NOTES. 



xlvii 



smnll, vis. 4'?61 (Laplace, Me'canique celeste, T. v. p. 46,) or 4'785 (Eduard 

 Schmidt, Le.hrb. der math. Geog. Bd. i. 387 nnd418). On Halley's hypo- 

 thesis of the earth being a hollow sphere, alluded to in the following page, 

 (and which was the germ of Franklin's notions respecting earthquakes), ?ce 

 Phil. Trans, for the year 1693, Vol. xvii. p. 563. " On the structure of ths 

 internal parts of the earth, and the concave habited arch of the shell." 



[Carlini's result, by the second method noticed by M. de Humboldt, requires 

 a correction which has not yet been applied to it, and which would probably 

 alter it considerably; namely, for the true reduction to a vacuum of the 

 vibrations of the pendulum observed at Bordeaux and on Mont Cenis. The 

 height above the sea of the station at Mont Cenis was 6374 English feet ; nnd 

 the difference in the density of the air, in which the pendulum was vibrated at 

 the two stations, must have been quite sufficient to occasion a verv sensible 

 error in the difference in the lengths of the respective pendulums computed 

 by the mode of reduction practised before Bcssel's discovery, alluded to 

 in page 26 of the text of Cosmos, was made. The pendulum employed by 

 Carliui was that of Biot (with few but valuable modifications) ; and the 

 true reduction to a vacuum for pendulums of that description has not yet been 

 experimentally investigated. As an instrument for ascertaining the density 

 of the earth, the pendulum is so much inferior to the torsion- balance employed 

 by Cavendish and lleich, and still more recently by Baily (whose results do 

 not appear to have been known to M. de Humboldt when this volume of 

 Cosmos was published), that if the true reduction to a vacuum of Biot's 

 pendulum were required only for the correction of the mean density of the earth 

 derived from the experiments on Mont Cenis, it might not be worth while to 

 undertake its determination : but it should not be forgotten that, until such a 

 determination has been made, the true results of the laborious experiments by 

 which M. Biot himself sought to ascertain the length of the seconds pendulum 

 at Paris, and at various other stations in France and elsewhere, are unknown : 

 there can be little doubt that the absolute lengths computed at the time will 

 have to receive very large corrections ; and though the relative lengths will 

 certainly be less seriously affected, they may be altered to a degree which 

 may influence, in part at least, the conclusions which M. de Humboldt has 

 drawn in Note 133, respecting the variations of gravity in the South of 

 France. E D ITOR.] 



( 1:5 ~) p. 162. To these belong the excellent analytical investigations of 

 Fourier, Biot, Laplace, Poisson, Duhamel, and Lame. Poisson, in his work 

 entitled " Theorie mathe'matique de la Chaleur," 1835, p. 3, 428 430, 436, 



