274 



SCIENCE. 



[Vol. VI., No. 138. 



The appearance of a new and useful family pecul- 

 iarity is a boon to breeders, who by selection in mat- 

 ing gradually reduce the preponderance of those 

 ancestral elements that endanger reversion. The 

 appearance of a new type is due to causes that lie 

 beyond our reach; so we ought to welcome every 

 useful one as a happy chance, and do our best to 

 domicile and perpetuate it. When heredity shall 

 have become much better, and more generally under- 

 stood than now, I can believe that we shall look upon 

 a neglect to conserve any valuable form of family 

 type as a wrongful waste of opportunity. The ap- 

 pearance of each new natural peculiarity is a faltering 

 step in the upward journey of evolution, over which, 

 in outward appearance, the whole living world is 

 blindly blundering and stumbling, but whose general 

 direction man has the intelligence dimly to discern, 

 and whoseprogress he has power to facilitate. 



A NEW THEORY OF COHESION. 

 Since a great part of the relations discussed in a 

 paper by Dr. H. Whiting, on a new theory of cohe- 

 sion (Proc. Amer. acad., xix. 353), are determined 

 by the equation between the pressure, volume, and 

 temperature of a given quantity of the substance 

 considered, a comparison of the form of this equa- 

 tion as given in this paper with forms previously 

 proposed affords the readiest means of comparing 

 the author's results with those of previous investiga- 

 tors. The equation proposed in 1873 by Van der 

 Waals has the form 



(p+^)(i-D"'=-^*' ''' 



that of the present paper (see p. 376, third equation) 

 may be written 



(p+.-^)(i-slO^ = ^^- 



(2) 



In both equations, p, v, and t denote pressure, vol- 

 ume, and absolute temperature : the other letters 

 denote constants, to be determined by the nature of 

 the substance considered. 



We may get some idea of the numerical difference 

 in the indications of these equations, if we observe 

 that the ratio of the volume of the critical state to 

 that which would be required by the laws of Boyle 

 and Charles is 0.375 by the first equation, and 0.536 

 by the second (the experiments of Dr. Andrews give 

 something like 0.414 for carbonic acid). Again : 

 the ratio of the volume of the critical state to that 

 at absolute zero would be 3 by the first equation 

 (which, however, was not intended to apply to such 

 a determination), and 3.58 by the second. 



The equation of Dr. Whiting has an important 

 property in common with that of Van der Waals. 

 If we use the pressure, volume, and temperature of 

 the critical state as units for the measurement of the 

 pressure, volume, and temperature of all states, the 

 constants will disappear from either equation, and 

 we obtain a relation between the pressure, volume, 

 and temperature (thus measured), which should be 

 the same for all bodies. From this property of his 

 equation, independently of the particular relation 



obtained. Van der Waals has derived a consider- 

 able number of interesting conclusions, which would 

 equally follow from the equation of Dr. Whiting 

 (see the twelfth and thirteenth chapters of the Ger- 

 man translation of the memoirs of the former, by 

 Dr. Roth, Leipzig, 1881). One of these is men- 

 tioned in Dr. Whiting's treatise, p. 427. 



It is well known that the equation of Van der 

 Waals agrees with experiment to an extent which is 

 quite remarkable when the simplicity of the equa- 

 tion is considered, and the complexity of the problem 

 to which it relates. But it was not intended to be 

 applied to states as dense as the ordinary liquid 

 state. Dr. Whiting's equation, on the other hand, 

 seems to have been formed with especial reference to 

 the denser conditions of matter, and, from the numer- 

 ical verifications which are given, would appear to 

 represent the ordinary liquid state, in some respects 

 at least, much better than the equation of Van der 

 Waals. The principal verifications relate to the 

 coefllcient of expansion and the critical tempera- 

 ture. When the pressure may be neglected, as in 

 the ordinary liquid state, equation (2) gives 



dt 3^ ^ 3 ^^ ' 



/dv\ ^ 

 where e is the coefficient of expansion l^ )• A 



very elaborate comparison is made between this 

 equation and the experiments of Kopp, Pierre, and 

 Thorpe. An empirical formula of Dr. Mendelejeff 

 is also considered, which gives 



de 



dt ^' 

 a value of de/dt about one-third as great as Dr. Whit- 

 ing's. We may add that the equation (1) of Van 

 der Waals would give 

 de 



dt 



= Se^ + 2te^, 



a value of de/dt about one-third greater than Dr. 

 Whiting's. The result seems to be that the indica- 

 tions of experiment lie between the formulae of Dr. 

 Whiting and Dr. Mendelejeff (pp. 424 ff. ). We may 

 conclude that they would not agree so well with that 

 of Van der Waals. 



Each of the equations (1) and (2) will give the 

 critical temperature when we know the coefficient of 

 expansion for a given temperature. Dr. Whiting has 

 calculated the critical temperature, by means of his 

 equation, for twenty-six substances for which this 

 temperature has been observed. The calculated and 

 observed values generally differ by less than ten 

 degrees Centigrade. An equation derived by Thorpe 

 and Riicker, in part from the formula of Mendele- 

 jeff above mentioned, and in part from a principle 

 of Van der Waals, gives about the same agreement 

 with experiment. We may add that the general 

 equation of Van der Waals, taken alone, would give 

 for the critical temperature tc the formula 

 _ 8(2^e + 1)2 

 ^^ ~ 27e(te + 1)' 

 which does not seem, from the test of a few cases, to 

 agree so well with experiment. 



