222 



NA TURE 



[January g, 1908 



rigidly as possible along its base and at its ends, and if 

 the plan of the upper edge is originally straight there 

 must be some horizontal displacement at the centre of the 

 length from the line joining the abutments, quite apart 

 from such displacement as may be due to the overturning 

 effect of the pressure on a vertical slab. The dam 

 resembles in some measure a built-in beam, and, recog- 

 nising this fact, some large dams have been built slightly 

 convex on the water face. 



If a balcony consisting of a plate of variable depth is 

 rigidly supported at its ends and along one side, I imagine 

 that the vertical displacement caused by a load at the 

 centre and front of the free edge of the balcony could 

 not be estimated without some regard for its end and side 

 supports, nor could the stresses due to it be easily deter- 

 mined. There would be some stress along the horizontal 

 fibres joining its ends, and the elevation of the front edge 

 of the balcony must show contraflexure, since its ends are 

 horizontal and the centre portion is concave upwards. 



Can we deny the existence of such effects, whatever 

 their magnitude may be, if a masonry dam is regarded 

 as an elastic body? An engineer should be conscious of 

 all the forces at work on a structure which he is design- 

 ing, and if these forces and their effects can be correctly 

 estimated, a design may be prepared having due regard 

 to the pliysical properties of the materials employed and 

 their liability to variation, owing to natural causes and 

 errors of workmanship. 



When the forces and their effects are in any measure 

 uncertain, the exercise of due caution, accompanied by 

 mature judgment based on experience, will usually lead to 

 a successful design. It does not seem probable that a 

 mathematical solution can be obtained for the stresses in 

 a homogeneous isotropic dam, rigidly fixed at its ends and 

 base, which can take account of the conditions existing in 

 practice. The solution of the theoretical case would be of 

 interest, but it is questionable to what extent it would 

 be applicable to practical conditions, in which dams are 

 not homogeneous and isotropic, and foundations and abut- 

 ments are not absolutely rigid. 



Engineers recognising these facts have used a simple 

 but approximate method of estimating the stresses in a 

 dam, based on the flexure of beams. The solution based 

 on the theory of elasticity, as presented by Prof. Pearson, 

 may be nearer the truth, but it may be questioned whether 

 this can be known to be the case in an actual dam. 



E. Brown. 



Echelon Spectroscope. 



Further observations on the secondary bands referred 

 to in my Ltter in Nature of January 2 (p. 198) seem to 

 indicate that they are faint spectra of a much higher order 

 than the primary spectra. 



Faint spectra of a very high order must be formed by 

 a series of beams that have suffered two reflections at the 

 external surfaces of the echelon. Each of these secondary 

 beams has traversed the echelon three times, and the re- 

 tardations of the beams form a series the common differ- 

 ence of which is seven times that for the series of beams 

 giving the primary spectra, taking the index of refraction 

 to be 1-5. These secondary beams would only have about 

 one six-hundredth of the intensity of the primary beams, 

 and I thought that the resulting spectra would be too faint 

 to be observed until I found that the reflections that take 

 place at the Interfaces of the echelon assist in forming 

 the same secondary spectra. 



Assume that each interface reflects the same very small 

 proportion of the light incident upon it, and neglect beams 

 that have been reflected more than twice. Imagine the 

 echelon being built up one plate at a time, commencing 

 with the largest. Each plate that is put on starts a series 

 of secondary beams and adds another term to each of the 

 ^e'lics started by the earlier plates. The retardations in 

 each of these series have the same seven-fold common 

 difference as the first series, and so they all help in form- 

 ing the secondary spectra. 



Each member of the series started by the iith pl.ite has 

 n times the intensity of the unit secondary beam produced 

 from the primary beam by two interface reflections, ron- 

 sequemly the iast few steps of the echelon are much more, 



NO. 1993, '^'OL. 77I 



effective in producing the secondary spectra than the steps 

 formed by the first few plates, and the clearness of the 

 secondary spectra given by the echelon may be much 

 improved by covering over, say, the first half of the whole 

 number ot steps built up. 



In this way better photographs of the secondary bands 

 have been obtained, and I hope to be able to test this 

 explanation of their formation quantitatively. 



H. Stansfield. 



The University, Manchester, January 6. 



The Photoelectric Property of Selenium. 



I HAVE to thank Mr. R. J. Moss (January 2, p. 198) 

 for the true explanation of the extraordinary increase of 

 conductivity of a selenium bridge enclosed in an exhausted 

 tube. The air pump employed, in the first instance, to 

 produce the exhaustions was the mercury pump of Topler, 

 and it occurred to me that the mercury vapour might be 

 objectionable. The enormous inagnitude of the effect, 

 however, induced me to ignore this vapour. The drop in 

 resistance was finally from 61 megohms to 9-7 ohms. 

 After seeing Mr. Moss's letter I made another bridge, 

 enclosed it in a glass tube, and exhausted this tube with 

 a Fleuss. The result was now an increase of resistance 

 in the bridge from 57 megohms to 110 megohms — an 

 increase which can be easily explained. Whether or not 

 the exhaustion produces increased sensitiveness to light 

 and other benefits I cannot yet say. Dr. Shelford Bid- 

 well's conjecture that there was a short circuit in the 

 bridge is the first explanation that naturally occurs, but 

 from the nature of the bridge no short circuit is possible. 

 The metallic parts are absolutely fixed, and separated by 

 thicknesses of glass or mica sometimes amounting to 

 I mm. 



The result proves the undesirability of exhausting by 

 mercury pumps in certain cases. 



O.xford, January 5. George M. Minchin. 



Musical Sands. 



In Nature of December 26, 1907 (p. iSS), Mr. S. 

 Skinner's recent exhibition of " singing " sand at the 

 Physical Society is referred to. These particular sands 

 were said to consist chiefly of angular grains. In all my 

 investigations, which have extended over a period of many 

 years, I have never been able to produce musical notes 

 from any sands composed of purely angular grains ; 

 indeed, as I have frequently stated, a certain proportion of 

 angular grains mixed with a musical sand will effectually 

 silence it ! I dealt fully with this point in my paper on 

 musical sand published in 18S8. Again, I have never yet 

 met with purely angular grains possessing smooth and 

 rounded surfaces — conditions which, with others, are 

 essential in the production of music from sands. Perhaps 

 Mr. Skinner meant subnngular grains? 



I do not think the explanation of the cause of the pheno- 

 menon suggested by Profs. Poynting and Thomson in 

 " Sound " (" Text-book of Physics ") meets the case. It 

 is based on the erroneous assumption that the sand-grains 

 are arranged as a number of equal spheres in contact. 

 If this supposition were correct, and the condition an 

 essential one in the production of notes, then my experi- 

 ments with many sands composed of highly spherical 

 grains (like the " millet seed," for instance) should have 

 yielded notes of the highest quality, instead of being, as 

 they all were, mute under the most favourable conditions. 



The late Prof. Tyndall, who took a great interest in my 

 work, and pensonally confirmed the results of my experi- 

 ments, agreed with my conclusions, and thought hardness 

 of grain an important consideration, believing that the 

 loudest notes might be emitted from ruby and diamond 

 sands — if I could get them ! I am under the impression 

 that if the theory proposed by Profs. Poynting and Thom- 

 son is tenable, it should be possible to obtain notes from 

 comparatively soft spherical seeds (like fig, &c.), but 

 though I have experimented with many kinds, I have not 

 been successful in this direction. I still think my friction 

 theory the simplest, and as inany leading men of science 

 have supported it, and no one has as yet disproved it, why 

 may it not be retained? 



Cecil Carus-Wilson. 



