18 Prof. J. Le Conte on the Discrepancy between the Computed 



Height 



in 

 metres. 



Old formulae for vacuum 



Corrected formulae for vacuum and height. 



and height. 



Using Bessel's factor. 



Using Baily's factor. 



L in metres. 



g in metres. 



L in metres. 



g in metres. 



L in metres. 



g in metres. 



70-25 i 0-993844842 



60 00 | 0-993848043 



00 0-993866779 



9-8088554 

 9-8088870 

 98090719 



993904427 

 0-993906539 

 0-993918906 



9-80944350 

 980946435 

 9-80958640 



993899941 

 0-993902053 

 0993914420 



9-8093992 



9-80942005 



9-8095421 



It will be observed that the numbers obtained by the corrected 

 formulae are larger than those by the old formulae — the error by 

 excess in the old formula for height not being sufficient in this 

 case to compensate for the error by deficiency in the old formula 

 for reduction to a vacuum. 



With these revised physical constants we are able to obtain a 

 more accurate value for the Newtonian velocity of sound. 

 Assuming the result deduced from the use of Baily's factor as 

 the standard, it appears that the value of g at Paris, at Regnault's 

 laboratory, 60 metres above the sea-level, is equal to 9*80942 

 metres, or 3.2-1837179 British standard feet. The value of h 

 being, as we have shown, equal to 7990*044 metres, it follows 

 that the Newtonian velocity of sound, or 



V^A= ^9-80942 x 7990-044 = 279-9602 metres, = 918-5212 

 English feet per sexagesimal second, at the temperature of 0° 

 Centigrade. 



As the ratio of the specific heat of air under constant pressure, 

 to its specific heat under constant volume, denoted by the frac- 



Q 



tion - or k in Laplace's formula, must be determined by actual 



experiment, different experimenters, as might have been antici- 

 pated, have obtained somewhat diverse results. Two experi- 

 ments of the extended series executed by MM. De la Roche and 

 Berard in 1812*, furnished Laplace with the data for deducing 

 the numerical value of this ratio. According to this mathe- 

 matician f, the ratio of the heat given out by air, when submitted 



to pressures p and//, will be=( - V = ( P. In the two ex- 

 periments referred to, p f = 1005*8 millims. s.ndp= 740*5 millims., 

 and the mean ratio of the heat given out in the two cases = 1*2396. 



Consequently we have 1*2396 = (^-V, or 1-2396= ^i^|)*. 



Hence we have £=1*42511. This number cannot be considered 

 very accurate, from the fact that the distinguished experimenters 

 neglected to free the air from aqueous vapour. From the experi- 



* Ann. de Chim. et de Physique, vol. lxxxv. p. 72 et seq. 

 t Mtcanique Celeste, vol. v. book 12. p. 128. Paris, 1825. 



