APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS. 265 



angled prism is interposed between this and the objective W, so that readings can be 

 easily taken. The tube Q is free to slide or rotate in its guide R, but, in order to 

 readily focus the wire, this latter is carried in a frame X, pivoted upon the Vernier plate 

 J, and adjusted by a screw V. 



The microscope arm S is secured to the cylinder C by a divided collar, the two 

 halves of which are pivoted on one side, and the free ends clamped by screws. 



If it is desirable to turn the telescope round or to release it altogether, the screw 

 may be thrown out of engagement. Readings are taken from one edge of the thick 

 wire, and as this edge is very distinct, it fatigues the 

 eye much less than a spider line or scratch upon 

 glass, which latter have the further disadvantage of being 

 of appreciable thickness. Fig. 5 shows the appearance 

 of the field of view of the reading microscope and the 

 wire P. 



No appreciable error is caused by the fact that the 

 divisions upon the glass scale of the microscope are 

 linear measurements, while the movement of the wire is 

 in a circle. For if ABC be the path of the wire and 

 AC the chord, then the error is the difference between the arc ABC and its chord 

 AC when the angle o( is a small quantity of the first order. 



I.e. ^A =r a -. 2r sin £L 



o fa a 3 a 5 \ 



m ( a 3 a 5 , * \ 



a small quantity of the third order, and therefore negligible. In practice this 

 is shown to be the case, as no difference can be observed between the parallelism of the 

 wire P and scale for any position of the former. The reading of the microscope scale 

 may therefore be taken as directly proportional to the angular displacement, and the 

 calibration is effected by moving the wire through a definite angle and noting the 

 equivalent reading of the micrometer eye-piece. 



It is essential that the graduated circle be set accurately upon the bar, with its 

 plane perpendicular thereto and its centre coinciding with the longitudinal axis of the 

 bar. An arrangement was devised to effect this, consisting of a pair of divided collars 

 a, the halves pivoted together at b, and secured by nuts c. The collars are wedge- 

 shaped, in radial section to engage with correspondingly wide-angled grooves, upon 

 the chuck plate and cylinder only the angled sides being in contact, so that the collars 

 are readily fixed or freed when required. The lower halves d of the divided collars are 

 connected by one or more distance pieces e, so that when the former grip their 

 respective grooves each piece has one degree of freedom with respect to the clamp, and 



