January 5, 1893] 



NATURE 



223 



to 'puir air particles apart. On p. 52 we are told 

 that the motions of particles of a water wave "are 

 always at right angles to the direction of the wave 

 itself." On p. 68 the author corrects this statement, 

 but in doing so, takes occasion to speak of a plane " in," 

 instead of 'passing through' the line of progression. 

 < )n p. 380 he describes harmonic partial-tones as 

 ■ modifying the quality of their fundamental," though he 

 obviously means the quality of the compound sound due 

 to the fundamental and other partial-tones combined. On 

 p. 387 it is said that the "ratios of frequencies" which 

 characterize particular sounds " are called intervals," and 

 that by dividing one note by another we obtain 

 the intervals between them. Language of this kind is, 

 indeed, hardly misleading, but it is certainly very slip- 

 shod. 



Before passing from the more generally acoustical, to 

 the more specially musical portion of Prof. Zahm's 

 volume, it is proper to point out one important respect 

 in which it has the advantage over most, or possibly all, 

 the manuals on the same subject which have preceded it. 

 This merit consists in giving a somewhat full account of 

 elaborate experimental researches on beats, combination- 

 tones and quality conducted by Dr. Koenig, the results 

 of which are to a considerable extent at variance with 

 conclusions previously announced by Prof. Helm- 

 holtz. In the opinion of our author, Dr. Koenig is 

 "one who, not excepting even the eminent German 

 philosopher just mentioned (Helmholtz), has contributed 

 more than any other person to the advancement of the 

 science of acoustics'" (p. 17). A more balanced judg- 

 ment, while placing great reliance on Dr. Koenig's ex- 

 perimental skill and on the superlative excellence of 

 the apparatus constructed by him, would probably attri- 

 bute to Helmholtzs opinion a preponderant weight in 

 interpreting and correlating the results of experiment. 

 Be that, ^however, as it may, Prof. Zahm has done 

 excellent service by popularizing the work so laboriously 

 performed, and so modestly placed on record, by the 

 eminent instrument-maker to whom no one who has put 

 his hand to acoustical work can fail to be under consider- 

 able practical obligations. 



The specifically musical are decidedly the least 

 meritorious parts of our author's performance. The 

 looseness of phraseology already complained of is here 

 at its worst. On p. 166 we are told that a ' comma,' 

 (;^J) is " the smallest interval used in music." A beginner 

 might easily take this to mean that notes differing by only 

 that interval were actually heard consecutively in a 

 musical phrase — of course an absurd supposition. Very 

 misleading, again, is the statement on p. 388 that tones, 

 like major and minor tones, that differ from each other 

 only by a comma " are considered in music to have the 

 same value." The only rational meaning to be got out 

 of it seems to be that in the equally tempered scale the 

 distinction between major and minor tones is obliterated 

 On p. 389 the notes of the diatonic scale, and their 

 relations, in respect to rapidity of vibration "to one 

 another," are set out, and it is added that all but the 

 second and the seventh of the intervals thus indicated are 

 consonant. The essential piece of information, that it is 

 not the intervals formed by these notes with " one 

 another," but with the tonic, that are in question, is with- 

 NO. 1210, VOL. 47] 



held, and so the reader is left free to suppose e.g. that the 

 tritone, F — B, is a consonance. On p. 390 the ' inversion ' 

 of intervals is mentioned without any explanation of its 

 meaning. 



Attention may well be called to a process of reasoning 

 which occurs on pp. 388-390. Prof. Zahm abruptly 

 introduces (p. 388) calculation by "frequency-ratios"; 

 assumes, without attempt at proof, that addition of two 

 semitones is performed by squaring the ratio J^, and then 

 remarks (p. 390) " From the foregoing we observe that 

 the sum of two intervals is obtained by multiplying, not 

 by adding their ratios together." An assumption in a 

 particular case is thus made to do duty as a general 

 demonstration. 



On p. 396 we read that " so perfectly does the interval 

 of the fifth answer the requirements of the ear that even 

 unpractised singers find it quite -natural to take a fifth to 

 a chorus that does not quite suit the pitch of their voice." 

 If, as this passage appears to suggest, practised singers 

 in America find it still more natural to accompany 

 melodies in consecutive fifths, wonderful effects may 

 surely be expected from the choruses to be heard at the 

 Chicago exhibition. 



On p. 429 our author describes a diagram by Helm- 

 holtz as concerned with the transposition of an interval 

 by an octave, whereas what it really deals with is the 

 enlargement of the interval in question by the addition 

 to it of an octave. On p. 430 he writes down, as con- 

 stituents of the chromatic scale of C, the notes E^, ¥\t, Bjj 

 and Cb. 



On p. 441, he tells us that in listening to such violin 

 players as Joachim, Wilhelmj, and others " one can 

 always hear distinctly the Tartini, or beat-tones, that 

 add such richness and volume to violin music." 



To gauge the amount of truth contained in this remark 

 it suffices to bear in mind that in the case of most major, 

 and of all minor consonant chords, Tartini's tones cause 

 a decided dissonance. Players who made them ' always 

 distinctly audible ' would soon be reduced to permanent 

 inaudibility themselves. 



Prof. Zahm's volume is creditably free from misprints : 

 the following have, however, been noted : 

 P. 23, 1. 16 ' period' for 'periods.' 

 P. 68, 1. 21 ' amplitude ' for ' amplitudes.' 

 P. 90, 1. 8 ' Ajugari ' for ' Agujari.' 

 P. 142, in diagram, B4^ for B4. 

 P. 152, in diagram I, Bi^ for B. 

 P. 388, 11. II and 12, G for F. 



GERLAND'S ETHNOLOGICAL ATLAS. 



Atlas der Volkerkunde. (Berghaus' Physikalischer Atlas, 

 Abth. vii.). Bearbeitet von Dr. Georg Gerland, Pro- 

 fessor a.d. Universitiit in Strassburg. (Gotha : Perthes, 

 1892.) 



ANTHROPOLOGY owes muchto Prof. Gerland, whose 

 completion of the two last volumes of the late Prof. 

 Waltz's " Anthropologie der Naturvolker '' is a monument 

 of that co-ordinated knowledge of fact which is the 

 source of sound principle. His new " Atlas of Ethnology," 

 while forming part of thegreat Physical Atlas of Berghaus, 

 may be obtained and used as a separate work by anthro- 



