370 Mr. Ilerapath on True Temperature, and the [Nov. 



Prop. XL Th eor. IX. 



If portions of the same vapour be confined in vacuo at unequal 

 temperatures over equal spaces of like condensing surfaces 

 respectively at the temperatures of the vapours, the ratio of the 

 contemporaneous increments of condensation will be equal to 

 that compounded of the ratio of the temperatures and the ratio 

 of the elasticities of the vapours. 



Let C, C, denote the condensations, T, T', the temperatures, 

 and E, E', the elasticities of the vapours; and let c, e, denote 

 the like things of another vapour, supposed to have the tempera- 

 ture T o P the former, and the megethmerin of the latter. 



Then by Prop. IX. 



C : c ::E :e 

 And by Prop. X. 



c : C l :: T 3 : T ■" 



But by Cor. 6, Prop. IX. of my former paper, 



T°- : T-' :: e : E 1 . 

 Compounding these ratios we get 



C : C :: ET : E 1 T . Q. E. D. 



Cor.— Because E is as M T- by Prop. VIII. of my last paper 

 in which M signifies the megethmerin; and because in the 

 same vapour the megethmerin is as the specific gravity S, we 

 have C as E T as ST'. That is, the incremental condensa- 

 tion is as the specific gravity and cube of the temperature of the 

 vapour conjointly. 



On this Cor. and the principle of vaporous tension, which I 

 shall presently demonstrate, depends the whole theory of hygro- 

 metry, when properly considered, a subject which now I must 

 dismiss with the bare mention of its name. 



Prop. XII. Theor. X. 



If any portion of vapour be mixed with any quantity of incon- 

 densible gas at the same temperature, and be contained with it 

 in a given space over a given condensible surface, the incre- 

 mental condensation will be the same as if there was no gas 

 present, and the whole space was occupied with the vapour 

 alone. Or the incremental condensation, ceteris paribus, of any 

 mixture of vapour with gas will be as the elasticity of the same 

 quantity of vapour occupying the same space as the mixture 

 does. 



Conceive the two airs to be so divided in strata parallel to the 

 condensing surfaces, that if the particles of each air were 

 uniformly disposed throughout the corresponding strata, each 

 air would be the same number of particles thick. Then because 

 the gas itself does not condense, the ratio of the incremental 

 condensations from the first stratum in each air, will, by what 



