540 



NATURE 



[January ib, 1913 



LETTERS TO THE EDITOR. 



I'llie Editor does not hold himself responsible for 

 opinions expressed by his correspondents. Neither 

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 the writers of, rejected manuscripts intended for 

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 taken of anonymous communications.^ 



The Double Refraction produced by the Distortions of 

 Elastic Bodies according to Volterra's Theory. 



The interesting experiments of Prof. E. G. Coker 

 on tfie application of optical methods to technical 

 problems of stress distribution have been described 

 in an article in Nature of December 5, 1912. This 

 article suggests that this would be an opportune 

 moment to publish, outside of Italy, the results of 

 researches whicli Sig. Trabacchi and I undertook 

 some 3'ears ago for a similar purpose (Rend. Lincei, 

 vol. xviii., 1909). There is this essential difference 

 from Prof. Coker 's experiments, that bur object at 

 tliat time was the experimental verification of precise 

 calculations deduced from Volterra's theory of elastic 

 "distortions" (.inn. dc I'Ecole Normale de Paris, 

 1907). 



The peculiarity of these distortions consists in the 

 entire freedom of the distorted bodies from the in- 

 fluence of external forces. Let it suffice to recall the 

 two simplest cases, namely those in which a small 

 slice, with faces cither radial or parallel, is removed 

 from a cylindrical ring of elastic matter, and the cut 

 surfaces then glued together. There exist accordingly 

 internal tensions, but no external forces ; this malies 

 the theoretical calculation quite rigorous, and the 

 experimental conditions very similar to the hypotheses 

 in the theory. I found it easy, starting from Vol- 

 teiTa's general formula, which permit the calcula- 

 tion, noint by point, of the tensions in the interior of 

 the cylinder, to prophesy the figures of double refrac- 

 tion which should be observed in polarised light 

 traversing the ring in the direction of its axis, and — 

 more precisely — the equations of the absolutely black 

 lines, corresponding to various orientations of the ring 

 with respect to the principal sections of the polarise- 

 analyser. 



In the case of a radial cut I was able to predict 

 the formation of a circle and a cross, the arms of 

 the cross being parallel to the sections of the 

 polarisers, irrespective of the orientation of the ring 

 in its plane. So far as can be calculated, the radius 

 of the circle depends only on the exterior and interior 

 radii of the ring, and not on the angular amplitude 

 of the cut. The circle is the locus of points wliere the 

 distortion is reduced to a uniform dilatation or com- 

 pression, that is, where the isotropy of the body is 

 unaltered. 



It was a less simple matter to foresee the aspect of 

 tlie phenomenon in the case of a cut with parallel 

 faces equidistant from the axis. In Fig. i the x axis 

 coincides with the faces glued together after the re- 

 moval of the slice. With the nicols parallel and 

 perpendicular to this axis, the theory demands the 

 formation of a black straiglit line in the direction of 

 the X axis, and of a curve of the fourth order, tangent 

 to the exterior circle at the extremities of the diameter 

 perpendicular to the .\- axis. In Fig. 2 are reproduced 

 the lines theoretically calculated when the nicols are 

 inclined 45° to the direction of the cut; in this case 

 one should observe a black line perpendicular to the x 

 axis, and two curves similar to the two branches of a 

 hyperbola ; there should be, furthermore, four isolated 

 black points at P, Q, R, S. The curves predicted are 

 not neutral curves, that is to say, curves without 

 double refraction, but isogonal curves, i.e. curves 



NO. 2255, VOL. 90] 



wherein the double refraction has a constant direc- 

 tion, that of the nicols. As a matter of fact, there 

 exists in this case no neutral line, but merely six 

 neutral points. 



These calculations were, at my suggestion, verified 

 in this institute by Sig. Trabacchi. He made use of 

 rings of freshlv prepared gelatine, and by their im- 



mersion in water avoided all possibility of accidental 

 double refraction wliich might result from adhesion 

 to the supporting glass plate. The ring, in a hori- 

 zontal plane, was lowered carefully in a glass dish 

 of water. The dish was illuminated from below by 

 polarised light coming from a black mirror ; a simple 

 optical device was used, which allowed the entire 



image of the ring to be projected through a nicol 

 of dimensions much smaller than those of the ring. 



Figs- 3. 4. and 5 reproduce the photographs 

 obtained. The first corresponds to the radial cut, the 

 others to the cut with parallel faces, with the light 

 polarised respectively parallel to, and at 45° from, the 

 direction of the cut. The correspondence with the 



