2 76 



NATURE 



[_yan. 23, 1879 



In the above statements the octare c—c' is for sim- 

 plicity supposed to be true. The actual error could be 

 readily allowed for, if required ; but in practice it is not 

 necessary to use c' at all, inasmuch as the third set of 

 beats can be counted equally well between g^ and c. 



Although at first sight the method just sketched looks 

 satisfactory, it is not practical in the case of the har- 

 monium, in consequence of the pitch of the various notes 

 not being sufficiently constant for the purpose, even when 

 the blowing is carefully conducted vith the aid of a 

 pressure-gauge. A small variation in the absolute pitch 

 of a chord when sounded under slightly varying pressures, 

 would not be of much importance, but the slightest 

 change of interval is fatal to the success of the method, 

 and such a change actually occurs. 



In order, therefore, to apply the fundamental principle 

 with success, it is necessary to be able to check the 

 accuracy of the interval which is supposed to be known, 

 at the same time that the beats are being counted. If the 

 interval be a major tone (9 : 8), its exactness is proved 

 by the absence of beats between the ninth component of 

 the lower, and the eighth component of the higher note, 

 and a counting of the beats between the tenth component 

 of the lower and the ninth of the higher note completes 

 the necessary data for determining the absolute pitch. 



The equal temperament whole tone (i "12246) is inter- 

 mediate between the minor tone (I'liiii) and the major 

 tone (i "12500), but lies much nearer to the latter. Re- 

 garded as a disturbed major tone, it gives slow beats, and 

 regarded as a disturbed minor tone it gives comparatively 

 •quick ones. Both sets of beats can be heard at the same 

 time, and when counted give the means of calculating the 

 absolute pitch of both notes. If x and_ybe the frequencies 

 of the two notes, a and b the frequencies of the slow and 

 quick beats respectively, 



whence 



9Jr — Zy — a 

 9 J — \ox = b, 



X = 9^-1-8^ 

 y = \oa-\-(^b. 



The application of this method in no way assumes the 

 truth of the equal temperament whole tone, and in fact 

 it is advantageous to flatten the interval somewhat by 

 loading the upper reed with a minute fragment of soft 

 wax, so as to make it lie more nearly midway between the 

 major and the minor tone. In this way the rapidity 

 of the quicker beats is diminished, which facilitates the 

 counting. 



It is impossible, of course, for the same observer to 

 count both sets of beats, and the counting of even one 

 set without the aid of resonators would present difficulties 

 to most unpractised persons. Great assistance may be 

 obtained by the choice of a suitable position. A room in 

 Avhich a pure tone is sounded is traversed by surfaces at 

 which the intensity of sound is very much reduced in 

 consequence of the superposition of vibrations reflected 

 from the walls and ceiling. By choosing as the place of 

 observation a position where theintensity of the beatswhich 

 are not to be counted is a minimum, and with the aid of 

 a resonator tuned to the pitch of the beats which are to 

 be counted, the listener is able to work with ease and 

 certainty. 



The course of an experiment is then as follows : — 

 The notes C and D are sounded, and the listeners 

 begin counting the beats at a given signal, whose pitch is 

 about d' and e" respectively. At the expiration of a 

 measured interval of time a second signal is given, and 

 the number of both sets of beats is recorded. 



In my experiments the interval of time was ten minutes 

 (in one case eleven minutes), and the rapidity of the beats 

 was about four a second. The listeners counted up to 

 ^n only, after each set of ten making a stroke with a 

 pencil on a piece of paper. The number of strokes was 



afterwards counted, multiplied by ten, and added to the 

 number which the listener was saying at the instant of 

 the second signal. The following are the details of the 

 actual observations : — 



September 16, 1878.— Period of observation ten minutes. 

 Numbers of beats 2392 and 2341. 



«=y92, ^=2341, i,i ^.^9X2392+8X2341^67-09, 



600 600 600 



for the frequency of the lower note C. 



September 17.— Period of observation ten minutes. 



2423 , 2302 . . ^ 



a = 2--y b = z^> giving x = 67 "04. 

 600 600 



September 18. — Period of observation ten minutes. 



2476 , 2261 



600 600 



September 19. — Period of observation eleven minutes. 



, giving X = 67*19. 



, giving .v = 67-29. 



2663 ^ ^ 2547 



600 ■ 



600 



The discrepancies are hardly greater" than maybe attri- 

 buted to errors in giving the signals, by which the intervals 

 may have been unduly lengthened or shortened by about 

 a second. On each day after the counting of the beats 

 between C and D, the harmonium was compared with a 

 Koenig fork whose nominal frequency was 64. In order 

 to obviate any objection arising from a mutual influence 

 of the notes of the harmonium, both C and D were 

 sounded at the same time as the fork. The beats between 

 C and the fork were counted for about ninety seconds, 

 during which time the fork was not bowed. In this way 

 the pitch of the fork came out on the four days respec- 

 tively as 64 "06, 64 "07, 64" 1 7, 63-98, that is somewhat 

 sharper than its nominal pitch, a result in agreement with 

 that obtained by other methods. 



The object of the experiments referred to was rather to 

 prove the practicability of a method so < unusually inde- 

 pendent of special apparatus, than to obtain a result 

 competing in point of accuracy with those of Prof. Macleod 

 and other experimenters on this subject. Nevertheless it 

 is believed that very accurate results might be obtained 

 by the introduction of certain modifications. Ten minutes 

 is near the limit of time over which beats can be con- 

 veniently counted by a single listener, but experiment 

 proved that it is perfectly possible for one 'listener to 

 relieve another without any break in the regularity of the 

 counting. Even without an extension of time a more 

 accurate result would be obtained if the listeners were 

 able to fix the time for themselves, as they might do for 

 example if they could conveniently observe the swinging 

 of a clock pendulum. In this way the error in the time 

 interval might be reduced to | second, which would 

 amount to but one part in 2400 in the case of a ten 

 minutes' observation. In consequence, however, of the 

 imperfect constancy of the pitch of the harmonium notes, 

 even when the blower is assisted by a pressure-gauge, 

 further attempts at accuracy would be useless unless the 

 comparison with the fork were simultaneous with the 

 other observations. In that case the result would be 

 entirely independent of variations in the harmonium 

 notes, and no difficulty would be experienced in carrying 

 out the method excepting the necessity for more ob- 



THE FISSURES OF THE CEREBRAL HEMI- 

 SPHERES IN UNGULATA 

 AN important memoir by Dr. Krueg on the cerebral 

 hemispheres of Ungulata has recently appeared in 

 the Zeitsch. wiss. Zool. After a review of the previous 

 papers that have appeared on this subject— but few in 

 number— Dr. Krueg describes his method of investiga- 

 tion. 



