Prof. Foster's Note on the foregoing Paper. 539 



Note on the foregoing Paper. By Professor G. C. Foster. 



On repeating the remarkable experiment which forms the 

 starting-point of Professor Beetz's interesting paper, I obtained, 

 as was of course to be expected, a result completely in accord- 

 ance with what he has described. A gg tuning-fork, by Konig, 

 making 384 complete vibrations per second (marked a Sol 3 768"), 

 the prongs of which were 115 millims. long by 15 millims. wide 

 and 7*5 millims. thick, was set in rotation by means of a lathe 

 at the rate of from eighteen to twenty turns per second. Under 

 these circumstances its tone rose almost exactly a minor third, 

 the alteration of pitch being judged of by comparison with an 

 organ-pipe whose note could be altered by means of a sliding 

 paper tube put on at the top. The effect upon the ear of the 

 rapid succession of beats which accompanied the tone of the ro- 

 tating fork was exactly that of a harsh discord, thus affording a 

 striking illustration of Helmholtz's theory of the nature of dis- 

 cords in general (Tonemjifindungen, pp. 251 et seq., also p. 293). 



The principle of Professor Beetz's beautiful explanation of his 

 experiments may be very simply illustrated by means of a pen- 

 dulum whose time of vibration is unequal in two planes at right 

 angles to each other. A ready and effectual means of construct- 

 ing such a pendulum was pointed out to me two or three years 

 ago by Professor Sir William Thomson : it consists in fastening 

 the two ends of a piece of string to two points in the same hori- 

 zontal line, the distance between them being considerably less 

 than the length of the string, and hanging a weight by a second 

 string to the middle point of the first. The strings and weight 

 thus form a pendulum of the shape of the letter Y. The total 

 length of the pendulum employed by me as an illustration of 

 Professor Beetz's experiments was 56 inches, and the length 

 from the middle point of the line joining the two points of sus- 

 pension (which were 20 \ inches apart) to the bottom of the fork 

 of the Y was 42 inches ; so that its time of vibration in the ver- 

 tical plane containing the points of suspension was half as great 

 as its time of vibration perpendicularly to this plane. On giving 

 the pendulum a small motion in the former plane and then sud- 

 denly causing the line joining the points of suspension to turn 

 horizontally about its middle point through 90°, the pendulum 

 still oscillated almost exclusively in its original plane, but its 

 time of oscillation was doubled and the amplitude also increased ; 

 on turning the line of suspension through 90° more, or back 

 again to its former position, the pendulum oscillated as at first. 

 In order that this experiment may succeed well, it is needful to 

 alter the position of the line of suspension as rapidly as possible ; 

 if it is turned slowly, the plane of oscillation of the pendulum 

 turns with it, and nearly to the same extent. 



