igo 



NATURE 



[June 19, 1890 



In addition to this, the areas for the representation of the 

 different parts of the body we found not to be continuous with 

 •each other, but that between the areas of representation (for 

 instance, of the face and the upper limb) there were regions of 

 inexcitable cortex showing a degree of differentiation not 

 obtained in the lower monkey. 



A further remarkable evidence of specialization was noticeable 

 in the fact that excitation of any one point elicited rarely more 

 than one movement, and only of one segment, e.g. simple flexion 

 -of the elbow. Consequently, any sequence of movement or 

 march was conspicuously infrequent. 



Finally, the character of each movement and its localization 

 was recorded. 



After the cortex had been removed, we proceeded to stimu- 

 late the fibres of the internal capsule, and the results obtained 

 confirmed those obtained from the bonnet monkey, and at the 

 same time showed the relative position of the cortical areas. 



The internal capsule was exposed by removing half of one 

 hemisphere by a horizontal section ; the outlines of the basal 

 ganglia were then transferred to paper ruled with squares of I 

 millimetre, and the resulting movement obtained by stimulating 

 each of these squares contained in the internal capsule was 

 recorded. The movements obtained correspond generally with 

 the results which we have in another paper presented to the 

 Royal Society, and read on December 12, 1889. 



Physical Society, May i6.— Prof. W. E. Ayrton, F.R.S., 

 President, in the chair. — Lord Rayleigh exhibited and described 

 an arrangement of Huyghens's gearing in illustration of electric 

 induction. This gearing consists of two loose pulleys mounted 

 on the same axle, with an endless cord laid over them, the loops 

 or bights of which carry weighted pulleys whose planes are 

 parallel to the axis on which the upper pulleys turn. If one of 

 ■the latter pulleys be started to rotate, the other one turns in the 

 opposite direction until such time as the speed of the first one 

 becomes constant. Whilst this constant speed is maintained, 

 the second pulley remains stationary, one weight being raised 

 and the other lowered, but on retarding the motion of the first 

 pulley, the second begins to turn in the same direction as 

 the first. It will be noticed that the phenomena are analogous 

 to those which occur in electric induction, where starting or in- 

 creasing a current in one circuit induces an opposite current in a 

 neighbouring circuit, whilst decreasing or stopping a current 

 induces one in its own direction. Lord Rayleigh pointed out 

 that in this apparatus there is nothing strictly analogous to 

 electric resistance, for the friction does not follow the same law. 

 The analogy, he said, was complete as regards there being no ' 

 change of potential energy, and the mathematical equations for j 

 the kinetic energy of the system are precisely the same as those i 

 given by Maxwell for electric induction. — Dr. S. P. Thompson | 

 made a communication on Dr. Koenig's researches on the 

 physical basis of music, in the course of which Dr. Koenig 

 performed numerous novel and interesting experiments, clearly 

 illustrating the subject to a crowded audience. After referring 

 to the classical researches of the great mechanician, and to the 

 remarkable precision with which his ingenious and unique 

 acoustical apparatus is constructed, Dr. Thompson said the 

 subject with which he wished to deal could be divided into two '• 

 parts, the first relating to beats, and the second to the timbre of 

 sounds. On the question of beats considerable discussion had 

 taken place as to whether they formed independent tones if they 

 were sufficiently rapid. Different authorities had come to different i 

 conclusions on the subject, the disagreement probably arising 

 from the impure tones used in their investigations. Dr. Koenig, 

 however, had succeeded in making tuning-forks whose sounds j 

 are very nearly pure tones, and by the aid of such forks had , 

 conclusively answered the question in the affirmative. Before ' 

 proceeding to show experimentally the truth of the conclusions 

 arrived at. Dr. Thompson said it was necessary to define exactly 

 the meaning of the term "harmonics." By this he meant tones 

 whose frequencies are true integral multiples of their fundamental. 

 This, he said, might seem to be identical with the ' ' upper partial 

 tones" of Helmholtz or the "overtones" of Tyndall, but such 

 was not the case, as the upper partial tones of piano- wires, &c., 

 are not true integral multiples of the fundamentals, for the rigidity 

 of the wire comes into play, and prevents the subdivision being 

 •exact. According to Helmholtz's theory, two tones harmonize 

 when they do not produce beats of sufficient slowness to grate 

 upon the ear, and the frequency of the two sets of beats were 

 supposed to be equal to the difference and the sum of the 

 frequencies of the two fundamental tones. In investigating the 



NO. 1077, VOL. 42] 



subject, Koenig finds it necessary to distinguish between primary 

 and secondary beats, and also that primary beats belong to two 

 categories. These categories he calls "inferior" and "superior" 

 respectively, and the frequencies of the two sets correspond 

 respectively to the positive and negative remainders obtained by 

 dividing the number representing the number of vibrations in 

 the tone of lowest pitch into the corresponding number for the 

 higher tone. For example, two forks of 100 and 492 vibrations 

 produce beats having 92 and 8 as their vibration frequencies, for 



and also 



492 = 100 X 4 -f- 92, 

 492 = 100 X 5 - 8. 



