Effect of Support and of Sc.r.a.ping.
The standard Vt3 fork held in its wooden support was compared with another fork on a resonator loaded with wax and making with standard about five beats per second. The standard was free from the cylinder. The beats were counted by coincidences with the ? second beats of a watch.
_Specimen._
Coincidences were marked--
At 32 seconds.
37 seconds.
43.5 seconds.
49 seconds.
54.5 seconds.
61.5 seconds.
61.5 - 32 = 29.5.
29.5 5 = 5.9 = time of one interval.
_Resume._
1 5.9 2 6.2 3 6.2 4 6.2 ---- Mean = 6.13 = time of one interval between coincidences.
In this time the watch makes 6.135 = 30.65 beats, and the forks make 30.65 + 1 = 31.65 beats.
Hence the number of beats per second is 31.65 6.13 = 5.163.
_Specimen._
Circ.u.mstances the same as in last case, except that standard Vt3 fork was allowed to trace its record on the lampblacked paper, as in finding its rate of vibration.
Coincidences were marked at--
59 seconds.
04 seconds.
10.5 seconds.
17 seconds.
77 - 59 = 18.
18 3 = 6.0 = time of one interval.
_Resume._
No. 1 6.0 seconds. 6.31 5 = 31.55 2 6.0 seconds. + 1.00 3 6.7 seconds. ---- 4 6.3 seconds.
5 6.5 seconds. 32.55 6 6.7 seconds. 32.55 6.31 = 5.159 7 6.0 seconds. With fork free 5.163 ---- ----- Mean = 6.31 seconds Effect of sc.r.a.pe = - .044
_Specimen._
Circ.u.mstances as in first case, except that both forks were on their resonators.
Coincidences were observed at--
21 seconds.
28 seconds.
36 seconds.
44 seconds.
51 seconds.
60 seconds.
60 - 21 = 39 39 5 = 7.8 = time of one interval.
_Resume_.
No. 1 7.8 seconds. 7.42 5 = 37.10 2 7.1 seconds. + 1.00 3 7.6 seconds. ----- 4 7.4 seconds. 38.10 5 7.2 seconds. 38.10 7.42 = 5.133 ---- (Above) 5.159 ----- Mean = 7.42 seconds. Effect of support and sc.r.a.pe = - .026
Mean of second determination was 256.094 Applying correction (sc.r.a.pe, etc.) - .026 ------- Corrected mean 256.068 Result of first determination 256.072 ------- Final value 256.070
NOTE--The result of first determination excludes all work except the series commencing July 4. If previous work is included, and also the result first obtained by Professor Mayer, the result would be 256.089.
256.180 256.036 256.072 256.068 ------- Mean = 256.089
The previous work was omitted on account of various inaccuracies and want of practice, which made the separate results differ widely from each other.
The Formulae.
The formulae employed are--
d"
(1) tan f = ----- r
2592000? D n (2) V = ----------------- f?
f = angle of deflection.
d" = corrected displacement (linear).
r = radius of measurement.
D = twice the distance between the mirrors.
n = number of revolutions per second.
a = inclination of plane of rotation d = deflection as read from micrometer.
B = number of beats per second between electric Vt2 fork and standard Vt3 Cor = correction for temperature of standard Vt3.
V = velocity of light.
T = value of one turn of screw. (Table, page 126.)
Subst.i.tuting for d, its value or dTsec a (log sec a = .00008), and for D its value 3972.46, and reducing to kilometers, the formulae become--