48 STUDIES, SCIENTIFIC AND SOCIAL chap. 



but furnish additional material for estimating the varying 

 thicknesses and densities of the earth's crust. The rate 

 of vibration of a pendulum of constant length depends 

 upon the force of gravity at the place, and thus variations 

 in that force can be determined with considerable ac- 

 curacy. Taking the number of vibrations in a day of a 

 seconds pendulum at the equator and at the sea-level as 

 86,400, the number of vibrations at any other latitude can 

 be calculated on the theory that the earth is a perfect 

 spheroid of revolution ; and geodetic observations show 

 that it has such a form. At any elevated station, whether 

 on an isolated mountain or on an extensive plateau, the 

 pendulum will vibrate more slowly on account of its greater 

 distance from the centre of gravity of the earth, while it 

 would vibrate more quickly on account of the additional 

 attraction of the elevated mass immediately beneath and 

 around it. These effects can be calculated, and the 

 balance of the two, applied to the normal rate for the 

 latitude, will give the theoretical rate due to the position 

 and altitude of the station. Experiments were made at 

 more than twenty stations in India, varying from the sea- 

 level to over 15,000 feet above it, and at all the higher 

 stations there was a deficiency of the observed as compared 

 with the calculated number of vibrations, of from one to 

 twenty-four vibrations in the twenty-four hours. In such 

 delicate observations there were of course some irregulari- 

 ties, but the fact of a greater deficiency at the higher 

 levels came out very clearly, and could be explained only 

 by a deficiency of subterranean density due to the roots of 

 the mountains displacing a denser substratum, as in the 

 case of the plumb-line experiments. 



Before leaving this subject of the " roots of mountains," 

 it will be well to refer to a remarkable corroboration of 

 their actual existence by evidence of a quite different kind. 

 It has already been pointed out that the rate of increase 

 of underground temperature would, if continued down- 

 wards till the heat equalled the melting point of rock, 

 give a mean thickness of the crust of about twenty miles. 

 But in places where the crust is so much thicker, as it is 

 supposed to be under mountains, the rate of increase 



