used in Mechanical Testing, 283 



have to be made, and two readings taken for each elongation. 

 Also the limit of accuracy of the cathetometer is hardly suf- 

 ficient for the purpose. 



Very often mechanical magnification by a lever is adopted. 

 But there are some difficulties in satisfactorily attaching a 

 lever- apparatus to the bar : if a leverage of 100 to 1 is adopted, 

 the fulcrum distance becomes very short, and the range of the 

 apparatus is limited. There is also some difficulty in the 

 calibration of the instrument to determine the value of the 

 readings. 



A micrometer-screw is sometimes used as a means of me- 

 chanical magnification. With this there is, again, the diffi- 

 culty of suitable attachment to the bar; and, as generally 

 used, it is difficult to ascertain when exact contact of the 

 screw is obtained without excessive pressure. 



There is a special difficulty in measuring the elongation of 

 ordinary test-bars which has been overlooked in the construc- 

 tion of most of the apparatus of this kind. It is difficult to 

 get test-bars which are rigidly straight. Even if the test-bar 

 is strictly straight, it is difficult to hold it in the testing- 

 machine, so that the resultant of the stress on any cross section 

 passes strictly through the centre of figure of the section. 

 Now if this condition is not satisfied, the bar becomes curved 

 during the test. The straightening of an initially curved bar, 

 or the curving of an initially straight one, introduce errors 

 in the measurements of very considerable amount. 



If the measurements could be made at the axis of the bar, 

 the errors of this kind with any amount of curvature likely 

 to occur would not be very serious ; but this is of course 

 impossible. The best that can be done is to measure at the 

 surface of the test-bar. But, in straightening, the surface of 

 the bar on one side lengthens and on the other shortens, and 

 thus introduces a not inconsiderable error of measurement. 

 If, as in many forms of elongation measuring-apparatus, the 

 measuring-points are two inches or more from the axis of the 

 bar, the errors become very large relatively to the elongations 

 to be measured. 



Let fig. 1 represent a bar bent in the plane of the paper, 

 the centre of curvature being 0. Then, if measurements 

 could be made on the axis of the bar, between the points a b, 

 the straightening of the bar would introduce an error equal 

 to the difference of the length of the chord a b and arc a c b. 

 With any amount of curvature likely to occur in a test-bar, 

 this error would not be very serious, (xenerally, how T ever, 

 the best that can be done is to measure the distance between 

 points a x b x on the surface of the bar. Then, since by 



