THEORY OF THE REFLECTING EXTENSOMETER. 99 
= = na approximately......... (4a) 
which may be employed whenever the extension or compression is 
very small, and when therefore #& is very small in relation to L. 
When however £ is not relatively small, the approximate formula 
is clearly unsatisfactory, since it is easily shewn that 
cos 2m _ ve 3B? < (3lLkt 
cos w SL. IAL 
I’ being the actual distance from the scale to that point on the 
mirror where the sight line meets it, see (2). 
This last equation indicates in a general way the order of the 
error committed in accepting the approximate formula. Although 
the value of w is not directly afforded by the instrument, but has 
to be derived from R# and L’, little is gained by the expansion in 
a series of convergent terms, because in extreme cases the con- 
vergence is not sufficiently rapid. The most convenient method 
of dealing with equation (4), is to find a correction z to be applied 
to the reading FR, such that the corrected reading 2’ will be 
e l 
dae ape O 
« will of course be a variable correction, to be obtained with the 
arguments #& and Z, from a table of double entry constructed for 
the lengths Z; for positive values of w it will be generally negative. 
Then with this corrected reading, the convenient relation expressed 
by formula (7) may be used rigorously. 
4. Construction of tables of corrections to scale-readings.—In 
order to construct tables of corrections, the dimensions of the 
extensometer apparatus must be taken into account. The contact 
bars’ EJ G, Fig. 1, supplied with the apparatus, and which deter- 
mine the length Z the extension of which is required, are of the 
following reputed lengths, viz., 30, 50, 100, 150, and 200 mm., in — 
order to meet the requirements of different sizes of test piece. — 
ee ee 
1 See also Figs. 3 and 4 of Professor Warren’s paper. 
