64 A. A. Michelson— Rate of Tuning-forks. 
oe. -hairs. Behind the fork the Geissler tube is placed hori- 
ontal. The appearances pated ed in the microscope at each 
Aash would then be as follov 
OO SOOOLOOE 
From these we can deduce the rate as before 
This method would probably give results almost if not quite 
as accurate as the preceding, and has the advantage of being 
more direct. The nearest whole number may be found by 
comparison with one of Kénig’s standards, or by the following 
method, 
The fork is, in turn, compared with two a whose 
times of vibration are ¢, and ¢,, ¢,—t, being sm 
Let n,=number of vibrations of the nay in time ¢,. 
Let »,=number of vibrations of the fork in time ¢,. 
n, and n, differing from a whole number by less than a small 
fraction, e.. 
1 
Let a,=number of beats of pendulum (1) per period = -. 
: 1 
Let a,=number of beats of pendulum (2) per panes 
c, and c, being small fractions less then e,. 
,=whole number nearest to 7,. 
Let N,=whole number nearest to ”,. 
Then n,+¢,=N, 
n,+0,= 
n,—n, +¢,—¢,=N,—N ok, a whole number. 
n,—n, +¢,—¢, is bens than 2(e,+e, 
If, therefore, 2, 4) is numerically less dan 4 then M=0, 
whence Nv= 
= — 
he =y~S =; — Fs ae ofS, 
Hight Feleta of the tas of an Ut, fork, made by the 
preceding method gave the following results 
Temp. Fahr. v. 8. v. s. at 60° F. Diff. from mean. 
54°0° 128°134 128°690 +000 
56°3 128°114 128°087 0°000 
58°0 128'102 128:087 0-000 
60°0 128-090 128:090 + 0°003 
62°2 128°077 128°093 +0°006 
63°0 128°060 128°082 —0°005 
64°5 128°050 128°083 —0°004 
73°5 127°984 128°084 — 0003 
