PROCEEDINGS OF SECTION A. 191k 
soon told severely upon the cutting edge of the diamonds used, 
although, in one instance, I ruled with the same diamond be- 
tween 200,000 and 300,000 lines without appreciable alteration 
in the character of the line cut. I am hoping to take up this 
particular work again at no distant date, with improved appli- 
ances and material, and consequently with greater prospects of 
SUCCESS. 
In concluding this paper, I have to acknowledge most valu- 
able assistance at the hands of several friends. More partiecu- 
larly, I am very greatly indebted to my friend Mr. William 
Stone, electrical engineer to the Victorian Railways, and Mr. 
James Wedeles, of Armadale. 
4—ON CERTAIN SURFACE AND VOLUME 
INTEGRALS OF AN ELLIPSOID, 
By->He ‘Gi Hoce. WA. 
Tue following paper is an application of the theorem 
JS{[(tutmv+nwydS= Sif (GE+4 gu yt gee, 
in which the first integral is taken over the sur ae of the ellipsoid 
ee = - 1=0, and the second through the volume 
enclosed by the ellipsoid, 7, v, w being, with their first deriva- 
tives, finite, continuous, single-valued functions of the variables 
2 
The method employed is illustrated by a few examples, and 
the results are embodied in a table. 
The direction-cosines of the normal at any point on the 
ellipsoid being = p ee Ls Zi , the surface-integral takes the form, 
2’ 
A=KE (+ oy, +r )as 
b C 
ExampLe I.—Let u =a’ x, v=? y,w =c* z; then (A) becomes 
—du,dv,dw 
Sip(e@+y+ 2PdS =ffprdS,andaz= 
=@V+R +c? = x(a’). 
Hence. //prdS=3(@)//fdV=3(@)V. Gi) 
Wiemann ae 
