4nalysis ofthelalours of the Royal Academy of France. 329 



7 '^^ _ ; _L ^'"—^^^ the 



first terms of the series are x = b-^c 7^^ - ^ r M + Lfc » " 



jequation we had before. 



2d. Letx" =0, oxxhx + V'x = h"a. Then as above lU + Vh 

 corresponds to z in the theorem. Let this receive an addi- 



tion c, so as to make it = L"a, then x—b + c ^.^^Lt + L''^) "" 



h-\.'L"a—Vb—hl.h 



3d. Let A-'' =a, then by the same mode iLi + L"^ + Ll + ^^^^ 



dh 



corresponds to z; and then x=b-\-c —-. :=.—- — 





L'"«-L"i— tL/— L1+ -rrr- . . 



, ilif! But It IS quite 



^ + Wr~^^ + ML6 + L-'A 

 M°- J; \ j' £ 



needless to pursue this further, as 1 think I have sufficiently exr. 

 plained the mode for any person to make formulae for himselt. 



LXXIX. Analym of the Labours of the Ttoyal Academy of 

 ■ Sciences of the Institute of France during the Year ISlb. 



PHYSICAL PART. 



By M, CuviER, Perpetual Secretary, 



Physics and Chemistry. 



It is known that different bodies, and especially different liquids, 

 are dilated by heat in very different proportions. 



M Gay Lussac has endeavoured to discover some law which 

 miWt indicate the regulation of these proportions. For this 

 pu?po.e in place of comparing the dilatations ot different liquids 

 above and below one uniform temperature, he sets out from a 

 fZt variable as to temperature but uniform as to the cohesion 

 of pa tides ; from a point where every liquid rises mto ebullition 

 under ^^wn pressure. And among those which he has tried, he 

 ha found two which, setting out from this point become ecpialy 

 dilated— these are alcohol and sulphuret ot carbon, winch boil, 

 ioi'me at 78-41, the second at 46'(;0. Exau.unng then 

 nto the analogies of these two liquids, M. Gay Lussac has dis- 

 ove ed thit they resemble in this pointj that the same velum. 



