1880.] 



Notes of Observations on Musical Beats. 



525 



another between forks 2 and 3, 4 and 5, &c, so that the same fork is 

 not nsed for two counts on the same day. Excite by striking with a 

 soft ball of fine flannel wound round the end of a piece of whalebone, 

 as a bow is not convenient unless the forks are tightly fixed. Each 

 blow or bowing heats, and hence flattens, and this tells if the experi- 

 ments on any one fork are long continued. Count each set of beats 

 for 40 seconds if possible, and many times over, registering the tem- 

 perature and the beats, and take the mean. Scheibler counted by a 

 graduated metronome, set constantly to an astronomical clock, when 

 the weight was at 60, to eliminate the effect of temperature, and he 

 altered the position of the weight (finally by a micrometer screw) so 

 that there were always four beats to each swing of the pendulum. He 

 seems to have attained extraordinary accuracy. Having counted all, 

 observe those forks which are near the octave of the lowest fork. 

 Find two such, beating with the octave (that is, the second partial 

 tone) of the lowest fork less than they beat with each other. Then the 

 sum of all the beats from the lowest fork to the lower of the two forks, 

 added to the beats of the octave (that is, the second partial tone) with 

 that fork, is the pitch of the lowest fork. Hence the pitch of all the 

 forks is known. The extra high forks are for verifying by the octaves 

 of several low forks, and for the purpose of subsequently measuring. 

 From such a tonometer any other can be made, and the value of each 

 fork at another temperature calculated. 



Scheibler made a 52-fork tonometer with infinite trouble, on another 

 plan, and counted it with marvellous accuracy. This tonometer, which 

 I have made many efforts to find, has absolutely disappeared and his 

 family knows nothing of it. But he left behind him a 56-fork tono- 

 meter, believed to proceed from 220 to 440 vibrations, and through the 

 kindness of Herr Amels, an old friend of the Scheibler family, who 

 obtained it from Scheibler's grandson, I have had the use of it for a 

 year. I had to count it as well as I could, just as if it had been a set 

 of forks such as I have described, and I found it was not what was 

 thought, but that only 32 sets of beats were 4 in a second, and the 

 other 23 sets varied from 38 to 42 in 10 seconds. I found also that 

 the extremes were probably of the same pitch as in the original 52-fork 

 tonometer. After then counting it as well as I could, and obtaining 

 219*27 vibrations in place of 219'67, at 69° F., I distributed the error 

 of 4 beats in 10 seconds, as 2 in 100 seconds, among 20 of the 23 sets 

 which were not exactly 4 beats in 10 seconds, leaving the first 3 sets, 

 which I had repeatedly counted and felt sure of, unaltered. Then I 

 reduced all the values from 69° to 59° F. Finally to verify my result 

 I measured by beats with Scheibler's forks as thus determined ; first 

 5 large forks of various pitches, which I had had made for me in 

 Paris, and then 4 forks of Koenig's belonging to Professor McLeod. 

 Professor McLeod himself kindly measured all of them, also, by his 



