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XXV. On a Compact Apparatus for determining Young's 

 Modulus for Thin Wires. By Charles H. Lees, D.Sc, 

 and Roger E. Grime, B.Sc* 



MANY who have determined Young's Modulus for a 

 material both by the bending of a beam and by the 

 stretching of a wire of the material, must have contrasted 

 the compactness of the apparatus used in the former with 

 the bulkiness of that used in the latter method. It was this 

 contrast which led us to attempt to devise a simple and 

 compact apparatus for testing Wires. The initial difficulties 

 met with in making the apparatus at the same time compact 

 and reliable proved much less serious than we anticipated, 

 and as the apparatus in its final form proved easy to use and 

 satisfactory, it seemed to us worth while calling the attention 

 of physicists to a method of determining Young's Modulus 

 for thin wires which does not appear to have received in 

 the past the attention it deserves. 



Theory of the Method. 



The method utilizes the depression produced in the middle 

 of a straight horizontal length of thin wiret, supported rigidly 

 at its ends, by a load applied at its middle point. 



If AB be a wire whose resistance to bending may be 

 neglected, of length 21, supported at A and B, and if a mass 



Fig. 1. 

 A V C 



v 

 My 



M, suspended at its middle point C, depress that point to D, 

 where CD = y, the downward force Mg at D is balanced by 

 the vertical components of the pull T in DA and DB ; 



i. e. M# = 2T cos CDB = 2T sin CBD, 

 or T=^cosec0 where 6 = CBD. 



When CBD = 0, and therefore M = 0, let T = T . Then 

 the change of length of a length originally I, due to the 

 increase of the pull of the wire from T to T is equal to 



* Communicated by the Authors. 



t Up to about No. 27 S.W.G. in the apparatus used. For thicker 

 wires the flexural rigidity renders it necessary, if an accuracy of 1 per 

 cent, is required, to treat the wire as an elastica. It is neither straight 

 nor is the tension in it constant, and the simple theory gives too high 

 values for the modulus. 



