June 29, 1882] 



NATURE 



20' 



Baltimore in December last. At the January meeting of 

 the Seminary, he read a paper "On Two Cases of the 

 Ouadric Transformation between two Planes," and has 

 subsequently read other papers, and been a contributor to 

 the Journal. But the result of his visit has been the 

 delivery of "a systematic and highly original course of 

 lectures upon Algebraical Geometry, in connection with 

 the Abelian and Theta Functions." 



These lectures, we hope, will be given, in book form, 

 to a more extended audience. Besides the ordinary class 

 lectures, given by the able staff of assistant professors, 

 some of whom are well known to mathematicians here, 

 short courses of lectures have been delivered by Mr. 

 C. S. Peirce (who has recently annotated and published 

 in the American Journal his father's fine work on " Linear 

 Associative Algebra "), on the Logic of Relatives, by Dr. 

 Story; on the Clebsch-Gordan invariantive theory ; and 

 by Dr. Craig, on the Construction and Direction of a 

 Riemann's surface (how these two la:t courses recall to 

 our minds a departed master.) 



Leibnitz somewhere says " Les mathcmatiques sont 

 l'honneur de l'esprit humain;" if this be so, then the 

 University has done well in assigning so great a part of its 

 time and resources to the study of the higher branches 

 of this department of knowledge. But indeed Johns 

 Hopkins is a true university, for it is catholic in its sym- 

 pathies, and enfolds in its wide embrace all branches of 

 culture and learning. 



In No. 13 is an abstract of a lecture before the students 

 by Dr. James Bryce, M.P., on our English universities. 



R. T. 



KCENIG'S EXPERIMENTS EX ACOUSTICS 

 I. 

 T N the volume mentioned below 1 Dr. Kcenig has collected 

 *■ the valuable series of researches in experimental acous- 

 tics that have been published by him chiefly in the Annalen 

 of Poggendorff and of Wiedemann during the past twenty 

 years. Many of these researches are well known in England, 

 having attained to " classic " importance, and their main 

 results are to be found embodied in all the best text-books 

 of acoustics. Other researches of more recent date are 

 yet known only to the few, but will doubtless win their 

 way to general knowledge before long. The most novel 

 points in the book are the late researches of its author 

 with the ingenious instrument known as the wave-siren. 

 This invention Dr. Kcenig has applied to support his 

 views upon the origin of the beats of imperfect con- 

 sonances, and also to investigate the influence of differ- 

 ences of phase upon the quality of tones. The general 

 nature of the wave- siren has already been explained in 

 the pages of Nature, but in the sequel we will 

 attempt to describe fully its most recent forms, as 

 applied in the last investigation. In addition to these 

 deeply interesting matters of recent research, there is a 

 mine of wealth contained in the volume. The first 

 chapter deals with the application of the graphic method 

 in acoustics ; an equally interesting chapter on mano- 

 metric flames and their applications occur a little further 

 on. Dr. Kcenig^s researches on the standard tuning-fork 

 or "diapason normal" are too well known to need com- 

 ment. The reader will find the whole series of papers 

 collected in Chapter XIII. He will also find notices of an 

 adjustible tuning-fork capable of giving a variety of tones, 

 of a curious tuning-fork clock, of new stethoscopes, of 

 instruments for producing continuous beats audible to a 

 large company of persons, together with researches on 

 the phase of vibration of two associated telephones, on 

 the fixed notes charcteristic of the different vowel sounds, 

 and on several other matters of great importance. He 

 must not, indeed, expect to find deep mathematical insight 

 nor folios of analytical equations. But he will find a 



' "Quelques Experiences d'AcousLque." Par Rudolf Kcenig. (Paris: 

 R. Kcenig, 27, Quai d'Anjou, 1882J 



perspicuous and fascinating record of experiments planned 

 with rare ingenuity, carried out with honesty, patience, 

 and consummate skill, by the man whose exceptional 

 abilities as experimentalist and constructor have done 

 more than those of any other physicist to make the 

 science of experimental acoustics what it is to-day. 



In the present article we shall refer in some detail to 

 Dr. Kcenig's researches on the influence of phase upon 

 the quality of sound. 



It has long been an accepted doctrine of acoustics 

 that every continuous sound possesses three recognizable 

 characteristics, viz., pitch, intensity and quality, and that 

 these three characteristics depend respectively upon the 

 frequency, the amplitude, and the degree of complexity 

 of x.\ e sonorous vibrations. The third of these charac- 

 teristics, the quality of a sound, has also been denomi- 

 nated "timbre" or " clang-tint" by those who affect 

 Gallic or Teutonic proclivities in scientific nomenclature. 

 Everyone now knows that, by whatever name this third 

 characteristic is called, it constitutes the almost indefin- 

 able yet perfectly recognizable difference which exists 

 between a note as played on one musical instrument and 

 the same note as played upon another. The notes may 

 be the same in pitch and in intensity, but there is a 

 residual difference in quality that the dullest ear cannot 

 mistake. 



It was by one of the finest pieces of scientific research 

 by Germany's greatest living physicist, that the true 

 cause of this mysterious "quality" was established. 

 Helmholtz's great work on The Sensations oj Tone takes 

 for its basis the fact that with every fundamental " tone " 

 or perfectly simple sound there co-exists a whole series of 

 " partial tones," which together with the fundamental 

 make up the mass of sound that we usually call a "note." 

 All our musical instruments yield us complex sounds in 

 which every fundamental is accompanied by a variety of 

 upper partial tones (sometimes called by mistranslation 

 "overtones" ; and also, by a far more serious mistake, 

 ? harmonics), the number of such upper partials and their 

 relative intensity being a consequence of the conditioijs 

 of vibration in the instrument. Hence instruments hav- 

 ing different kinds of vibrating parts — strings in one, 

 reeds in another, columns of air in another — will emit 

 tones that vary in number and intensity of accompanying 

 partial tones ; and the ear taking the mass of complex 

 vibration as a whole will pronounce that there is a 

 difference in quality. Helmholtz' s theory, in short, asserts 

 that the quality of a tone depends on the following points : 

 firstly, whether there were any upper partials present ; 

 secondly, what those upper partials were ; thirdly, what 

 their relative intensity toward one another and toward 

 the fundamental note might be. Thus, for example, 

 the thin quality of the notes of wide, stopped organ-pipes, 

 which contrasts both with the full rich quality of the piano- 

 forte notes, and with the harsh, strident, irrepressible 

 notes of the harmonium, becomes intelligible when it is 

 rendered plain that in the first case there is an almost 

 complete absence of upper partials, that in the second the 

 partials, though numerous, are loud only for such partial 

 tones as are concordant with the fundamental, while in 

 the third discordant partials, loud and shrill mingle with 

 the fundamental. 



But there is a negative proviso in Helmholtz's theory 

 of a very important kind, namety, that differences in 

 quality of tone depend " in no respect on the differences 

 in phase under which these partial tones enter into 

 composition." ' 



This negative law, which Helmholtz has sought to 

 confirm by various experimental proofs, is a consequence 

 of the hypothesis that the ear unconsciously analyzes 

 complex sounds into their simple elements — the partial 

 tones — each simple (partial) tone actuating a separate 

 part of the nerve-structures of the ear. Before Helm- 



1 Helmholtz. Sensations of Tone (Ellis's Translation) p. 186. 



