366 PROCEEDINGS OF SECTION A. 
L=fff{(4(@+e+w)-V-f(p))pds... mi (2) 
where f(p) is the potential energy per unit mass due to strain 
and ds is an element of volume. Eq. (1) gives 
fat(8L4S/f(EX+nV+lZ)pds+/S (EP, + 1h. +bp,)aS) (3) 
where (€, 7, ¢) is the virtual displacement, (X, Y, Z) an external 
bodily force independent of V, and (A, A, 2, ) the stress per unit 
surface at the boundary. If by means of the displacement the 
point would move from P to P' and if / be the value of any 
quantity at P before displacement, “+ 6 will be supposed to 
mean the value at P’ after displacement. Thusé(pds)=0,du=¢ 
Hence, 
a FSIS Eur nor bw) pds+J/(Elenmetn)p'f aS 
SI RAE +” ECe'P eal] + 0s 
where /' stands for df//dp and where (/, m, x) are the direction 
cosines of the normal outwards. From equation (3) we obtain 
the surface equations 
=p kh FAS 
(say), shewing that the stress is a hydrostatic pressure of 
magnitude p* 7’; and the volume equations 
bee AO tec ee (5), 
and two similar ones. 
Notice that p’/' = £ gives f= — fp dv' where v' is the volume 
of unit mass. This is the ordinary expression for the potential 
energy of strain per unit mass. 
5.—ON THE DESIGNING OF TRANSIT 
INSTRUMENTS. 
By Professor Krrnot, M.A., C.E. 
THE transit instrument is an appliance of cardinal importance to 
the astronomer. By its means he determines the relative positions 
of the heavenly bodies, and upon the accuracy of its indications 
all his calculated results depend. It is therefore of the utmost 
importance that this instrument should be in every respect as 
perfect as it can be made. 
The transit instrument consists of a telescope attached at right 
angles to an axis, which latter is provided with a graduated circle, 
