relation to the Constitution of the Earth'' s Crust. 5 



in the fourth edition of his ' Figure of the Earth/ to which 

 work Col. Herschel acknowledges himself indebted*. 



I propose, in what follows, to compare the vibration-num- 

 bers at some of the meridian stations of the great Indian arc 

 uncorrected for local attraction, but simply reduced to the 

 sea-level f, with what they ought to be there did no elevated 

 tract exist ; and the result will show how much local attrac- 

 tion need be called upon to account for. Then, if a given 

 hypothesis respecting the constitution of the Earth's crust 

 fairly meets the requirements in several instances, it will 

 afford a fairly strong presumption that the hypothesis has a 

 foundation in reality. 



It will be convenient to refer other stations to Punnse as a 

 base. It is situated near Cape Comorin, at the southern ex- 

 tremity of the peninsula, in latitude 8° 9' 28" N. But since 

 Punnse is 48 feet above the sea, it will be better to make the 

 reduction, small though it be, to the sea-level there, once for 

 all. 



We shall employ the following symbols in the calculations, 

 the numerical values being taken from the ' Account of the 

 Pendulum Operations ' already referred to. 



c=the radius of the earth =20,926,000 feet = 3963 



miles. 

 e=the elipticity, =0*0034483. 

 m = ratio of centrifugal force to gravity at the equator, 



= 0-0034674. 

 h = height of the station. 

 1 = latitude of the station. 

 V = latitude of Punnse. 



N= number of vibrations at Punnse in twenty-four hours 

 when reduced to the sea-level. 

 N + SN=the observed number at another station. 



r =the Earth's attractive force at the equator, 

 the force of gravity at the station. 

 sGr = the change in G- corresponding to one vibration, 

 where 5=0*0000023148. 

 & = the thickness of the cooled crust, taken as 25 miles. 

 p = the density of the crust, mountain, and its root, 



taken as 2*68. 

 cr = the density of the substratum, taken as 2*96. 

 A = the height of the station. 

 u — the chord of the semiarc of the spherical cap. 

 t = the depth of the root below the bottom of the crust. 

 w = the chord of the semiarc of the root of the mountain. 



* Op. oit. p. [151]. 

 f Op. cit. p. [120]. 



