and the Observed Velocity of Sound in Air and Gases. 17 



were not made with pendulums which were in these respects 

 comparable with those used for the determination of the length 

 of the seconds' pendulum, we are perhaps warranted in regard- 

 ing Mr. Baily's factor as the more trustworthy. BessePs factor 

 gives a difference of 2*59, and Baily's 2*395 in the number of 

 vibrations in a mean solar day above the old reduction numbers, — 

 in each case the pendulum being assumed to make 86400 vibra- 

 tions in a mean solar day*. Hence it follows that by BessePs 

 factor M. Biot's seconds' pendulum was 0*0596 millimetre too 

 short, by Baily's factor it was 0*0551 millimetre too short. 

 Consequently the deduced value of g was 0*5881, or 0*5438 

 millimetre too small, according as the former or the latter cor- 

 rection is employed. 



But there is another element in deducing the exact length of 

 the seconds' pendulum (and by consequence the value of g), in 

 which the old reductions are erroneous ; the error being in an 

 opposite direction to the foregoing. Dr. Thomas Young pointed 

 out, what M. Poisson subsequently more fully demonstrated, that 

 the formula usually employed for reduction to the level of the sea 

 is too great, in that it takes no cognizance of the attraction of 

 subjacent land lying above the sea-level f. Assuming L = the 

 length of the seconds' pendulum at the point of observation, 

 I/ = its length at a station H units of height lower, and R = the 

 earth's radius for the latitude of the station, the old formula is 



,L' = L + L.^; 



whereas Poisson's investigations, according to Professor Miller J, 

 give us 



L'=L + L. 1,32H 



XL 



as the corrected formula. The experiments of MM. Biot, 

 Mathieu, and Bouvard at the " Salle de la Meridienne " of the 

 observatory of Paris, 70*25 metres above the sea, and in latitude 

 48° 50 7 14" North, give us L = 0*993844842 metre §. It must 

 be borne in mind that this number was obtained by the use of 

 the old formula for reduction to a vacuum. The value of R for 

 the above latitude = 6365360 metres. The following Table, 

 computed from the foregoing corrected data, furnishes results 

 which may be regarded as the best which experimental science 

 affords. 



* Vide Table, given by Baily in Phil. Trans, for 1832, p. 433. 



t Young, in Phil. Trans, for 1819, p. 70 et seq. Poisson's Traite de 

 Mecanique, 2nd ed. vol. i. p. 495. Paris, 1833. 



X Phil. Trans, for 1856, p. 784. 



§ Biot's Traite Elementaire d'Astronomie Physique, 3rd ed. vol. ii. 

 Table at p. 466. Paris, 1844. 



Phil. Mag. S. 4. Vol. 27. No. 179. Jan. 1864. C 



