628 



Lieutenant Eennt on the Constants of 



Now, it is established by experiments which admit of no controversy, that 

 barometric observations made under such circumstances give heights altoge- 

 ther too great, and this agrees with statements made by Ramond himself, who 

 tells us, in his second memoir, that at the tops of mountains, as also on the 

 plains and in the bottoms of valleys, the barometric observations of the fore- 

 noon as of the afternoon give heights so much the less than those made at noon, 

 as the moments in which they are made are the more removed from noon. 

 Now, as Laplace's constant was calculated from observations made at noon 

 iu the fine weather of the summer months, which invariably gave heights greater 

 than the true heights, if employed in calculations made with a correct constant, 

 it follows, as a mathematical certainty, that the constant thus determined must 

 be too small ; because the error in excess, arising from such observations, is 

 caused by the fact that the arithmetic mean of the temperatures, as given by 

 the detached thermometers, is greater than the real mean temperature of the 

 atmospheric column, situate between the stations of the barometric observation. 

 Now, the well-known formula of barometric calculations is 



/f=Cxlog|x(l + z/-±^ 



or C = 



H 



1-f/ 



t + t' 



xlog 



B 

 B 



in which equations, C represents the constant of the formula ; H is assumed 

 as the correct height of one station above the other ; B, B' are the true pres- 

 sures of the atmosphere ; I is the expansion of air for one degree of tempera- 

 ture, and t, t' are the temperatures as given by the detached thermometers. 



tA-t' 

 Now, if in these equations, —5- be too great, it is obvious that C must be too 



small. Thus we have double testimony to induce us to believe the constant of 

 Laplace to be too small. 



It is, however, consolatory that in giving up Laplace's constant, it is to 

 make room for another, obtained in a better way, and subject only to such 

 small errors as are inseparable from the mode of obtaining the ratio of the 

 specific gravity of dry air to that of quicksilver. I have not the least hesita- 

 tion in declaring my belief that the new constant, thus obtained, being subject 

 only to such error, is very much to be preferred to a constant calculated from 



