426 



NATURE, 



\Aprit r, 1875 



having distinct powers, and either" of wliich may take the posi- 

 tion of root or prime ; these coexistent tones, whatever the 

 previous independent ratio of string and reed as regards pitch, 

 will always, when thus yoked together, be one an octave higher 

 than the other. Singularly, too, it is not necessary that the 

 lower ol these fundamentals should be the pitch-note to the ear; 

 its apparent character may be that of a sub-tone. Generally, 

 the higher fundamental is the leading tone, and for this reason, 

 that the predominance of one or of the other may be determined 

 by character and by condition. In the reed, amplitude of 

 excursion is the measure of its attainment of strength. In the 

 string, tension is more effectual for power than amplitude is. 

 String-tone thus gains by limitation of excursions of the string, 

 whilst at the same time reed-tone is at a disadvantage from the 

 restriction imposed by tension on the play of the reed. Con- 

 trariwise with a lighter string, power may be allotted to the reed, 

 also by tubes, by partial occlusion of orifice, by coverings or 

 shadings, the reed-tone can be modified in a variety of degrees ; 

 it may lead in trumpei-like vigour, or be heard only in quiet 

 undertone accompanying the higher sound. 



These two notes are rigorously exact in relative pitch, and 

 when both have intensity, although different in kind, they pro- 

 duce other tones, as in the stop of the organ called the " Great 

 Quint," the tone of one pipe added to another that produces a 

 lone a fifth higher, gives rise to a third tone an octave loiver, but 

 never perfectly, except on the same conditions, exactness of 

 pitch and intensity, with, as a rule, the higlier note voiced the 

 strongest. The reed and string necessarily, if preceding jjropo- 

 titions are true, being in relation an octave apart, give rise to 

 summation tones, first to the fifih, and these again to octave, 

 tenth, and the rest in due order, but differing in intensity. In 

 harmonic scale those possible would be octave, twelfth, super- 

 octave, seventeenth, &c., and so here, if reckoned from the 

 lowest tone as the root ; but summation tones seem to require 

 for their perfect production the same conditions as named 

 above (or diflerence tones ; so that relatively the ocave becomes 

 by its voicing the leading tone, it fixes the pitch for the series in 

 reference to itself, and thus the ear has cognisance of the tenth, 

 not of the seventeenth. This major tenth to the tonic, so unmis- 

 takeable that it could not be gainsaid, was always a puzzle 

 viewed as harmonic. Why it was so clear will readily be per- 

 ceived when calculated as summation twice fulfilled. 



The general supposition is, that because it is a string that is in 

 action with the reed, therefore a stringy tone is in consequence 

 obtained, the proof being that a stringy tone is actually heard. 

 On the coirtrary, the true actioir of the string, whence arises the 

 peculiaj'ity of violin or violoncello, does not take place. What 

 then? In a curious way effects are gained vvhich naturally simu- 

 late the quality. By stringy quality musicians mean the tone of 

 the bowed string. Amateurs talk eloquently in their way of the 

 string-tone and its beautiful purity, of tlie reed-tone and its 

 abominations, rrot heeding that the best judges of quality in 

 sound class the stringy quality as the nearest allied to reed 

 quality. Hence, organ-builders regard all the stops which best 

 imitate the viola trrbe, the geigens and gambas, as decidedly 

 reedy in character, otherwise they would be poor representatves. 

 The violoncello so characteristic in tone has always its introduc- 

 tory harmonics ; these are sharp to the fundamental tone in 

 whrch they merge, even as, I have shown in a former paper, the 

 harmonics of the gamba organ-pipe are. Octaves of a free- 

 string are always sharp to the note of the whole string. Then 

 we have also rhe roughness, the grip, and bite of the bow. The 

 sharpness is minute, yet sufficiently potent to give definite cha- 

 racter. The ear IS as easily deceived as the eye — the imitation 

 may pass for the real. It we consider what is the effect on the 

 ear of this sharpness, which does not reach the region of beats, we 

 shall find it to be a breezy effect ; in the delicate " voix celestes " 

 of a fine organ when finished by true artists, we have it displayed 

 — ^just a freshening touch of sharpness, and no more. From a 

 breeze to a rough wind is only gradation of similaiity. Return 

 now to the combination of reed and string : the effect as of a 

 stringy quality is gained by the breeziness of the outward stream 

 of air distinctly heard, by the roughness of the abrupt closing and 

 opening of passage to a highly-excited reed, by the tendency of 

 a highly resilient reed to a more rapid pace, curbed though it 

 inevitably is to the pace possible to the string it is paired with, 

 thus adding an element of roughness to the sound-board, and in 

 completeness of likeness there are the summation-tones mimick- 

 ing those harmonics which are present in the fulness of the 

 violoncello tone. 



