30 M. G. Kirchhoff on the Relation of the Lateral Contraction 



of drawn wires ; it cannot, therefore, be assumed with certainty 

 that the section is a circle j but it may be assumed without 

 appreciable error that the section is an ellipse, in which the 

 square of the eccentricity may be neglected. By this assump- 

 tion the influence of the deviation of the section from the 

 circular shape may be eliminated. It is simply necessary to 

 turn the bar about its axis by 90°, to fix the arm A' B' again 

 horizontal on A', and to observe for the second time the change 

 of form which the rod experiences if the weight P' is suspended 

 at B\ The torsion must then be found to be as great as in the 

 first position of the rod, but in general the flexion will be 

 different. The torsion in either of the positions, and the arith- 

 metical mean of the two flexions are as great as the torsion and 

 the flexion would be if the section of the rod were a circle 

 whose radius is the mean of the two semidiameters of the elliptical 

 section. 



The arm A' B' is not easily brought exactly at right angles to 

 the axis of the rod ; a slight obliquity influences the flexion, but 

 not the torsion. This influence I have endeavoured to neutralize 

 in the following manner : — The arm A' B' is half of a cross rod 

 B' D' ; after the weight P has acted at B', I suspend it at D', and 

 take the mean of the flexions observed in both cases. The 

 torsion must be the same in both cases if the axis of the rod 

 passes through the middle of B' D'. If this condition is not 

 fulfilled the torsions are different, but their mean is then as 

 great as the torsion would be if the length of each arm were 

 exactly equal to half of B' J)', 



In order to render myself independent of the supposition that 

 the part of the rod at A exactly retains its position, if the weight 

 P is suspended to the end of its lever arm, I made the arrange- 

 ment that the rod A A' is the half of a bar A' A", which supports 

 at A" a cross rod B" D" of the same dimensions as B' D', and a 

 mirror C /; , upon which a second telescope is directed. The rod 

 is fixed at A in a piece of thin metal plate ; equal weights are 

 suspended at B' and B", or at D' and D", and the image of the 

 same scale is observed in both mirrors. 



The apparatus which I have used is represented in perspective 

 in fig. 2, Plate I. On the wall of the observing-room four 

 boards, A, B, B, C, are fixed ; on one of these, A, the scale is 

 fixed, and on two others the two telescopes ; the last supports the 

 rod which is to be experimented upon. On the board A and at 

 right angles to it, are two horizontal arms a, a; on each of these 

 are fixed two small pieces of wood projecting inwards, through 

 which the screws «, a are passed from below. The scale rests on 

 these screws, and is made horizontal by means of a level. The 

 scale is printed on paper, and stretched upon a glass plate. 



