Critical Temperatures and Thermal Expansions. 431 



Let us next suppose the connection broken immediately 

 after the discharge. No fresh tubes enter any layer; so that 

 putting u = 0, we have from (6) 



u = 



r\ 



+ 



1 



dX, 



dt ' 



^1= 



x, : 



v e~ 



**k H 





or 



where X x is now the value of the electric intensity at any time 

 t after the connection is broken. 



Substituting from (15) and putting E for the initial value 



OfE, , v 4**, 



X 1 = E Q-47r/: 1 Cjrn (16) 



The value of E at any time is 



E = %X! + #2X2 + . . . 



47rfc, , ,„, x ink., 



I -4flr*xC y x e-^ +(*-4**fl )<**T^ +...|.(17) 



=E {(^-4.CE)f^'... 



The instantaneous discharge obtained at any time £ will be, 

 as before, CE. 



If the terms be arranged in descending order of magnitude 



of -A then the exponentials are also in descending order of 



1 

 magnitude, or the negative terms decrease more rapidly than 



the positive, and E is positive. 



LVIII. Note on a "Relation between the Critical Temperatures 

 of Bodies and their Thermal Expansions as Liquids" By 

 T. E. Thokpe, Ph.D., F.B.S., and A. W. Kuckek, M.A., 

 F.R.S* 



A PAPER bearing the above title was published by us 

 in the Journal of the Chemical Society of London for 

 April 1884, and has recently been discussed by MM. A. Bar- 

 toli and E. Stracciatij. As these gentlemen have done us 

 the honour to make use of a formula deduced by us from the 



* Communicated by the Physical Society : read April 10, 1886. 

 t Ann. Chim. Phys. Mara 1886, p. 384. 



