mm.
For the first 10 turns 0.99570
20 turns 0.99570
30 turns 0.99573
40 turns 0.99577
50 turns 0.99580
60 turns 0.99583
70 turns 0.99589
80 turns 0.99596
90 turns 0.99601
100 turns 0.99606
110 turns 0.99612
120 turns 0.99618
130 turns 0.99625
140 turns 0.99630
NOTE.--The micrometer has been sent to Professor Mayer, of Hoboken, to
test the screw again, and to find its value. The steel tape has been sent
to Professor Rogers, of Cambridge, to find its length again. (See page
145.)
Measurement of the Distance between the Mirrors.
Square lead weights were placed along the line, and measurements taken
from the forward side of one to forward side of the next. The tape rested
on the ground (which was very nearly level), and was stretched by a
constant force of 10 pounds.
The correction for length of the tape (100.006) was +0.12 of a foot.
To correct for the stretch of the tape, the latter was stretched with a
force of 15 pounds, and the stretch at intervals of 20 feet measured by a
millimeter scale.
mm.
At 100 feet the stretch was 8.0
80 feet the stretch was 5.0
60 feet the stretch was 5.0
40 feet the stretch was 3.5
20 feet the stretch was 1.5
--- ---
300 23.00
Weighted mean = 7.7 mm.
For 10 pounds, stretch = 5.1 mm.
= 0.0167 feet.
Correction for whole distance = +0.33 feet.
The following are the values obtained from five separate measurements of
the distance between the caps of the piers supporting the revolving mirror
and the distant reflector; allowance made in each case for effect of
temperature:
1985.13 feet.
1985.17 feet.
1984.93 feet.
1985.09 feet.
1985.09 feet.
-------
Mean = 1985.082 feet.
+.70. Cap of pier to revolving mirror.
+.33. Correction for stretch of tape.
+.12. Correction for length of tape.
--------
1986.23. True distance between mirrors.
Rate of Standard Ut₃ Fork.
The rate of the standard Ut₃ fork was found at the Naval Academy, but as
so much depended on its accuracy, another series of determinations of its
rate was made, together with Professor Mayer, at the Hoboken Institute of
Technology.
_Set of determinations made at Naval Academy._
The fork was armed with a tip of copper foil, which was lost during the
experiments and replaced by one of platinum having the same weight,
4.6 mgr. The fork, on its resonator, was placed horizontally, the platinum
tip just touching the lampblacked cylinder of a Schultze chronoscope. The
time was given either by a sidereal break-circuit chronometer or by the
break-circuit pendulum of a mean-time clock. In the former case the
break-circuit worked a relay which interrupted the current from three
Grove cells. The spark from the secondary coil of an inductorium was
delivered from a wire near the tip of the fork. Frequently two sparks near
together were given, in which case the first alone was used. The rate of
the chronometer, the record of which was kept at the Observatory, was very
regular, and was found by observations of transits of stars during the
week to be +1.3 seconds per day, which is the same as the recorded rate.
Specimen of a Determination of Rate of Ut₃ Fork.
Temp.=27° C. Column 1 gives the number of the spark or the number of the
second. Column 2 gives the number of sinuosities or vibrations at the
corresponding second. Column 3 gives the difference between 1 and 11, 2
and 12, 3 and 13, etc.
July 4, 1879.
1 0.1 2552.0
2 255.3 2551.7
3 510.5 2551.9
4 765.6 2551.9
5 1020.7 2552.1
6 1275.7 2552.0
7 1530.7 2551.8
8 1786.5 2551.4
9 2041.6 2551.7
10 2297.0 2551.5
-------
11 2552.1 255.180 = mean ÷ 10.
12 2807.0 + .699 = reduction for mean time.
13 3062.4 + .003 = correction for rate.
14 3317.5 + .187 = correction for temperature.
-------
15 3572.8 256.069 = number of vibrations per second at 65° Fahr.
16 3827.7
17 4082.5
18 4335.9
19 4593.3
20 4848.5
The correction for temperature was found by Professor Mayer by counting
the sound-beats between the standard and another Ut₃ fork, at different
temperatures. His result is +.012 vibrations per second for a diminution
of 1° Fahr. Using the same method, I arrived at the result +.0125.
Adopted +.012.
_Résumé of determinations made at Naval Academy._
In the following table the first column gives the date, the second gives
the total number of seconds, the third gives the result uncorrected for
temperature, the fourth gives the temperature (centigrade), the fifth
gives the final result, and the sixth the difference between the greatest
and least values obtained in the several determinations for intervals of
ten seconds:
July 4 20 255.882 27.0 256.069 0.07
5 19 255.915 26.4 256.089 0.05
5 18 255.911 26.0 256.077 0.02
6 21 255.874 24.7 256.012 0.13
6 9 255.948 24.8 256.087 0.24
7 22 255.938 24.6 256.074 0.05
7 21 255.911 25.3 256.061 0.04
8 20 255.921 26.6 256.100 0.02
8 20 255.905 26.6 256.084 0.06
8 20 255.887 26.6 256.066 0.03
-------
Mean = 256.072
In one of the preceding experiments, I compared the two Vt₃ forks while
the standard was tracing its record on the cylinder, and also when it was
in position as for use in the observations. The difference, if any, was
less than .01 vibration per second.
_Second determination_.
(Joint work with Professor A.M. Mayer, Stevens Institute, Hoboken.)
The fork was wedged into a wooden support, and the platinum tip allowed to
rest on lampblacked paper, wound about a metal cylinder, which was rotated
by hand Time was given by a break-circuit clock, the rate of which was
ascertained, by comparisons with Western Union time-ball, to be 9.87
seconds. The spark from secondary coil of the inductorium passed from the
platinum tip, piercing the paper. The size of the spark was regulated by
resistances in primary circuit.
The following is a specimen determination:
Column 1 gives the number of the spark or the number of seconds. Column 2
gives the corresponding number of sinuosities or vibrations. Column 3
gives the difference between the 1st and 7th ÷ 6, 2nd and 8th ÷ 6, etc.
1 0.3 255.83
2 256.1 255.90
3 511.7 255.90
4 767.9 255.93
5 1023.5 255.92
6 1289.2 256.01
7 1535.3 255.95
-------
8 1791.5 255.920 = mean.
9 2047.1 - .028 = correction for rate.
-------
10 2303.5 255.892
11 2559.0 + .180 = correction for temperature.
-------
12 2825.3 256.072 = number of vibrations per second at 65° Fahr.
13 3071.0
In the following _résumé_, column 1 gives the number of the experiments.
Column 2 gives the total number of seconds. Column 3 gives the result not
corrected for temperature. Column 4 gives the temperature Fahrenheit.
Column 5 gives the final result. Column 6 gives the difference between the
greatest and least values:
1 13 255.892 80 256.072 0.18
2 11 255.934 81 256.126 0.17
3 13 255.899 81 256.091 0.12
4 13 255.988 75 256.108 0.13
5 11 255.948 75 256.068 0.05
6 12 255.970 75 256.090 0.05
7 12 255.992 75 256.112 0.20
8 11 255.992 76 256.124 0.03
9 11 255.888 81 256.080 0.13
10 13 255.878 81 256.070 0.13
-------
Mean = 256.094
Effect of Support and of Scraping.
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 ⅕ second beats of a watch.
_Specimen._