84 



NATURE 



[October 4, 191 7 



matter, which might, however, in some cases be 

 fuller and more recent. The volume, as a whole, 

 gives a good idea of the amazing strides which 

 Chile has made during the last century. The great 

 drawback, however, to volumes of this nature, 

 especially when they are anonymous, is the lack 

 of critical spirit. In that respect this volume 

 does not escape. The picture is painted in colours 

 that are often too bright, with the result that it 

 leaves one with the impression of a country so 

 bountifully endowed by Nature as to be almost 

 without drawbacks. For example, the chapter 

 on climate, without ignoring the heavy rainfall, 

 strong winds, and gloomy weather of the far 

 south, contrives to give them considerably less 

 space than the more beneficent Mediterranean 

 climate further north. Apart from this griticism 

 there are few omissions in the book, but some 

 authentic account of the little-known Chilean 

 possessions of Juan Fernandez and Easter Island 

 might have been added. 



The English is weak in places ; sometimes the 

 meaning must be guessed, and there are misprints 

 on nearly every page. But the most serious charge 

 against the book is the absence of an index and 

 a good map. The only map is a crude, small- 

 scale one of the railways. The numerous 

 illustrations are excellent, but some of the expense 

 they have entailed might profitably have been 

 lavished on sketch maps in the text. 



The Journal of the Institute of Metals. Vol. xvii. 



Edited by G. Shaw Scott. Pp. x + 384. 



(London : The Institute of Metals, 1917.) 



Price 2 15. 

 The above volume contains the papers presented 

 at the spring meeting of the Institute of Metals, 

 of which an account has already appeared in the 

 columns of Nature. In addition, it contains 

 the verbal discussion and written communications 

 to which the papers gave rise. It is quite clear 

 from these that the council, in organising a 

 symposium of papers on metal melting, chose a 

 subject which aroused very considerable interest 

 among the members, and that some really valu- 

 able information was elicited and has now been 

 placed on record in a form which should be of 

 considerable utility. Equally clear is it that the 

 subject will repay further investigation. The 

 authorities of the Royal Mint are to be commended 

 for having permitted Mr. Hocking to publish so 

 much data based on many years' practice. Mr. 

 Teisen's account of Hermansen's furnace was a 

 very important contribution to the symposium. 

 This producer-gas-fired crucible furnace is the 

 outcome of the fact that owing to the scarcity of 

 fuel and metal in Scandinavia, prices of these 

 commodities are high in those countries as com- 

 pared with Great Britain. Consequently it was 

 necessary to build a more economical furnace than 

 the type ordinarily used. The latter part of the 

 volume contains the usual abstracts of current 

 papers dealing with non-ferrous metals and alloys, 

 and the present volume of the Journal, taken as a 

 whole, should prove to be one of the most useful 

 published by the Institute. 



NO. 2501, VOL. 100] • 



LETTERS TO THE EDITOR. 

 [The Editor does not hold himself responsible for 

 opinions expressed by his correspondents. Neither 

 can he undertake to return, or to correspond with 

 the writers of, rejected manuscripts intended for 

 this or any other part of Nature. No notice is 

 taken of anonymous communications.] 



On the Alterations of Tone oroduced by a Violin- 

 "Mute." 



Experiments on the "wolf-note" of the violin or 

 'cello (see Nature, June 29, and September 14, 1916,. 

 and Phil. Mag., October, 19 16) isuggest an explanation 

 of the well-known and striking alterations in the tone 

 of the instrument produced by a " mute," which at 

 first sight seems somewhat difficult of acceptance, viz. 

 that they are due to the lowering of the pitch of the 

 free modes of vibration of the entire body of the 

 instrument produced by the added inertia. This view 

 of the action of the mute (which was suggested by 

 way of passing reference in my paper on the " wolf- 

 note ") has, I find, excited some incredulity, and its- 

 correctness has, in fact, been questioned in a note by 

 Mr. J. W. Giltay in the Phil. Mag. for June, 1917* 

 The following brief statement may therefore be of 

 interest as establishing the correctness of my view of 

 this important phenomenon : — 



If Ni, N2, N,, etc., be the . frequencies of the free 

 vibrations of the body (in ascending order), the fre- 

 quencies as altered by the addition of the " mute " are 

 determined by equating to zero the expression (see 

 Routh's " Advanced Rigid Dynamics," Sec. 76), 



(Ni=^ - «2) (N./ - «2) X etc., - arr^in./- «2) (n/ - n-) x etc., 

 where a is a positive quantity proportionate to the 

 added inertia^ and n., n^, etc., are the limiting values 

 of N,, N3, etc., attained when the load is increased 

 indefinitely [n, = o, and n2<Ni, W3<N2_, etc.]. The 

 forced vibration due to a periodic excitation of fre- 

 quency n is determined by the same expression, being 

 inversely proportional to it except in the immediate 

 neighbourhood of points of resonance. The sequence 

 of the changes in the forced vibration produced by 

 gradually increasing the load is sufficiently illustrated 

 by considering a case in which n lies between Nf 

 and No. If n,<n., the load decreases the forced vibra- 

 tion throughout, but if n>n2, the load at first increases 

 the forced vibration until it becomes very large, when 

 j n coincides with one of the roots of the equation for 

 ■ free periods, subsequent additions of load decreasing it. 

 The increase in the intensity of tone indicated by this- 

 theory has actually been observed experimentally by 

 Edwards in the case of the graver tones and harmonics 

 of the violin {Physical Review, January, 191 1). Ed- 

 wards's observation that the intensity of tones and har- 

 j monies of high pitch is decreased by "muting" is also- 

 fully explained on this view, as in the case of the 

 higher modes of free vibration of the instrument a 

 very small load would be" sufficient to make the 

 frequencies approximate to their limiting values. 



Comparison of the effects of loading the bridge of 

 the instrument at various points on the free periods 

 and the tones of the instrument furnishes a further 

 confirmation of the foregoing theory. For instance, 

 on a 'cello tried by me, the lowering of the " wolf- 

 note " pitch produced by a load fixed on either of the 

 feet of the bridge was small compared with that 

 obtained by fixing it on top of the bridge, and the 

 observed " mute " effect was correspondingly smaller. 

 In fact, the alterations of free period produced by 

 loading furnish us with quantitative data regarding 

 the relative motion of different parts of the instrument, 

 and of their influence in determining the character of 

 its tones. C. V. R.-vm-ax. 



Calcutta, August 28. 



