1878.] 



Strain in a Glass Fibre. 



149 



leave after it lias ceased a strain which, decreases in amount as time 

 elapses, and that the principle of superposition is applicable to these 

 strains, that is to say, that we may add the after-effects of stresses, 

 whether simultaneous or successive. Boltzmann also finds that, if 

 0(£)t be the strain at time t resulting from a twist lasting a very short 



A 



time t, at time t=0, (£>(t)= — , where A is constant for moderate values 



of t, but decreases when t is very large or very small. A year ago I 

 made a few experiments on a glass fibre which showed a deviation 

 from Boltzmann's law. A paper on this subject by Kohlrausch (" Pogg. 

 Ann.," 1876) suggested using the results of these experiments to exa- 

 mine how Boltzmann's law must be modified to express them. Pro- 

 fessor Kohlrausch's results indicate that in the cases of silver wire and 

 of fibre of caoutchouc Boltzmann's principle of superposition is only 

 approximate, and that in the case of a short duration of twisting 

 A 



(t) =— , where a is less than unity ; in case of a long duration of 



twisting he uses other formula?, which pretty successfully express his 

 results, owing in part no doubt to the fact that in most cases each 

 determination of the constants applies only to the results of one dura- 

 tion of twisting. In a case like the present it appears best to adopt a 

 simple form involving constants for the material only, and then see in 

 what way it fails to express the varying conditions of experiment. In 

 1865 Sir W. Thomson published (" Proceedings of the Royal Society ") 

 the results of some experiments on the viscosity of metals, the method 

 being to determine the rate at which the amplitude of torsional vibra- 

 tions subsided. One of the results was that if the wire were kept 

 vibrating for some time it exhibited much greater viscosity than when 

 it had long been quiescent. This should guard us from expecting to 

 attain great uniformity in experiments so roughly conducted as those 

 of the present paper. 



2. The glass fibre examined was about 20 inches in length. Its 

 diameter, which might vary somewhat from point to point, was 

 not measured. The glass from which it was drawn was composed 

 of silica, soda, and lime; in fact, was glass No. 1 of my paper on 

 "Residual Charge of the Leyden Jar" ("Phil. Trans.," 1877. 

 In all cases the twist given was one complete revolution. The de- 

 flection at any time was determined by the position on a scale of the 

 image of a wire before a lamp, formed by reflection from a light con- 

 cave mirror, as in SirW. Thomson's galvanometers and quadrant elec- 

 trometer. The extremities of the fibre were held in clamps of cork ; 

 in the first attempts the upper clamp was not disturbed during the 

 experiment, and the upper extremity of the fibre was assumed to be 

 fixed ; the mirror also was attached to the lower clamp. This arrange- 

 ment was unsatisfactory, as one could not be certain that a part of the 



VOL. XXVIII. m 



