60 MEASUREMENT OF COUPLES. 



moment of breaking the elongation of a silk thread is - , of which 



two-thirds are permanent elongation when the stretching weight is 

 lessened. The influence of temperature and of the hygrometric 

 state would be about half as much as with hairs.* 



Coulomb cites an experiment in which a small copper cylinder 

 an inch long (2707 cm.), weighing 6 grains (0-3187 gm.), and 

 suspended to a cocoon fibre an inch long, made its oscillation in 

 40 seconds. From these numbers we get for the torsion coefficient 

 of a single silk fibre i cm. in length, in C.G.S. units, 



= 0-003254. 



A silver wire, to have the same coefficient of torsion, must have 

 a diameter of 0*00595 mm '> an d would only support without breaking 

 a weight of o'8i8 gr. ; while the cocoon thread can carry 10 grammes, 

 or 13 times as much. In order to support the same weight, at least 

 13 of such wires must be used, or a wire whose section is 13 times as 

 great. In the second case the coefficient would be 169 times that of 

 the cocoon thread. 



These numbers show the advantage of using cocoon threads in all 

 suspensions like those of magnets, in which the movable system has 

 of itself a directive force, and where it is desirable to diminish that 

 of the suspension as much as possible. By joining these threads 

 parallel to each other, so that they are all under the same tension, a 

 bundle can be obtained which is as strong as necessary, and the 

 torsion couple of which is almost the sum of the couples for each 

 of the threads. When we seek to diminish the torsion couple, a 

 bundle of parallel threads is always better than a single thread 

 of the same total section. If we could neglect the effect arising 

 from the distance of the points of support, the resulting couple 

 with a single thread would be proportional to the square of the 

 section that is, to the square n 2 of the number of equivalent 

 threads, and therefore n times greater than the couple constituted 

 by these n threads. 



714. BIFILAR BALANCE. We may, on the other hand, take 

 advantage of this very distance of the wires to produce a torsion 

 couple. This is the principle of the bifilar balance, first used by 



* Ann. de Chitn. et de Phys. [2], Vol. xxvi., p. 367. 1824. Report of 

 FRESNEL on Babinet's Hygrometer. 



