1885.] 



Note on a previous Paper, 



327 



out a meridional section of the sphere. The numbers written on the 

 curves give the values of 19A, when the radius of the sphere is unity. 

 The point marked is that where A vanishes. 



The dotted curve is the ellipse of separation (e) cutting the circle 

 in colatitude 35° 16'. 



Over the polar cap and at the surface 19A is constant and equal to 

 6 ; at the surface from colat. 35° 16' to the equator 19A increases 

 from 6 to 18, varying as the square of the sine of the colatitude. 



At the centre 19 A is 48, being eight times the polar superficial 

 value. 



Beginning with the first sentence of p. 203 the remainder of § 5 

 will hold good. It is well to observe, however, that where surface 

 stress-difference is spoken of, it must be taken as referring to the 

 polar caps only, the stress- difference at the equator being three times 

 as great. It is worth while comparing the figure 1 of the paper 

 (Plate 19) with the figure now given. 



We now come to the case of — 



The Stresses due to the even Zonal Harmonics. 



The complete determination of the regions within which N 2 — N 3 

 and N 3 are the proper measures of stress- difference might be 

 somewhat difficult. As, however, these harmonics are only used for 

 the determination of stress -difference in the equatorial regions, it is 

 sufficient to find the boundary of the regions for that part of the 

 sphere. 



We see from (22) that y{(P-R) 2 + 4T 2 } only differs from P-R 

 by terms which depend on the square of the sine of the latitude. 

 Hence as far as the first power of sin I we have 



N^F-Wi, N 2 = Q—Fi, N 3 =R-Wi. 



Therefore if we neglect terms depending on the square of the sine 

 of the latitude, we have from (22), 



g=V+V, ^=V+V, jk=W+v<fl?- 



Then substituting, for A Q) B , &c, their values from (23), (24), (26), 

 and effecting some easy reductions, we find, 



jS- ; 2 (i+2)(a3-r*). 



^=-[i(»-+l)(i+2)+il(a 5 -^)-i^^. 

 r* * t — l 



VOL. XXXVIII. 2 A 