To assure those who would doubtfully accept the above inter* 

 pretation, let me take an illustration of a practical nature as a 

 verification. Why is it possible to make in a harmonium from 

 free reeds alone a good imitation of violoncello quality ? Because 

 an analogous procedure can be adopted. This is the analysis of 

 how it is done. Keeds of " eight-feet tone " of a firm character, 

 rather slow in speech in consequence, but coming into play at a 

 bound without hesitation ; then in combination reeds of " sixteen- 

 feet tone," these reeds finely curved, elastic, sensitive, quivering 

 to a breath, their tone comes on at first as a breeze, it is sharp in 

 a minute degree, but as the reeds gain power by amplitude, they 

 flatten in pitch, as is the nature of bass reeds ; ascending the 

 scale, a small reed giving the twelfth may be added with advan- 

 tage. In summary this is what we have : reeds relatively sharp 

 to each other, the roughness, the breezy effect, and the accom- 

 panying harmonic offspring, together making the mimaphonic 

 violoncello. Organ-pipe, violoncello, harmonium, and string- 

 organ thus show a family likeness and give countenance to the 

 interpretation. 



The beauty of Mr. Hamilton's Invention is that It is not 

 limited to string-tone, that by giving predominance of power to 

 either agent, reed or string, through long ranges of variation, 

 many cl.isses of tone as distinct as diapason, horn, flute, trumpet, 

 and others can be satisfactorily imitated, and if its present 

 promises of success are fulfilled, the name of string-organ by 

 which it will be known will be amply justified. 



Hermann SxtiTH 



r.S. — Mathem.aticians decide that the problem of the instru- 

 ment is that of a loaded string. This appears to me a one-sided 

 view, taken under limited experiments. Practically, some details 

 of their conclusions are not corroborated ; there are several 

 elements entering into the composition not heeded, and a wider 

 experience would show that the problem is equally that of a 

 loaded reed. Here is an instance. I have in action a reed with 

 pin attached ; it sounds C sharp ; and a string which, iirdepen- 

 dently sounding, gives the F below. These, when conjoined, pro- 

 duce the G between. The note of the string is thus raised a 

 whole tone ; consequently the weight of the oscillating string is a 

 lo.ad on the reed. — 11. S. 



The Law of Muscular Exhaustion and Restoration 



Your issue of Jan. 28 is just received, containing a paper (vol. 

 xi. p. 256) by Prof Frank E. Nipher, wherein he condemns 

 as "entirely unreliable" his fii'st series of experiments on the 

 subject of the exhaustion of the muscles of the arm by mechanical 

 work. A like condemnation he pronounces in the February 

 number of the Aiiuricait Journal of Science. 



All the experiments in question, new as well as older, having 

 been made at this laboratory, I beg leave to correct the above 

 statements of Prof. Nipher. His new experiments are not so 

 radically different from the old ones ; on the contrary, both series 

 demonstrate exactly the same general lauK The true law is, as 

 Prof Jevons in his first communication to Nature already felt 

 it, logarithmic. So indeed vary most of the vital processes, 

 because niolecularly they are comparable to the vibrations of a 

 pendulum in a resisting medium. (See Fechner, Exner, Wundt, 

 Deiboef, and others.) I'hat the law has so long been overlooked, 

 so far as muscular action is concerned, is probably due to the 

 fact that the progressive restoration of the muscular tissue dis- 

 turbs the function for small weights, while ."-tructural derange- 

 ments (evidenced by pain) cause a like perturbation for higher 

 values of the weight. 



If we consider a system of muscles independent of continued 

 circulation (no restoration) and keep the burden iv (kgr.) low 

 enough to cause no paiir, then the time n (m seconds) during 

 which the statical work can be sustained, or the number j}f times 

 n, that the same cycle of motions can be performed until exhaus- 

 tion takes place, I have found to be — 



.. _ ^ 1 



h" 



(I) 



or log n — a - 6 '0 ) 



where log A = a ; log B := b. 



In the five series at hand the following are the values of the 

 constants : — 



I.— Statical Work. a b 



1. Prof. Jevons, Series III., holding weight ... 2'433 o'i4S0 



II. — Dynamical Work. 



2. Prof. Jevons, Series II., pulley and cord ... i'968 o'0476 



