482 Mr. J. Prescott on the 



words, they are now twice as far apart as before, the spacing 

 of the secondary maxima remaining the same. 



The analogy between the secondary maxima and the fringes 

 produced by a rectangular aperture of the same size as the 

 ruled surface, can be studied to advantage by means of coarse 

 gratings made by ruling four or five lines on a piece of smoked 

 plate glass, and making the lower third of the grating clear 

 by wiping out the lines. Sun or arc light filtered through 

 red glass should be used with a small spectrometer, the 

 grating and aperture being covered in succession or used 

 simultaneously. 



XL VI. On the Figure of the Earth. By J. Prescott, M. A., 

 Lecturer in Mathematics at the Manchester School of 

 Technology*. 



I SHALL assume that the figure of the earth is an oblate 

 spheroid of small ellipticity and I propose to find this 

 ellipticity. I shall also assume that the figure is the same as it 

 would be if the earth were wholly liquid. There can be little 

 doubt that the figure obtained on these assumptions is not 

 far from the actual shape. For, the earth's crust is probably 

 not rigid enough to resist the forces pulling it into this 

 shape. 



It is necessary first to find the potential, at an external point 

 on the axis, of a thin shell bounded by similar oblate spheroids 

 whose generating curves are 



a 2 ^ b 2 ' 



a 2 W/ 2 + 



where b 2 (l + a) = (b + &b) 2 =b 2 + 2bBb, 



or jx*2-r; 



and b is the polar semi-axis. 



Let P be the external point, the centre of the shells, 

 Q~P = r, (a — b)=ebj K = the gravitation constant, p = density. 

 The mass of a thin ring of the shell between the planes y 



and y+ By is 



7rp(^ 2 2 — ^l 2 )% 



== TrpacrBy. 



* Communicated by the Author. 