A set of " superior " beats of 8 per second and an "inferior" 

 beat-tone of 92 pertsecond may be heard when two such forks are 

 sounded together. These primary beats or beat-tones act as 

 independent tones and produce secondary beats. Tertiary ones 

 may also be obtained, To demonstrate the existence of beats 

 to the large audience assembled. Dr. Koenig had provided two 

 large tuning-forks with resonators about 4 feet long. One of the 

 forks gave 64 vibrations per second, and the other 128, but the 

 latter had sliding weights, whereby its frequency could be made 

 anything between 128 and 64. Adjusting the weights so as 

 to give 72, and bowing both forks, the beats of about 8 per 

 second were distinctly heard at the extremity of the room. By 

 varying the weights so that the fork gave 80, 85^, 96, io6f , 112, 

 120, and 128 vibrations successively, beats of various frequencies 

 were produced, and it was remarkable to note that tones of 64 

 and 120 produced 8 beats a second exactly like 64 and 72. 

 When the forks made 64 and 96 vibrations — i.e. at an interval 

 of a fifth — -then the inferior and superior beats agree in frequency, 

 viz. 32, and by careful observation a low tone of about this pitch 

 could be heard. If the tones sounded simultaneously differ by 

 more than an octave, the same law for the numbers of beats holds 

 good, whilst Helmholtz's difference and summation tones law, is 

 inapplicable. This was shown by sounding a fork and its 

 double octave slightly mistuned by weighting ; slow beats were 

 quite evident, although the difference in the frequencies 

 of the primary notes was large. Similarly forks vibrating 

 approximately at rates in the proportions i : 5 and i : 6 

 gave slow beats. Coming to the main question, as to whether 

 beats when sufficiently rapid blend into tones just as primary 

 shocks do. Dr. Thompson briefly recalled the various arguments 

 for and against such an effect, and then Dr. Koenig proceeded 

 to experimentally prove the affirmative. Taking two forks tuned 

 to 2048 and 2304 vibrations respectively (ratio 8 : 9) and sound- 

 ing them simultaneously, the middle C of the piano (256) was 

 distinctly heard. The same beat tone resulted from forks having 

 frequencies in the ratio of 8 : 15, whose negative remainder was 

 256. Various other tones were sounded simultaneously in pairs, 

 and in all cases the corresponding beat-tone was quite distinct. 

 In these experiments the existence of nodes and loops in air was 

 particularly noticeable, for as Dr. Koenig turned the tuning-forks 

 in his hand, the intensity of the beat-tones heard at a particular 

 spot varied enormously. The experiments were carried a step 

 further by impressing vibrations of different frequencies on one 

 and the same body : the beat-tones in this case were quite per- 

 ceptible. In carrying this out. Dr. Koenig had constructed steel 

 bars of approximately rectangular section, whose periods of 

 vibrations were different in two directions at right angles. 

 Striking one face of the bar a certain note resulted, whilst a 

 blow on an adjacent face produced a different one. When the 

 bar was struck on the edge joining the two faces, both the notes 

 could be heard as well as the beat-tone resulting therefrom. 

 The experimenter had gone still further, and made such bars so 

 short that neither of the fundamental notes are within the limits 

 of audition, but the resulting beat-tone can be heard quite dis- 

 tinctly. In all cases the frequency of the beats agrees with that 

 calculated from Dr. Koenig's formula, and secondary beats follow 

 the same law. It was then pointed out that not only beats, but 

 the maxima of a series of pulsations varying in intensity will, if iso- 

 chronous andsufficiently rapid, give tones, just as a series of primary 

 shocks do. This was illustrated by tuning-forks, and by directing 

 a stream of air issuing from a slit against a notched rim of a 

 rotating disk. A further confirmation was given by a modified 

 disk siren ; in this the holes, instead of being of the same size all 

 round a circle, increase to a maximum and then decrease again, 

 there being several sets of such holes in one circumference. 

 When this was put in operation, notes corresponding in pitch to 

 the number of holes and also to the number of sets of holes, 



