298
Table XIV.
Observations of Moments of Inertia of Magnets made from the 1st January, 1898, till the 1st March, 1899.
Date.
H. K. M. T.
Time of one vibration.
Cent.
Temp. Torsion. Log T Log K
Magnet
No.
No.
Bar Magneto- meter No.
Observer.
h. m.
1898 Feb. 12,................
12 56 p.
5o.8910
19°.45
7.86
1.53982 | 3.44966
14,.
1 18 p.
5 .8980
23 .25
6,80
1.540153.44916 55
>>
17
"
15,.
1 3 p.
5.8991
22.3
6.49
1.540463.44907
181816
55
55
55
21,.
3 31 P.
5.9711
19.6
4,61
1.55125 3.44959
55
"
و"
24,
3 28 p.
5.9640
14.9
5.81
1.551033.44943
管
" May 11,
3 42 P.
5.9058
29.15
4.41
1.540123.44948
55
13 13 13 13
55
55
83
10121888
55
F. G. F.
55
*
55
83
""
83
93
55
83
"
4 59 p.
5.9827
28 ..7
4.41 1.551443.44972
55
83
83
19
33
"
July 19,.......
4 19 P.
5.9842
31 .05
4.52.1.55125 | 3.44967
55
83
83
"
5 43 P.
5.9822
29 .85
4.46 1.55116 3.45002
55
83
55
27
"
"
27
"
20,
1 15 P.
5.9148
32 .2
4.52
1.54090 13.44970
55
55
55
"
""
Nov. 22,.....
1 22 P.
5.8991
20.4
7.30
1.54083 3.44922
55
55
55
"}
3 30 p.
5.9743
21.3
7.13
1.551673.44962 55
83
55
"J
"
22
"
Dec. 20,......
3 20 p.
5.9114
22.6
8.30
1.542363.14887 *55
55
83
>>
4 16 P.
5.9530
21.8
8.28
1.54859 3.44862
831
83
22
"
*
32
"
JJ
27
"
#
י
Feb. 25,.....
སྨད མ ལ བསླུ མ མ མཤྩ
21,
1 30 p.
5.9098
21.6
8.27
|1.542283.44895
55
83
19
12 38 p.
5.9505
20 .3
8.54
1.548473.44873 55
83A
83
3 23 P.
5.9092
21 .2
8.10
1.54225 3.44867 55
55
83
ور
4 11 P.
5,9505
21.1
7.80
1.54828 3.44875
83A
83
12
22,.....
12 37 P.
5.9064
20.7
8.69
1.54196 3.44907
55
83
"
1 34 P.
5.9835
22..3
8.58
1.55296 3.44912
55
83
83
4 20 P.
5.9089
22.2
8.23
1.54205 3.44931
55
55
83
3 24 P.
5.9831
22.5
8.23
1.552853.44964
55
83
83
+
12 56 p.
5.0185
16 .6
2,00
1.400123.44859
83
83
83
}}
May 9,......
4 46 P.
5.0527
31.3
4.38
1.404123.44907 83
33
83
19
37
July 18,......
3 49 P.
5.1090
28. 6
5.14
1.414253.44830
83
83
83
""
”
19,.....
1. 5 p.
5.1110
30.5
4.19
1.414223.44846
83
83
83
"
Nov. 23,.
**
12 26 p.
5.1755
20.2
4.60
1.42668 3.44876
83
83
83
""
Dee. 30,..
1 12 P.
5.1855
20..9
6.60
1.428403.44823
83
83
83
3 38 p.
5.1872
21.25
6.45
1.428633.44812
83
83
83
"
"
ל
Dec. 23,
3 13 P.
5.5191
20.7
3.03
1.481653.46847
83A
83A
83
+9
28,
1 17 p.
6.6161
22..3
7.12
1.481173.46886 83A
83A
83
3 50 p.
5.5201
23 .3
7.00
79
"J
""
29,...***
}}
1 7 p. 3 44 p.
5.5179
22.4
7.83
5.5183
22.4
7.28
1.481603.46870 83A 1.481463.46875 83A 1.481523.46858
83A
83A 83
83A 83
83A
83
ཊྛ བྷ བྷ ; དྷནྟཊྛནྟཊྛསྡུདཋ བ
* Magnet No. 55 was cleaned and readjusted at the end of November, 1893.
In order to compare the results obtained with the different instruments it is necessary to know the probable errors so as to be able to judge how much of the difference is due to chance and how much to other causes. The probable errors may be estimated to be about the following: rate of chronometer 0.1, torsion (for 90°) 0'.1, temperature (°.5, induction 2 %, observed period of vibration 0.0004, moment of inertia 0.00012, circle readings 10", value of P 1.0. The following errors in the value of the horizontal force (expressed in units of the fifth decimal) are caused by these errors in the elements by error of temperature 4, through vibration, and 4, through deflection, by induction-error 1, by vibration error 4, by moment of inertia 5, by defective circle readings 4, by wrong P 20. The probable error of a horizontal force is therefore about 0.00022. In England, where the horizontal force is only half of that in Hongkong, the probable error also ought to be about half of that in Hong- kong.
From direct comparison of observations a smaller value of the error (say 0.00013) might be obtained as they are often reduced without changing K and P. The moment of inertia was deter- mined at 25° Cent. for magnet 55 by using its own bar to be 3.44938±0.00007 and by the bar supplied with No. 8 to be 3.44968±0.00008. After cleaning it came out as 3.44901 0.00009 by its own bar, as 3.44941+0.00023 by the bar of 83, and as 3,44874+0.00005 by the bar of 83A. These differences may be caused by minute internal cavities in the different bars. The moments of inertia adopted for each magnet have been observed with its own bar. A part of the differences of the results obtained with different magnetometers is due to this cause.
It has been suggested that the differences between magnetometers are due to traces of magnetic metals in the magnetometers. In Hongkong we have not found any perceptible difference between the old instrument made in 1883 and the new instrument made in 1897.
With reference to the induction coefficient, this has been obtained for both the horizontal and vertical position of the magnet by aid of the following formulæ :-
m tan
-")
Ha
X tan } (6+6')
= and
My
m tan (4—4') tani X tan 4 (4+¢')