1877.] 81 [Konig. 
accord with the French La,, does not hesitate to affirm that all these forks, 
including those even of my large tonometer, which he has probably never 
examined, are necessarily inexact. Not having at my disposal the instru- 
ment used by Mr. Ellis, I confess that I find myself under some embarass- 
ment in stating at once by what error of construction this instrument, in 
the hands of Mr. Ellis, has given results so extraordinary. Fortunately, 
Ican refer to a letter from M. Helmholtz addressed to Mr. Appunn and 
published by the latter himself in a paper on the acoustic theories of M. 
Helmholtz. This letter speaks of an instrument of exactly the same char- 
acter; and made by the same maker, and sufficiently explains the surpris- 
ing discoveries of Mr. Ellis. ‘‘I have examined your tonometer several 
times,’’ writes M. Helmholtz to Mr. Appunn, ‘‘and I am astonished at 
the constancy of its indications. I would not have believed that reeds 
could give sounds so constant as those given by your apparatus, thanks to 
your method of regulating the current of air. The instrument, it is true, 
varies a little with the temperature, as do also forks ; and hence it can be 
used for determining the absolute number of vibrations, only when one 
can work in a room heated by a stove. By the aid of an astronomical 
chronometer, I have counted the beats, and believe that your seconds pen- 
dulum must have been slightly inexact, because, though the number of 
beats agree very well among themselves, the absolute number obtained is 
not 240 but 237 to the minute. The temperature, which was rather low 
during my experiments, may count for something ; but even this influence 
may be eliminated by counting the beats to the end of a major-third, which 
took me a quarter of an hour. In this way I have found for my Paris fork 
435.01 vibrations, which agrees to the ;5355 nearly with the official num- 
ber, 435 vibrations.”’ 
This letter proves that the entire number of beats in the octave of the 
tonometer tested by M. Helmholtz was 437 >< 64 = 252.8, and that its fun- 
damental note was 505.6 single vibrations instead of 512. On comparing 
this note of 505.6 single vibrations with a fork giving actually 512 single 
vibrations, Mr. Ellis would find the latter to be 6.4 single vibrations more 
acute and, without doubt, would consider it as giving 518.4 single vibra- 
tions. Now for my forks giving 512 single vibrations, he has found 516.7 
only, with the tonometer which he used. Whence it would seem that the 
fundamental note of this latter instrument had become more nearly exact 
than that of the tonometer examined by M. Helmholtz, since the number 
of its vibrations is 507.3. This note, however, still remains quite distant 
from its true value. 
The fact that M. Helmholtz succeeded, with an instrument of this sort 
(and one too, even less perfect than that used by Mr. Ellis) in finding the 
number of vibrations of the official French fork to be exact, by first deter- 
mining the correction needed for his instrument, is evidence that Mr. Ellis 
has neglected to determine a similar correction required for his tonometer. 
He has too hastily declared that these small tonometers with harmonium 
reeds are the most perfect and the most exact in existence. It would cer- 
PROC. AMER. PHILOS. soc. xvir. 100. kK 
