1821.] Causes of Calorific Capacity, Latent Heat, fyc. 371 



we have before shown, be equal to the ratio compounded of the 

 ratio of the numbers of vaporous particles in the stratum, and 

 the ratio of the numbers of returns which two corresponding 

 particles make in the same time. 



Take A' for the megethmerin of the vapour in the vacuum, and 



A for that of the mixture of vapour and gas ; and # A 1 will be as 

 the number of strata of the mixture in a given length, and & A 

 as the same thing of the vapoiir. And because the megethmerin 

 of the vapour must be equal to the number of particles of vapour 



A' 

 in the same space in the mixture, -— will be as the number of 



V A 



vaporous particles in the first stratum of the mixture, and 

 -^=, as the same thing in the pure vapour ; therefore, the ratio 



# A 1 



A' A 1 



of these numbers is equal to that of l/~r- to v— , or of ^A 1 to 



#A. But the temperatures, and, therefore, the velocities of the 

 vaporous particles being equal, the ratio of the numbers of 

 returns to the condensing surfaces of corresponding particles will 

 be equal to that of the paths described inversely, or to that of the 

 cube roots of the megethmerins : or, in the present case, equal 



to that of <KA to ^A 1 . Compounding this ratio with the last, 

 it will make a ratio of equality. Therefore, the incremental con- 

 densation is the same in the first stratum of the mixture as in 

 the first stratum of the vapour. By a similar train of reasoning, 

 the same may be shown to be true with the second, third, and 

 higher strata to the rath, from which no condensations may be 

 supposed to take place. The sums, therefore, of all these cor- 

 responding condensations, that is, the incremental condensa- 

 tions of the two airs, must be equal. Q. E. D. 



Cor. I. — By this and the preceding proposition, it appears that 

 if C be the incremental condensation of any vapour on a unity of 

 surface in vacuo at the temperature T and elasticity E ; and if 

 S be the area of the condensing surface, C will be as EST, 

 which is a general equation from which all the phenomena of 

 the condensation of vapours may be deduced ; and is equally 

 true whether the vapour be in vacuo, or mixed with any quantity 

 whatever of gas. 



Cor. 2. — From this theorem it follows, that the temperature 

 remaining the same, the condensation of vapour mixed with gas 

 is neither increased nor diminished by the elastic force of it in 

 conjunction with the gas, but is entirely proportional to the 

 elastic force it would have if it occupied the same space with all 

 'he gas withdrawn; a fact which pheenomena confirm. 



Prop. XIII. Tiieor. XL 



In every vapour confined over the surface of its generating 



2 b2 



