Application of the Kinetic Theory of Gases to Gravitation. 117 



so (6) becomes 



sinh qz __ 



~~Y~~ " [-(Tx-Tj) coshpZo} 



I \ (T + T 3 ) ooshp^-^ + T,) cosh^ {(T -T 3 ) coshp^ 



h r . (T^-T^sinhpZ ' V ; 



which is a form convenient for calculation. 



9. So also for the second method (§ 5), we can write down 

 the value of the quantities occurring in the right hand of (10), 

 T'-T _ (Tx-T,) s inhK-(T -T 3 ) sinh^ . 

 dT ~ ^(Tocosh^-Ticosh^g ' K ' 

 da 



and similarly for the small tf's, of which a set t , t l7 t 2 , t z have 

 been observed. In this case there is no loss of heat in passing 

 through the crystal ; so we ought to have 



dx dx 

 which gives the condition 



Ti + Tg ^ cosh^ . 



T H-T 3 -cosh^ J ^ 



and unless this condition is satisfied there is some error in the 

 experiment, and it is useless to proceed. 



I have to express my thanks to my brother, Mr. Alfred 

 Lodge, of St. John's College, Oxford, for several suggestions 

 in the writing out of the above and for some improvements in 

 the notation. 



In the second part of this communication some practical 

 details will be given, together with the results of some trials 

 of the method now going to be made. 



University College, London. 



XVII. Application of the Kinetic Theory of Gases to Gravita- 

 tion. By S. Tolver Preston*. 



No. Ill.f 



1. TN the last Number of the Philosophical Magazine is a 



J- short paper by Mr. James Croll on Le Sage's Theory 



of Gravitation, in which he alludes to a difficulty that has 



* Communicated by the Author. 



t For two preceding parts, see Philosophical Magazine, September and 

 November 1877 (under title " On some Dynamical Conditions applicable 

 to Le Sage's Theory of Gravitation "). 



