Dec. 26, 1878] 



NATURE 



187 



they had used another property for their priestcraft, but the 

 account of this he wotUd reserve for the lecture at the Royal 

 Institution. 



"On the Torsional Strain which remains in a Glass Fibre 

 after Release from Twisting Stress," by J. Hopkinson, D.Sc, 

 F.R.S. It has long been known that if a wire of metal 

 or fibre of glass be for a time twisted, and be then re- 

 leased, it wlU not at once return to its initial position, but 

 will exhibit a gradually decreasing torsion in the direction of 

 the impressed twist. The best method of approximating to an 

 expression of the facts has been given by Bolt23nann (" Akad. 

 der Wissensch. zu Wien," 1874). He rests his theory upon the 

 assumption that a stress acting for a short time will leave after 

 it has 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 ^ (/) t be the strain at time t resulting from a 



twist lasting a very short time t, at time ^ = o, ^ (/) = - , 



where A is constant for moderate values of /, 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. 



The glass fibre examined was about 20 inches in length. 

 The glass from which it was drawn was composed of silica, 

 soda, and lime — in fact, was glass No. I of my paper on 

 "Residual Change of the Leyden Jar" {.Phil. Trans., 1877). 

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

 deflection at any time was determined by the position on a scale 

 of the image of a wire before a lamp, formed by reflection fi-om 

 a light concave mirror, as in Sir W. Thomson's galvanometers 

 and quadrant electrometer. 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 extre- 

 mity of the fibre was assumed to be fixed ; the mirror also was 

 attached to the lower clamp. This arrangement was unsatis- 

 factor)', as one could not be certain that a part of the observed 

 after-effect was not due to the fibre twisting within the clamps 

 and then sticking. The difficulty was easily avoided by employ- 

 ing two mirrors, each cemented at a single point to the glass 

 fibre itself, one just below the upper clamp, the other just above 

 the lower clamp. The upper mirror merely served, by means of 

 a subsidiary lamp and scale, to bring back the part of the fibre 

 to which it was attached to its initial position. The motion of 

 the lower clamp was damped by attaching to it a vane dipping 

 into a vessel of oil. The temperature of the room when the 

 experiments were tried ranged from 13* C. to lyZ" C, and for 

 the present purpose may be regarded as constant. The lower 

 or reading scale had forty divisions to the inch, and was distant 

 from the glass fibre and mirror 38I inches. Sufficient time 

 elapsed between the experiments to allow all sign of change due 

 to after-eflfect of torsion to disappear. In all cases the first line 

 of the table gives the time in minutes from release from torsion, 

 the second the deflection of the image from its initial position in 

 scale divisions. 



Experiment VI. — Twisted for 121 minutes. 



* i I 2 3 4 5 



Scale divisions 191 170 148 136 I26i lipj 



7 



Scale divisions 



10 



97 



IS 30 65 90 



84^ 63! 41 i 34 



120 589 

 28 3i 



The time was taken by ear firom a clock beating seconds very 

 '.i^tinctly. 



The first point to be ascertained from these results is 



aether or not the principle of superposition, assumed by Boltz- 

 :iiann, holds for tor.-ions of the magnitude here used. 



If the fibre be twisted for time T tl.rough angle X, then 

 the torsion at time / after release will be X [^{^ (T + /) - tf, [t)\ 



"^ i.i) = f t> {.t) dt. 



If now T = /-J -f/2 + ^3+ . • • ^ve may express the effect of 

 ae long twist m terms of several shorter twists by simply noticing 



+{^ (i + h + t^)-^[t + h+t^+t^)] +, &c.] 

 •Apply this to the preceding results, calcukiting each experi- 



ment from results for shorter time. Let xt be the value of i^ 

 (T -f /) - t|/ (/), that is, the torsion at time t, when free, di\'ided 

 by the impressed twist measured in same imit ; we obtain the 

 following tables of comparison : — 



Results for T = 121 compared with those from T = 20. 



