66 



SCIENCi:. 



[Vol. I., No. 3. 



in which p, v, and t denote the specific pressure, 

 volume, and absolute temperature of the gas; k is the 

 specific heat at constant volume; o expresses what 

 fraction of total kinetic energy, kt, is progressive ; r 

 is the mean distance of the molecules; and B the 

 mean intermolecular attraction ; the summation being 

 taken for all possible pairs of molecules. 



This investigation depends upon d'Alembert's equa- 

 tion expressing the relation of the force acting to the 

 linear acceleration of the mass moved. 



The present paper proceeds to employ Euler's equa- 

 tion, expressing the relation of the couple acting to 

 the angular acceleration of any material body, to find 

 an analogous equation for the mean rotary motion 

 of bodies in a state of stationary rotation. An equa- 

 tion is obtained precisely analogous to that found for 

 progressive motion. But, since the intermolecular 

 attractions cannot accelerate the rotaiy motion, they 

 do not appear in the equation, which can finally be 

 written in the form 



a'kt = ipv (2) 



in which a' expresses what fraction the mean rotary 

 energy is of the total kinetic energy. Two cases, 

 however, must be excepted from the general equation 

 (2). The first of these is that of molecules which 

 are smooth figures of revolution, such as diatomic 

 molecules may be supposed to be ; and the second is 

 that of smooth spheres, such as monatomic mole- 

 cules may be. In these two cases it is shown that 



a'kt = pv, and a'kt = 0, 

 respectively. 



It is further shown, that, in case a variation of 

 state occur, that the variation of the last term in (1) 

 must be always negative, or zero, when the tempera- 

 ture is augmented, as appears from comparisons of 

 the formula with Thomson and Joule's experiments 

 on the free expansion of gases in passing a porous 

 plug, with Andrews's experiments on carbonic-acid 

 gas above the critical temijerature, with Berthelot's 

 principle of maximum heat, and with- mechanical 

 systems in motion under the control either of gravi- 

 tation or of elastic forces. 



An investigation is then made of the ratio of the 

 specific heat at constant pressure to that at constant 

 volume in imperfect gases ; the result of which, for 

 molecules of more than two atoms, may be expressed 

 in an equation of the form 



k = ;!- - ih + J;(5 + i)c . . . . (3) 

 in which k is the ratio of the specific heats in ques- 

 tion; b expresses what fraction of the total kinetic 

 energy exists in the form of atomic vibration within 

 the molecule ; c, which is very small, expresses what 

 fraction the work done against intermolecular at- 

 tractions is of the same quantity ; and i is the expo- 

 nent expressing what inverse jiower of the distance 

 between the molecules may be taken as the approxi- 

 mate law of intermolecular attraction, i is always 

 taken as greater than unity, and usually greater than 

 3; while the value ijroposed by Maxwell is .5. The 

 experimental values of k lie between 1.83 and 1.25. 

 If the value of c be assumed to be zero, as it is in 

 perfect gases, then a lies between zero and j; and, if 

 c is not zero, a must exceed y for some of the more 

 complex gases; i.e., the energy of vibration of the 

 atoms within the molecules may exceed one-fourth 

 of the mean kinetic energy of the gas. 



In the case, however, in which the molecules con- 

 sist of but two atoms each, the equation obtained is 

 k = l--tb + i(i + i)c. ... (4) 

 in which the value of h must be much smaller than 

 when the number of atoms is larger. The experi- 

 mental values lie between 1.41 and 1.39; and for air, 

 for which k has been more accurately determined 



than for other gases, the accepted value is, according 

 to Wiillner, 1.405; in which the influence of the term 

 containing c is perceptible. The value, however, of 

 k, derived from Regnault's most accm'ate determina- 

 tion of the velocity of sound, is 1.395. For molecules 

 consisting of one atom each, the equation obtained 

 Is 



ifc = f-|6 + i(2 + i)c. . . . (5, 



The experimental value of k, as found for vapor of 

 mercury (the only known monatomic gas), by Kundt 

 and Warburg, is 1.67. 



This ratio has been previously investigated by 

 Boltzmann and by Watson, by the help of general- 

 ized co-ordinates expressing the number of degrees 

 of freedom of the system ; but it has not been found 

 possible to assume any integral number of degrees 

 of freedom which would cause the value found for k 

 to agree with experimental results. The opinion is 

 expressed by the author, that this method is unsuited 

 to the investigation of this question, because any 

 elastic connection or attractive forces neither allow 

 perfect freedom, nor impose absolute restraints, such 

 as are contemplated by the method. 



So far as known, this investigation explains, for 

 the first time, what Watson, on p. 39 of his treatise, 

 regards as "the great difficulty In the establishment 

 of the kinetic theory of gases on the molecular hy- 

 pothesis." 



CONSEQUENCES OF SPLEEN 

 EXTIRPATION. 



In a preliminary notice [Centralhl. med. wissensch., 

 1882, 900) Winogradow describes the results of spleen 

 extirpation, as manifested in the blood, lymphatic 

 glands, and bone-marrow of dogs, several of which 

 were kept alive in good health for more than two 

 years after the splenotomy. 



After the operation the number of red corpuscles 

 in a cubic millimetre of blood always falls in a short 

 time, occasionally within a few days. This diminu- 

 tion is most marked from a hundred and fifty to two 

 hundred days after the splenotomy, when in some 

 cases the red corpuscles are less than half their nor- 

 mal number. Later they become again more abun- 

 dant. In the first twelve months the size of the red 

 corpuscles is not altered: after that there is found a 

 gradually increasing proportion of abnormally small 

 specimens; and the red corpuscles of exceptionally 

 large size, of 'which some are always fouud in normal 

 dog's blood, entirely disappear. The white blood 

 corpuscles show no morphological change; their 

 absolute number is sometimes increased, sometimes 

 diminished. 



In one case, a hundred and thirty-two days after 

 the splenotomy, there was found marked enlarge- 

 ment of most of the lymphatic glands. They were 

 much softer than normal, and red on section, espe- 

 cially in the cortical layer, looking much like splen- 

 ic tissue. This coloration depended mainly on red 

 blood corpuscles which were abundant in the lymph 

 channels of the gland ; and was in part due to de- 

 posits of brownish-red pigment, which Winogradow 

 ascribes to the detritus of broken-down corpuscles. 



The marrow in the central cavity of nearly all the 

 long bones was red-colored, and presented the gen- 

 eral appearance of the red marrow of the cancellated 

 bony tissue of young dogs. This color was due to 

 red corpuscles lying outside the blood-vessels in the 

 spaces of the proper marrow tissues. 



Later (five hundred and seventeen to seven hun- 

 dred and sixty days after the spleen removal) similar 

 but less marked divergences from the normal struc- 



