376 



Rev. 0. Fisher on 



arrived ! * Mr. Blake does not appear to have realized the 

 argument from cap sectors, because he writes of a cap sector 

 beneath the ocean " and another cap sector beneath the land/'' 

 This was not the idea which I tried to work out. 



The subject will be made more intel- 

 ligible by means of a diagram. The defi- 

 nition of a cap sector was borrowed from 

 the fifth volume of the 'Account of the 

 Great Trigonometrical Survey of India/ 

 where approximate expressions for the ver- 

 tical attraction at the apex A of a sector 

 will be found. In my work a cap sector 

 under consideration may be supposed to 

 be partly in the oceanic area and partly 

 in the land ; the object being to de- 

 termine what different arrangements in 

 regard to density and thickness of the 

 layers in any part of it would have equal effects in contri- 

 buting to gravity at the point A, it being known from 

 M. Faye's investigations f that, when A is on the ocean, 

 gravity will be the same for all positions of A. 



The exact expression for the attraction at A for a complete 

 circular cap is given in Pratt's ' Figure of the Earth,' 4th ed. 

 § 68 ; and to alter it to the case of a sector it is only needful 

 to replace 2tt by the sector angle a. 



His expression is of course obtained for the Newtonian 

 law of attraction, and it would be absurd for the case of 

 nature to assume any other J. Putting a for the sector angle 

 instead of 2tt, t for the density of the sector, t for its thickness, 

 and a for the radius A, it can obviously be expanded in a 

 series so that 



vertical attraction at A 



where /(#), <j>(0), y\r(d), &c. are (not "unknown" but) known 

 functions of 0, 



* * Physics of the Earth's Crust/ 2nd edit., bottom of p. 246. Also 

 Appendix to the same, p. 7. 



t Comptes Hendus ) Ma,Tch 22, 1886. 



J In fact the ocean could not be in equilibrium unless the spherical 

 shells attracted to their common centre, which could only be in the cases 

 of the laws of the direct distance and of the inverse square* 



