284 Prof. W. C. Unwin on Measuring-Instruments 



straightening the lines a 0, b become parallel, the error 

 introduced is the difference between a x b x and the arc a c b ; 



Fig. 1. 



>* 



.y 



S 



s' 



and this is much more serious. Most commonly, however, 

 measurements are made between points on clips fastened to 

 the bar at 1 or 2 inches distance from its surface, such as 

 a 2 b 2 . Then the error introduced by straightening is the 

 difference between a 2 , b 2 and the arc a c b ; and thi s may be a 

 serious error, even with a very small amount of initial cur- 

 vature. 



If simultaneous measurements are taken of a x b x and a 3 b s , 

 the mean of these will have no greater error than the mea- 

 surement of ab. That is, the mean of measurements on two 

 sides of the bar reduces the error due to initial or induced 

 curvature to the same amount as a measurement actually 

 made at the axis of the bar. 



Prof. Bauschinger, of Munich, appears to have been the 

 first to recognize the importance of this double measurement 

 symmetrically on the two sides of the bar. He has always 

 used an apparatus in which a finger, or touch-piece, attached 

 to one end of the bar, presses on a roller attached to the other 

 end. As the bar extends, the roller rotates by friction ag ainst 

 the finger. A mirror is attached to the roller ; and the amount 



