14 Kev. 0. Fisher on Variations of Gravity and their 



Let be on the true sea-level, Q on the disturbed surface, 

 P the station, CQ = z, Q P = h the observed height of the sta- 

 tion; because the levels of the theodolite will always be parallel 

 to what the surface of the water would be, were there a canal 

 cut from the coast to beneath the station. 



Then we require the potentials of the two portions, C Q and 

 P Q, of the cylinder at the point Q. That of C Q, of height z, 

 will be found to be 



z 2 

 If we expand, and neglect terms in -a, this becomes 



a^{*«-£ + £*;}• 



Pratt neglects the last term, in which we shall follow him. 



The potential of P Q at Q will be of the same form, only 

 having h—z in the place of z : and that of the root may also 

 be got from the above expression, mutatis mutandis. Hence, 

 treating for the present purpose the plateau and the root as 

 cylinders of radii u and w respectively, we have the whole 

 potential at Q made up of that of the sphere, -+- that of the 

 cylinder of thickness h— z, radius u, and density p, at a 

 point at the end of its axis, + that of the cylinder of thick- 

 ness 0, radius u, and density p, at a point at the end of 

 its axis,— that of the cylinder of thickness £, radius w y and 

 density cr— /z,, at a point distant z + k from its end. Treating 

 the last as the difference of two potentials, we have by what 

 has been already proved, 



g x rise of the sea-level =gz = 27rp((h—z)u— - — -^- J 



+ 27rp(zu-j) 

 + 29r(cr- / i){( g + ^ + 0» g - (g+ g +0 ' -((^ + ^)to-^^)} 



