748
THE HONGKONG GOVERNMENT GAZETTE, 13tя MAY; 1599.
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 Temp. vibration. Cent.
Torsion. Log T* | Log =*K
Magnet
No.
No.
meter No.
Bar Magneto- Observer.
h. m.
1898 Feb. 12,......
12 56 p.
5*.8910
19.45
7'.86
1.539823.44966
14,.
1 18 p.
5.8980
23 .25
6.80
1.540153.44916
15,
1 3 p.
5.8991
22..3
6.49
1.540463.44907
21,
3 31 p.
5.9711
19 .6
4.61
1.55125 | 3.44959
17
23
"1
24,.
3 28 p.
5.9640
14.9
5.81
1.55103 3.44943
22
May 11,.
July 19,.
22
19
*
29
"
Nov. 22,.
"
Jy
"
Dec. 20,.
"
""
"
"
15
""
多重
12
}}
""
#
""
""
1 AND AN A
3 42 p.
5.9058
29.15
4.41
1.540123.44948
4 59 p.
5.9827
28.7
4.41
1,551443.44972
4 19 p.
5.9842
31.05
4.32
1.551253.44967
5 43 p.
5.9822
29.85
4.46 1.551163.45002
20,.
115 p.
5.9148
32 .2
4.52 1.540903.44970 55
1 22 p.
5.8991
20.4
7.30 1.540833.44922
13 13 13 13 13 13 13 13 13 13 13
55
55
55
55
55
55
83
55
83
55
55
$3
55
83
55
83
12 13 13 08 03 00 53 13
18 18 18
55
F. G. F.
55
}
55
19
83
29
93
"
83
83
"
83
"
55
23
55
55
"
55
55
"
3 30 p.
5.9743
21..3
7.13
1.551673.44962
55
83
55
""
3.20 p.
5.9114
22.6
8.30
1.542363.44857
55
55
83
""
4 16 p.
5.9530
21.8
8.28
1.54859 3.44862
55
83A
83
11
21,.
1. 30 p.
5.9098
21.6
8.27
1.542283.44895 55
55
83
"
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
19
4 11 p.
5.9505
21.1
7.80
1.54828 3.44875 55
83A
83
29
12 37 p.
5.9064
20.7
8.69
1.54196 3.44907 55
55
83
"
1 34 p.
5.9835 22.3
8.58
1.55296 3.44912 55
83
83
4.20
5.9089
22.2
8.23
1.542053.44931
55
55
83
25
"}
"
3 24
5.9831 22..5
8.23
1.55285 3.44964 35
83
83
**
**
27
Feb. 25,.
12 56 p.
5.0185
16,6
2.00
1.40012 3.44859 83
83
83
May 9,
4 46 P.
5.0527
31 .3
4.38
1.40412
3.44907 83
83
83
" July 18,
3.49 p.
5.1090
28.6
5.14
1.41425
3.44830 83
83
83
33
""
"
19,*
1 3 p.
5.1110
30.5
4.19
1.41422 3.44846 83
83
83
Nov. 23,
12 26 p.
5.1755
20.2
4.60
1.426683.44876 83
83
83
"
"}
Dec. 30,..
1 12 p.
6.1855
20..9
6.60
1.42840 3.44823 83
83
83
"
"
>>
}}
"1
3.38 p.
5.1872
21.25
6.45
1.42863 3.44812
83
83
83
"
Dec. 23,.
"J
3 43 P.
5.5191
20.7
3.03
1.481653.46847
83A
83A
83
31
28,.
1 17 p.
5.5161
22..3
7.12
1.48117 3.46886
83A
83A 83
21
33
"
39
"
"
3.50 p.
5.5201
23.3
7.00
"
33
29,......
1 7 p.
5.5179
22.4
7.33
3 44 p.
5.5183
22.4
7.28
1.48160 | 3.46870 1.481463.46875 83A 1.48152 3.46858 83A
83A
83A 83
51
83A 83
83A 83
"
33
"
* Magnet No. 55 was cleaned and readjusted at the end of November, 1898.
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. 83 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 duc 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 formula:-
1
m tan (p-p”) X tau (+')
and
m tan
(4-4”) tani X tan † (6+ø')