Mr Barlow on the Laws of Eleetro-Magnetic Action. Ill 
necessary for us to admit errors which would not be admissible 
in other cases. 
If the law we have supposed were the exact law in this case, 
then the tangent of each mean angle of deflection, multiplied 
by the square root of the length of the wire, would be a con- 
stant quantity ; and therefore, conversely, this product or con- 
stant quantity in any one case, divided respectively by the square 
roots of the several lengths, ought to give the tangents of the 
angles of deflections due to these lengths ; and in this way we 
are enabled to submit our law to the test of observation, as in 
the following Table; in which we have taken tan 15°S7' X \/98 
= 2*7659, for the constant quantity in the first series, and 
tan 8^ 13' x v^98= 1*4283 in the second series. 
Comparison of Computed and Observed Deflections. 
Length 
of 
Wire. 
Distance \ Inch. A = 
21°. 
Distance 1^ Inch. A 
31°. 
Deflection 
deduced 
from Ob- 
servation. 
Computed 
Deflection 
tan 15° 37' V98 
Errors. 
Deflection 
deduced 
from db- 
servation. 
Computed 
Deflection 
tan 8° 13' a/98 
Errors. 
VL 
VL 
0 / 
O / 
/ 
838 
4 55 
5 28 
4-0 33 
798 
5 26 
5 35 
4-0 
7 
758 
6 46 
5 44 
— 1 
2 
718 
7 17 
5 54 
— 1 
23 
678 
7 4 
6 4 
— 1 
0 
638 
8 31 
6 15 
—2 
16 
598 
8 10 
6 27 
— 1 
43 
558 
8 17 
6 41 
— 1 
36 
518 
8 30 
6 56 
— 1 
34 
478 
8 44 
7 13 
—1 
31 
438 
9 81 
7 32 
-~1 
59 
O' / 
398 
9 25 
8 1 
— 1 
24 
3 20 
4° 6 
4-0%6 
358 
9 38 
8 19 
—1 
19 
3 43 
4 25 
4-0 42 
318 
9 52 
8 49 
— 1 
3 
3 31 
4 35 
-fl 4 
278 
10 1 
9 25 
— 0 36 
3 39 
4 33 
-hi 14 
238 
10 18 
10 10 
—0 
8 
4 45 
5 17 
4-0 32 
198 
11 8 
11 7 
— 0 
1 
4 49 
5 48 
4-0 59 
158 
12 21 
12 25 
4-0 
4 
4 30 
6 39 
-hi 59 
118 
13 53 
14 17 
+ 0 
24 
6 46 
7 29 
4-0 43 
98 
15 37 
15 37 
0 
0 
8 13 
8 13 
0 0 
The errors in the fourth and seventh columns are, as has been 
already observed, rather too considerable to enable us to decide 
with certainty respecting the accuracy of the law assumed ; at 
the same time, they are loo small to allow us to suppose that 
