506 



Mr. Lubbock on the Heat of Vapours 



1.3.5.7 

 2.4.6.8 



/ 4 + 



3.5 .7 

 2.4.6 



5.7 



7h*f 



h* 



h f 3 + 1.2.2.4 h2 f 2 + 1 . 2.3 . 2 + 1 . 2 . 3 . 4 



2.3.5.7 hf3 _V.J-7 hif2 _ 



'.7 



\^2 2.4.6 



^22.4 



^21.2.2 



A 8 / 



2 4 /** 3*. 5. 7 33.7 3<ft* 



43 7 



1.2.3 ^4.2 



* 3 /- 



44 



1.2.3.4 ^1 



= *« + 



45 



1.2.3.4.5^-5 



= h* + &c. 



=aJi +^| l+xKr _ l) _ / ( 2 ^-_|) 

 + «*{-l_ s vr+|-^ ; »}— |-*/(^a-.i)+ |-/ 2 } 



when the higher powers of f and h are rejected, and this expres- 

 sion agrees with that given by Mr. Ivory, Phil. Trans., 1838, p. 

 207. 



a (1 + *) V *■ 



VTi ~ = 2036 S 



In atmospheres which extend to an infinite distance m (or a" in 

 the notation of this treatise) is infinite and e always = 1, so that in 

 this case the method employed by Mr. Ivory in p. 211 of his me- 

 moir, Phil. Trans., 1838, would seem at least to require further 

 elucidation. Mr. Ivory has avoided this consideration, which 

 would otherwise arise with the atmosphere which he has assumed, 

 by imposing an arbitrary limit to the altitude of his atmosphere, 

 while, however, if I am not mistaken, upon his own assumption, 

 the density and the pressure are still finite. When n is large the 

 numerators of the separate quantities of which the quantity A 2 . { 



in p. 211 is composed become large also. 



I do not find in Mr. Ivory's paper any remarks tending to prove 

 that the quantities which he has discarded depending upon the 

 higher powers ofy* and h are incapable of producing any sensible 

 effect ; taken separately they are by no means insignificant. Nor 

 do I think it follows as a matter of course, even if the positive and 

 negative terms are numerically of equal value at the horizon, and 

 so fortunately cut one another out, that the same thing will happen 

 necessarily at ail other altitudes. Unless the approximation is 

 pushed so far as to secure the retention of all the sensible terms, or 

 those which fairly come within the limits of the errors of observa- 

 tion, any comparison of the result with the valuable table of M. 

 Bessel is illusory and only calculated to lead to incorrect conclu- 



