] 84 Lord Rayleigh on a Statical Theorem. 



mity rested on the upper surface of the bar at the marked points. 

 In this way there was no uncertainty as to the exact point at 

 which the weight was applied. The measurements of deflection 

 were made with a micrometer-screw reading to the ten-thou- 

 sandth of an inch, the contact of the rounded extremity of the 

 screw with its image in the upper surface of the glass being ob- 

 served with a magnifier. The reading in each position was 

 repeated four times, with the following results. 



Case 1. W hung at A. Deflection observed at B : — 

 W on. W off. 



79 

 82 

 79 

 76 



Mean . . 79 



1473 

 1473 

 1476 

 1474 



Mean . . 1474 

 The deflection at B due to W at A was therefore 1395. 

 Case 2. W hung at B. Deflection observed at A : — 

 W on. W off. 



50 

 47 

 45 

 45 

 Mean . . 47 



1447 

 1449 

 1445 

 1446 



Mean . . 1447 



Accordingly the deflection at A due to W at B was 1400. 



The difference of the two deflections, amounting to only about 

 \ per cent., is quite as small as could be expected, and is almost 

 within the limits of experimental error. 



In the second experiment the test was more severe, B being 

 replaced by another point B f 7 \ inches distant from A, instead 

 of only 5 inches. The deflections in the two cases here came out 

 identical and equal to 993 divisions, W being the same as before. 

 With W at A, the deflection at A was about 1 700 ; and with W 

 at B', the deflection at B' was 760. 



The theorem here verified might sometimes be useful in de- 

 termining the curve of deflection of a bar when loaded at any 

 point A. Instead of observing the deflection at a number of 

 points P, it might be simpler to measure the deflections at the 

 fixed point A, while the load is shifted to the various points P. 



For the benefit of those whose minds rebel against the vague- 

 ness of generalized coordinates, a more special proof of the theo- 

 retical result may here be given. The equation of equilibrium 

 of a bar (whose section is not necessarily uniform) is 



£( B 30= Y *> w 



* Thomson and Tait's ' Natural Philosophy,' § 617. 



