500 Prof. E. G. Coker on a Machine for applying 



into view on the scale, but no error is caused thereby. If 

 the specimen is bent in a plane at right angles to the former, 

 then the change in the reading is (# — <£)/, where and cj> 

 are the alterations of angle at the ends and 21 is the length 

 of the specimen under observation. Since the bending is 

 uniform 6 = $> and no correction is necessary. Bending in 

 any other plane can be resolved into components in the 

 vertical and horizontal planes, and therefore falls under the 

 preceding cases. In order to effect the adjustment required, 

 both the wire and the microscope slide in adjustable tubes 

 provided with graduated scales, and the movement to bring 

 the wire into focus is divided between them. To check the 

 setting of the wire in the central position it is convenient to 

 apply a uniform bending moment, and then to observe if any 

 change takes place in the reading. The position for no change 

 in the reading can be found in a few seconds. 



In experiments where the bending moment is constant and 

 the twisting moment is varied, no adjustment is practically 

 required during the elastic life of the specimen; and even 

 when the bending moment is variable the adjustment is 

 practically negligible, as the length of the specimen under 

 test is only a few inches. 



The instrument is used for observations of the angular 

 change due to bending by adjusting the wire in the hori- 

 zontal plane passing through the axis of the specimen, and 

 at a fixed distance away from the central plane, as shown in 

 fig. 7. Thus if the wire is at a distance x from the central 

 plane, and the specimen is subjected to a uniform bending 

 moment, the reading will be (l-\-x)Q — (I — x)6 = 2x0, and this 

 is a measure of the angular change 6 between the ends, since 

 any correction involves higher powers of 6 which are negligible 

 for elastic strains. 



The instrument may therefore be used for measuring strains 

 due to bending or twisting, and the single calibration required 

 for both sets of readings is effected when the instrument is 

 in position on the specimen. 



With the usual notation the value of Young's modulus 

 can be calculated from the equation EI^?/ 2 '/ 'dx 2 ! = M, from 

 which we obtain EI^ = Ml for determining E. Similarly the 

 rigidity modulus for specimens of circular sections may be 

 calculated from the equation C = TI/I 2 2 . The ratio of C to 

 E can also be readily obtained from the value ad^O^ where 

 a is an instrument constant: values of Poisson's ratio may 

 be determined in this way without calculating C and E 

 separately. As an example, we may take the case of a test 



