Small Strains in Bars subjected to Twist. 525 



the screw may be thrown out of engagement. Since the 

 difference between an arc and its corresponding chord is an 

 infinitely small quantity of the third order when the arc is an 

 infinitely small quantity of the first, the readings of the micro- 

 scope-scale may be taken as directly proportional to the angular 

 displacement, and the calibration is effected by moving the 

 wire through a definite angle of, say, 10', and noting the 

 equivalent reading of the micrometer eyepiece. 



This instrument is furnished with an improved form of 

 clamp (fig. 3), consisting of a pair of divided collars, a, the 

 halves being pivoted together at b, and secured by nuts e. 



Fig. 3. 



The collars are wedge-shaped in radial section to engage 

 with corresponding wide-angled grooves upon the chuck- 

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

 that the collars are readily 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 this can be suppressed 

 by a pin or by the frictional grip of the collars, thereby 

 causing the parts to act as one rigid whole for setting the 

 instrument on the bar. 



The two main parts of the apparatus are set in their respec- 

 tive collars ; the bar is then passed through and the screws 

 adjusted. The clamp is then removed, leaving the two pieces 

 at the correct distance apart, while the graduated circle has 

 its plane perpendicular to the bar, and is chucked accurately 

 thereon. 



The graduated circle of this instrument is carried by a self- 

 centering chuck of somewhat novel form, and a section through 

 this is shown by fig. 4, while a perspective view of the arrange- 

 ment is shown by fig. 5. 



There are three centering-screws, A', the outer cylindrical 

 ends of which are supported in guides, B', and prevented from 



Phil Mag. S. 5. Yol. 46. No. 283. Dec. 1898. 2 