Xt observed 

 Xt calculated 



t 

 Xt observed 

 Xt calculated 



c"oo979 



10 



497 

 670 



15 



433 

 600 



I 



871 

 1070 



30 



32s 



500 



2 



758 

 950 



65 



212 



380 



3 



697 

 880 



90 



174 



350 



4 



648 

 830 



120 

 144 



5 

 612 

 780 



589 

 18 



7 



556 

 73'3 



The three last tables agree in indicating a large deviation from 

 the principle of superposition, the actual effect being less than 

 the sum of the separate effects of the periods of stress into which 

 the acual period may be broken up. Kohlrausch finds the same 

 to be the case for india-rubber, either greater torsions or longer 

 durations give less after-effects than would be expected from 

 smaller torsions and shorter periods. 



The deviation from formula <p it) = — appears to indicate 



A 



the form ^ (/) = -, o being less than, but near to, unity. If 



a = o'95 we have a fairly satisfactory formula. 



Xt = A' (r^, Y_ f"), where A' =^-when T = 121. 



In the following table the obser\-ed and calculated values of 

 Xt when T = 121 are compared. A' being taken as 0*032. 



of A ranging from 0-0017 to 0*0022. Boltzmann for a fibre, 

 probably of a quite different composition, gives numbers firom 

 which it follows that A = 0-0036. 



In my paper on "Residual Change of the Leyden Jar," that 

 subject is discussed in the same maimer as Boltzmann discusses 

 the after-effect of torsion on a fibre, and it is worth remarking 

 that the results of my experiments can be roughly expressed by a 



formula in which <p (/) = C. For glass No. 5 (soft crown) 



a = 0-65, whilst for No. 7 (light flint) if is greater ; but in the 

 electrical experiment no sign of a definite deviation from the law 

 of superposition was detected. 



Geological Society, November 20.— R. Etheridge, F.R.S. , 

 vice-president, in the chair.— Rev. James Crompton and John 

 DennLs Paul were elected Fellows. — The following communica- 

 tions were read : — On the upper greensand coral fauna of 

 Haldon, Devonshire, by Prof. P. Martin Duncan, F.R.S. The 

 author in this paper stated that since the publication of his 

 supplement to the British fjssil corals, published by the 

 Palseontographical Society, several new corals have been ob- 

 tained at Haldon by Mr. Vicary, cf Exeter. Twelve additional 

 species were noticed, of which ten were new. This brings the 

 total number of species in the Haldon Greensand up to twentj-- 

 one. The new species are thus distributed : — Aporosa : Oculi- 

 nidae (i), Astneidse (3), Fungidae (5); Perforata: Turbmariae 

 (2) ; Tabulata (i). The paper concluded with remarks on the 

 genera and species represented, from which it appeared that the 

 coral fauna of Haldon is the northern expression of that of the 

 French and Central Eiu-opean deposits, which are the equivalents 

 of the British upper greensand. Ihe Haldon deposit was 

 formed in shallow water, and the corals sn-ew upon the rolled 

 debris of the age. — Notes aa. Pleurodon aj}.uls, sp. ined., Agassiz, 

 and description of three spines of cestracionts from the lower 

 coal-measures, by J. W. Davis, F.G.S.— On the di-tnbution of 

 boulders by other agencies than that of icebergs, bv C. E. 

 Austin, C.E., F.G.S. 



December 4. — Henrj' Clifton Sorby, F.R.S., president, in 

 the chair. — Rev. William H. Allen, George Grey Butler, 

 John Dixon, Rev. William Downes, B.A., Joseph Drew, 

 M.D., Arthur Tom Metcalfe, E. P. Monckton, M.A., 

 Albert J, Mott, Philip LuUey Sclater, Ph.D., F.R.S., 

 William Hobbs Shrubsole, and Alexander Thuey, were elected 



