j AND ITS CONNECTION WITH THE THEORY OF HEAT. 435 
= AE (rn aie heh AM id 2 
To determine the second part of the integral we have the condition, that the 
quantity of atomic atmosphere enclosed within each surface at which a @ has 
some given value, is invariable; that is to say 
(00675, +8Vaq + 9r 7) (cove a9) dn 
Hence 
koag 
—=ifON 2s oh) (km. aD) 
kaAg 
ko,MVe a, 

dagp= 
The value of the second part of the integral (23) is now found to be:— 
kbA@ 
“at Lf] ¢8apazayae= ae acv fie moo bad 
=— 2-5 a ae Peer mir aoa src 
In the double integral, let A = log. V be put for £ ¢, G for w, and H for the 
single integral, as in equation (9.) Then the double integral becomes 
= Te Han=~ GG" by Ba (10) 
ip eae 
G, dr 

Also because e, MV = e ae by eq. (9), and | = =F (r —k), the second part of 
the integral (23) is found to ot 

r eicidial 
dH, 


h ae 
(7—k) (674 +oV0) & dr: (23 B.) 
Hence, adding ae (23 A.) and (23 B.) we find for the total variation of 
latent heat 
_hp @ los oe 1 d* log, H. 
dq= 4B r—«) {or sh Via (ay + a) } esw (od ) 
To express this in terms of mete which may be known directly by expe- 
riment, we have by equations 10 and 9 :— 
dH, 
i, Hav +0-F=0, , that is to say, 



