98 G. H. KNIBBS. ' 
and the mirror U/ before rotation, be denoted by Z; then the 
distance ZL’ to the point 1M,” where the telescopic sight-line 7M— 
assumed to be identical with /G—will strike the mirror after 
rotation, will be 
2 
L'=L+ 3 (vers o+sin tan ) + ee sin® w tan w—etc...... (2) 
the minus sign being taken when the contact piece GHZ is on the 
opposite side of the test specimen, the mirror however, facing as 
in the illustration Fig. 1. 
A little consideration will shew that in any case, the term in/? 
can never be sensible, because neither the measurement of the 
distance Z, nor the reading of the scale can even approximately 
attain to the order of precision involving its retention. Hence it, 
and all higher terms may be rejected. Again, for the same reasons, 
the circular functions enclosed within the brackets may be written 
as }sin®, $ arc?, or $ tan®, without involving sensible error. 
Reducing the above expression in the manner indicated, and mul- 
tiplying by tan 20, so as to obtain the distance 7U, which is the 
difference R of the scale readings before and after the stress is 
is applied ; we have 
RL tan 2 (1+ SF tan* Soe ee (3) 
an equation which accurately defines the relation between the 
reading of the scale and the original distance of the mirror there- 
from, in terms of the prism rotation. Remembering that powers 
of » higher than the second may, when multiplied by a small factor 
like 1/Z or 1/L, be certainly rejected as insensible, we get from 
these equations expressing the values of ¢ and R, viz. from (1) and 
(3), after some slight reduction, 
Som gy E(t pines BF tanto ne eee (4) 
Similarly for a negative reading of the scale, we may simply regard 
fF and w as negative and leave the signs unchanged. 
When o isso small that its cosine may be taken as unity, and its 
sine as zero, this equation is reduced to the approximate formula 
given by Professor Warren, viz., 
