1821.] Causes of Calorific Capacity, Latent Heat, fyc. 369 



that of the lengths of the paths, or to the subtriplicate ratio of the 

 megethmerins. Therefore, the ratio of the increments of con- 

 densation from the first strata is equal to that compounded of the 

 duplisubtriplicate and the subtriplicate of the megethmerins, that 

 is, it is equal to the simple ratio of the megethmerins. But by 

 the laws of gases demonstrated in my last paper, the ratio of the 

 megethmerins, the temperatures being equal, is equal to the ratio 

 of the elasticities ; therefore, the condensations from the first 

 strata have a ratio equal to that of the elasticities of the vapours. 

 And by a similar train of reasoning, we might show the same 

 thing to hold good in the second and higher strata ; for the par- 

 ticles of the second and superior strata which do actually come 

 in contact in a given time with the condensing surfaces are as 

 the arithmeridones, and the number of their returns as the lengths 

 of the paths inversely, the same as in the first strata. Therefore, 

 if we carry on the reasoning to the «th strata, from which in the 

 given time no condensation takes place, the sums of the conden- 

 sations from all the strata, or the increments of the condensations 

 in the two media will have the same ratio as the condensations 

 from the first strata ; that is, the ratio of the elasticities. 



Prop. X. Theor.VIII. 



If the megethmerins of two portions of the same vapour con- 

 fined over equal and like condensing spaces be equal, I say the 

 contemporaneous increments of condensation will have a ratio 

 equal to the triplicate ratio of the temperatures. 



The forces to produce union at the times of collision being 

 alike, the ratio of the contemporaneous condensations would be 

 equal to that of the numbers of times the most adaptable sides of 

 two corresponding particles in the two media come in contact 

 with similar parts of the condensing surfaces. But the megeth- 

 merins being the same, the times of contact are in a ratio equal 

 to that of the velocities or temperatures ; and the number of 

 times a particle turns a particular face towards a given part of 

 space in a given time, is as its velocity about its centre of gravity. 

 But this velocity is as the force which occasions it, namely, the 

 intensity of collision or temperature of the medium. Therefore, 

 the forces to produce union and the megethmerins being alike, 

 the ratio of the contemporaneous condensations will be equal to 

 that of the squares of the temperatures. 



Again, the particles being nearly equal, and the unions being 

 supposed to take place when they are moving nearly parallel and 

 towards the same parts, the tendency to union at each collision, 

 and, therefore, the number of unions in a given time, will be as 

 the force producing that tendency ; that is, by what I have 

 shown in my former paper, as the temperature of the medium. 

 Compounding this ratio with the other before found, the ratio of 

 the contemporaneous condensations will be equal to that of the 

 cubes of the temperatures. Q. E. D. 



New Series, vol. n. 2 b 



