ON THE DIRECTIVE POWER OF MAGNETS. 
497 
The expressions for forces which concern us now are those given by the general 
X Y 
formulae for — and — . And a moment’s glance at these will show that they explain the 
jtt jJ* 
apparent position of the pole at the very extremity of the coil : for, in order to ascer- 
tain the values of the forces in a plane at right angles to the axis passing through the 
extremity of the coil, we must make a=90°, sin a= 1, cos a=0; and if the other end 
of the coil be very distant, $ may be taken =0, sin $—0, cos (6=1. Substituting these 
values, it will be seen at once that X, the longitudinal force, =0, while Y, the transversal 
force, has a value, which indicates a force directed to the extremity of the coil. 
In order to make a complete comparison, I have, for all the eighteen stations treated 
in the former Tables, taken the values of a, (3, andj> graphically. For b I have adopted 
0'45, and for b-\-c 0-7 ; these numbers correspond to the internal and external surfaces 
of the coil, hut they appear to me best to represent (though doubtless with some inac- 
curacy) the quantities used in the theoretical investigation. Then I have (with the 
kind assistance of Edwin Dunkin, Esq., of the Iloyal Observatory) made the complete 
calculation of the formulae for every station. As the numbers first obtained were not 
immediately comparable, I have made them more nearly so by trebling the numbers 
given by theory and doubling those in the preceding Table. The results are as 
follows : — 
Longi- 
tudinal 
ordinate. 
Trans- 
versal 
ordinate, 
or p. 
a. 
/3. 
Result of theoretical 
calculation. 
Theoretical result 
trebled. 
Ex25erimental result 
doubled. 
X. 
Y. 
X. 
Y. 
X. 
Y. 
0-0 
2-26 
o 
16 1 
10 
o 
18 
40 
160 
0 
— 480 
0 
- 432 
0 
1-34 
2 - 26 
157 
15 
15 
40 
— 
168 
+ 30 
- 504 
+ 90 
- 480 
+ 76 
2*68 
2-26 
151 
0 
13 
25 
— 
208 
+ 82 
- 624 
+ 246 
- 630 
+ 240 
4-02 
2-26 
140 
20 
11 
35 
— 
297 
+ 206 
- 891 
+ 618 
- 900 
+ 650 
5-36 
2-26 
121 
55 
10 
15 
— 
354 
+ 503 
— 1062 
+ 1509 
— 1100 
+ 1 696 
6-7 
2'26 
91 
0 
9 
20 
— 
38 
+ 855 
- 114 
+ 2565 
- 160 
+ 2960 
7-7s 
1-70 
58 
25 
6 
10 
+ 
543 
+ 771 [ 
+ 1629 
+ 2313 
+ 2020 
+ 3260 
8-2 
0-74 
28 
0 
2 
35 
+ 1417 
+ 688 
+ 4251 
+ 2064 
+ 4960 
+ 2340 
0-0 
3-73 
151 
0 
29 
0 
__ 
124 
0 I 
- 372 
0 
- 368 
0 
1-34 
3-73 
145 
30 
24 
42 
— 
128 
+ 32 
- 384 
+ 96 
- 378 
~|- 82 
2-68 
3-73 
137 
20 
21 
30 
— 
139 
+ 77 
- 417 
+ 231 
- 400 
+ 208 
4*02 
3*73 
126 
10 
18 
57 
— 
150 
+ 148 
- 450 
+ 444 
- 434 
+ 424 
5-36 
3-73 
110 
5 
16 
58 
— 
109 
+ 243 
— 327 
+ 729 
- 246 
+ 766 
6-7 
3-73 
91 
0 
15 
27 
— 
20 
+ 295 
- 60 
-f- 88o j 
- 114 
+ 848 
7-83 
3-44 
73 
0 
13 
2 
+ 
80 
+ 308 
+ 240 
+ 924 
+ 200 
+ 872 
8-82 
2-8 
54 
5 
10 
0 
+ 
179 
+ 281 
+ 537 
+ 843 
+ 528 
-j - 820 
9-49 
1-82 
34 
35 
6 
10 
+ 
318 
+ 223 
+ 954 
+ 669 1 
+ 950 
+ 676 
9-7 
0-73 
14 
25 
2 
5 
+ 
456 
+ 120 
+ 1368 
+ 360 
+ 1336 
+ 372 
In spite of some discordances in the large forces (which it was impossible to measure 
with accuracy), there is enough of agreement to show that confidence may be placed 
in the method of theoretically computing the attraction of the galvanic coil. 
