816 Depression due to a Load at Centre of an Elastic Chain. 



The distances b in the above equation are measured 

 vertically from the horizontal straight line joining the points 

 of support. The position of this zero point on the scale on 

 which the depressions are measured is best determined by 

 tilting the frame holding the chain or wire till the chain 

 or wire is vertical, clamping it in position under a tension 

 sufficient to keep it straight, then taking the measurements 

 while the chain or wire is still vertical. If the clamping and 

 measurement cannot be done with the wire in a vertical posi- 

 tion, the zero may be determined with the chain or wire, the 

 frame and the scale on which the measurements are taken all 

 horizontal, so that the plane of bending of the wire is at right 

 angles to the line of measurement. 



In the case of the thin wires used by Mr. Grime and myself* 

 the mass of the wire was neglected. If taken into account it 

 makes a difference in the final value of e which in most cases 

 is less than 1 per cent. The experiment with the thickest 

 wire used, no. 27 S.W.Gr. copper, and the lowest initial tension 

 T = 380 g. t is recalculated below, the zero from which the 

 depressions are measured being calculated from the value of 

 the initial tension T . 



Copper wire, no 27 S.W.G., half length 26-50 cm. 



Mean diameter *0412 cm. Area of cross-section '00133 sq. cm. 



Density of copper 8*95. Mass per cm. a ='0119. 



Mass of half the wire m = '315 grams. 



T 



c = -5 = 31930 cms. 



b = c (cosh i _!) = !- = -0110 cm. 



M. 



grs. 



M-J-m. 

 grs. 



b 



cms. 



b 



M T 4-w M 2 +w 

 b, b 2 



b\ 



v-v- 



Mj-J-wa M 2 -j-ra 







«■ 







•315 



•0110 



28-64 





•0001 









15 



1532 



•3740 



40-96 



21-64 



•1399 



•2534 



85-4 



1-17x10" 



25 



25 32 



•5035 



50-28 



1805 



•2535 



•2183 



82-7 



113 „ 



35 



3532 



•5985 



5901 





•3582 









Mean e ... 1*15 XlO 1 



The result obtained by neglecting the mass of the wire 

 was 1'17 x 10 12 . In this case the more accurate gives a result 

 2 per cent, less than that obtained by the simpler theory. 



* Phil. Mag. ix. p. 258 (1905). 

 t Ibid. p. 264. 



