92 Mr. J. J. Guest on the Strength of 



being shown at the right-hand side, and the telescope or 

 source o£ light being upon the left. The amount of twist of 

 the specimen is determined by observing the change of 

 reading of the scale by means of a telescope, the scale being 

 observed by reflexion at both of the mirrors. 



The second was the method selected, it being easily appli- 

 cable to specimens of varying lengths. 



The mirrors are mounted upon frames resting upon the 

 spheres c l5 c 2 , d ; e x , e 2 , f of the grips, which are left vacant 

 by the withdrawal of the adjuster. The two frames are 

 exactly similar. The angle c l5 c 2 , d is a right angle ; the 

 contact of the frame with c 1: b is made by means of a tri- 

 hedral hole mounted on a screw, with c 2 by means of a fixed 

 V-groove, and with d by means of a plane at the end of a 

 screw. The normals to the mirrors can be adjusted within 

 certain limits by the use of these screws. The various surfaces 

 are kept in contact by the use of the springs shown in 

 fig. 4. 



Had the other method been adopted, one or both mirrors 

 would have had to have been mounted upon sliding bars so 

 that they could have been adjusted opposite to one another, 

 when the grips (for torsion purposes) were placed at various 

 distances apart. No special adjustment, however, would 

 have been required to secure accuracy. 



If, in the inclined mirror case, we consider the lower grip 

 stationaiy and the top mirror alone to twist, it is very evident 

 that the twist of the upper mirror is the same as the angle 

 through which the reflexion of the optical axis of the reading- 

 telescope is turned, and is therefore, to the second order of 

 small quantities, equal to the change of scale-reading divided 

 by the distance from the telescope to the scale. The lower 

 grip, however, must be allowed to twist in order that the 

 stress in the specimen between the grips may be of the 

 normal type, uninfluenced by the, proximity of the holders ; 

 in the following investigation it will be shown that, when 

 a certain adjustment is made, the scale-reading divided by the 

 distance from the specimen to the scale is equal to the twist 

 of the specimen between the grips, at any rate as closely as 

 the tangent of the angle is equal to the angle. 



36. Proof that the Torsion-Mirrors measure the Twist. — 

 The light from the scale first strikes the upper mirror, 

 and is thence reflected on to the lower mirror, where- 

 by it is reflected to the telescope. In order, however, to 

 ascertain the effect of a simultaneous twist of the two grips, 

 we shall take the line in the reverse direction, and consider 

 the optical axis of the telescope and the direction of its 



