350 Mr, Hcrapath on the Causes, Laws, and principal [May, 



same hold good with the ratios of the first and second volumes, 

 then will the ratio of the first elasticities be equal to that of tlie 

 second. That is, the volumes and temperatures of two gases 

 always preserving ratios of equality, however much these volumes 

 and temperatures may vary, the elasticities will maintain a given 

 ratio. This is precisely what follows from cor. 2 to the preced- 

 ing prop. 



Cor. 2. — Supposing the same things to hold good, respecting 



■ {; : ;■} ' 



the temperatures, the theorem becomes r, : 1 :: < 1 : e, J. ; that 



Lv : 1 J 



is, the ratio of the second volumes is equal to the ratio com- 

 pounded of these three ratios ; namely, the direct ratio of the 

 first elasticities, the inverse of the second, and the direct of the 

 first volumes. 



N. B. The same things will also hold good in both these 

 corollaries, if the two ratios of temperatures, instead of beings 

 ratios of equality, are equal. 



Cor. 3. — In the construction of Mr. Leshe's differential ther- 

 mometer, it is supposed, when the two balls are of equal temper- 

 atures, that the elasticities and volumes are also equal. Therefore 



in this case, e, t, and v, are each unity, and ^, : 1 :: \/ < ^' * -. i- 



which, because the alteration in volume is but trifling, is nearly 

 equal to \/ e, : 1. Hence, if we know the ratios of the second 

 volumes and elasticities, we also know the ratio of the second 

 temperatures ; or if we know only the ratio of the second elasti- 

 cities, this ratio of the second temperatures is nearly ascertained ; 

 and, therefore, one of the second temperatures being known, the 

 other, and the difference of the two, become known. But the 

 ratio of the volumes is easily ascertained, by admeasurements 

 previous to the making of the instrument ; and the difference in 

 the elastic forces is determined by the difference in the altitudes 

 of the fluid in the two legs, from which and by keeping one of 

 the legs at a certain temperature, and by having measured the 

 elastic force of the gas at that temperature, before the finishinap 

 of the instrument, we shall be enabled to obtain the difference 

 and ratio of the two elasticities, and thence the temperature of 

 the gas in the other leg. 



I have for want of time but just mentioned this ingenious and 

 useful little instrument, whose theory is contained in the preced- 

 ing prop, but he that wishes to be fully acquainted with its 

 merits and the variety of purposes to which it is applicable, may 

 consult Mr. Leslie's Essay on Heat and Moisture, pubHshed a 

 few years since. 



Scholium. 



It has in cor. 5 to prop. 8 been remarked that the augmen- 

 tations of volume in mercury and any gas have so nearly a givea 



