328 



Note on a previous Paper. 



[Apr. 30, 



From this we see that N x is always positive but vanishes at the 

 surface, N 2 is always positive but does not vanish at the surface, and 

 N 3 is always negative. 



Hence at the surface and for some distance beneath it, the stress- 

 difference is jN" 2 — N 3 ; but below the surface at which ~N X becomes 

 equal to N" 2 , we have Nj— N 3 as the stress-difference. 



This surface is determined by 



i*(i + 2)(a*-rZ)=i*(a*-r*)+-—a?. 



i — 1 



r 2 ft 4 



whence - 2 =^— r 



Solving for the successive even values of i, we find, when 



i=2, -=0, as we already know. 



a 



i=4, -=08944, 



a 



i=6, -=0-9562, 



a 



7=8, -=0-9759, 

 a 



i=10, -=0-9847. 

 a 



In the paper ISTj^—Ng was always taken as being the stress-difference, 

 and we now see that even when z=4, the region is very thin in 

 which this is untrue and where IST 2 — N 3 is the proper measure. For 

 the higher harmonics it soon becomes negligeable. 



This explains the transition from the incorrectness of the treatment 

 in the paper of the case of the second harmonic to the correctness of 

 the treatment of the mountain ranges. 



On looking at § 7 and the accompanying figures we see that the 

 maximum stress-difference occurs far within the region within which 

 N 2 becomes the mean principal stress. Thus § 7 may be permitted to 

 stand, save that in fig. 4, Plate 19, the ordinates of the curves 

 <£=4, t=6, &c, are to be slightly augmented at the surface where 

 r — a. It is easy to see what small alterations are to be made in 

 Table VI, and in the subsequent discussion, but clearly nothing 

 material from a physical point of view need be amended. 



It may be remarked in conclusion that, whilst it is proper to correct 

 the mathematical errors in this paper, the physical conclusions remain 

 untouched. 



