THEORY OF THE REFLECTING EXTENSOMETER. 107 
Fig. 1. If however the apparatus be disposed as shewn in Fig. 3 
of Professor Warren’s paper, that is to say, if two mirrors both 
facing the same way are read, the error is cancelled in forming 
the sum of the two results, consequently the disposition of the 
apparatus shewn in his illustration is to be preferred. 
10. Lrror from rotational movement of test-piece.—Although 
test-specimens are so held that they shall not be subject to rotation, 
yet to the order of small quantities under consideration, they can- 
not be regarded as incapable of such movement. Let p denote a 
small angle of rotation of the test-piece, in the plane containing 
its longitudinal axis and the scale, p being considered positive 
when in the same direction as the mirror, and let z denote the 
scale-reading correction due to this movement following on the 
application of stress, then 
R? 
z= * Io L' sec? 2w = = 2p (L'+—, ) oon (12) 
the minus sign applying to the case for the mirror on the remote 
side of the test-piece. The following series of corrections for a 
rotation of 10’, equivalent to a movement of about 3; inch in the 
axis of a 12 inch specimen, will give some idea of its siniitindlie 
TasLe IV. 
Corrections for rotational movement of axis of test-piece: Z = 1135. 
e-reading 0 100 200 300 400 500mm. 
Correction 10’ rotation + 6:60 666 681 7:07 7:43 788mm, 
As in the preceding case these corrections can be eliminated 
by disposing the apparatus as shewn in Fig. 3 of Prof. Warren’s 
Paper, for the variation of these corrections is not rapid. 
ll. Disposition of the apparatus in testing and general.—In 
order that defects in the construction of the apparatus may have 
nO appreciable influence on the results it affords, and that the 
@pplication of the scale-reading correction treated in §4should be _ 
rigorously accurate, it is desirable to adopt, in testing, the dis- 
Position of the apparatus hereinafter indicated. 
