1881.] On the Musical Pitch of Harmonium Reeds. 413 



of any number, such as the modulus of any other system of logarithms 

 can be found, and its reciprocal, whence the radix for that system can 

 be calculated by simple multiplication. This is sufficient to show the 

 practicability of the present method, and generally the comparatively 

 small trouble which it would occasion for the first construction of 

 logarithmic tables. 



VI. " On the Influence of Temperature on the Musical Pitch of 

 Harmonium Reeds." By Alexander J. Ellis, B.A., F.R.S., 

 F.S.A. Received January 17, 1881. 



In my " Notes of Observations on Musical Beats," I stated (" Proc. 

 Roy. Soc," vol. 30, p. 532) that the influence of temperature on 

 harmonium reeds was, so far as I was aware, unknown. Since then 

 I have made some observations which at least approximately deter- 

 mine it, but there are so many sources of small errors (stated below) 

 that still more uncertainty must attach to the results, than to the 

 determination of the influence of temperature on the pitch of tuning- 

 forks (ibid., p. 523). Roughly we may say that the pitch of harmo- 

 nium reeds is affected in the same direction as that of tuning-forks 

 (heat flattening and cold sharpening), and very nearly to twice the 

 amount, that is, by about 1 in 10,000 vibrations for each degree 

 Fahrenheit. The following is the process pursued with the exact 

 figures obtained : — 



Towards the end of November, 1879, in the South Kensington 

 Museum, with artificial temperatures (observed in each case) varying 

 from 53° to 60° P. on different days, I determined the beats which all 

 the reeds of Appunn's treble tonometer (ibid., p. 527) made with 

 Scheibler's forks (ibid., p. 525). On 1st September, 1880, and again 

 on 3rd September, 1880, at constant natural temperatures of 73° and 

 79° P. respectively, I took the beats of twelve of the reeds (the same 

 on each occasion) with the same forks of Scheibler with which I had 

 measured those reeds in November, 1879. 



It is, of course, impossible to say whether either forks or reeds were 

 precisely of the same temperature as the air. The reeds were inclosed 

 in the wooden chest of the tonometer, which had been reposing in a 

 glass wall-case in the same room during he night, and might not 

 have fully acquired the general steady temperature of the room. The 

 beats for each reed were counted 10 times each for 10 seconds, with 

 each of two, and sometimes three forks, and the mean of each set of 

 beats was employed. The known pitch of the forks at 59° P. (ibid., 

 p. 525) was then reduced to the temperature of the observation on the 

 supposition that the number of vibrations altered by 1 in 20,000 for 



