure, so that the bodies will repel each other. 



If both bodies are colder than the air at a distance, everything 

 will be reversed ; the axis will be a line of minimum pressure, 

 and the bodies will attract each other. 



If one body is hotter, and the other colder, than the air at a 

 distance, the effect will be smaller ; and it will depend on the 

 relative sizes of the bodies, and on their exact temperatures, 

 whether the action is attractive or repulsive. 



6. If the bodies are two parallel discs, very near to each 



other, the central parts will produce very little effect, because 



d^O 

 between the discs the temperature varies uniformly and -— = o. 



Only near the edges will there be any stress arising from 

 inequality of temperature in the gas. 



7. If the bodies are encircled by a ring having its axis in the 

 line joining the bodies, then the repulsion between the two 

 bodies, when they are warmer than the air in general, may be 

 converted into attraction by heating the ring, so as to produce a 

 flow of heat inwards towards the axis. 



8. If a body in the form of a cup or bowl is warmer than the air, 

 the distribution of temperature in the surrounding gas is similar 

 to the distribution of electric potential near a body of the same 

 form, which has been investigated by Sir W. Thomson.^ Near 



the convex surface the value of — -, is nearly the same as if the 



dh^ 



body had been a complete sphere, namely, 2T - , where T is the 



excess of temperature, and a is the radius of the sphere. Near 

 the concave surface the variation of temperature is exceedingly 

 small. Hence the normal pressiure on the convex surface will 

 be greater than on the concave surface, as Mr. Crookes has 

 shown by the motion of his radiometers. 



Since the expressions for the stress are linear as regards the 

 temperature, everything will be reversed when the cup is colder 

 than the surrounding air. 



9. In a spherical vessel, if the two polar regions are made 

 hotter than the equatorial zone, the pressure in the direction of 

 the axis will be greater than that parallel to the equatorial plane, 

 and the reverse will be the case if the polar regions are made 

 colder than the equatorial zone. 



ID. All such explanations of the observed phenomena must 

 be subjected to careful criticism. They have been obtained by 

 considering the normal stresses alone, to the exclusion of the 

 tangential stresses ; and it is much easier to give an elementary 

 exposition of the former than of the latter. 



If, however, we go on to calculate the forces acting on any 

 portion of the gas in virtue of the stresses on its surface, we 

 find that when the flow of heat is steady, these forces are in 

 equilibrium. Mr. Crookes tells us that there is no molar 

 current, or wind, in his radiometer vessels. It may not be easy 

 to prove this by experiment, but it is satisfactory to find that the 

 system of stresses here described as arising from inequalities of 

 temperature will not, when the flow of heat is steady, generate 

 currents. 



1 1 . Consider, then, the case in which there are no currents of 

 gas, but a steady flow of heat, the condition of which is 



g.0. -»,=-..., =0. 



df^ 



(In the absence -of external forces, such as gravity, and if the 

 gas in contact with solid bodies does not slide over them, this is 

 always a solution of the equations, and it is the only permanent 

 solution.) In this case the equations of motion show that every 

 particle of the gas is in equilibrium under the stresses acting on it. 

 Hence any finite portion of the gas is also in equilibrium ; 

 also, since the stresses are linear functions of the temperature, 

 if we superpose one system of temperatures on another, we also 

 superpose the corresponding systems of forces. Now the sys- 

 I Reprint of Parers on Electrostatics, f. 17?. 



