Mr Barlow on the Lctws of Electro-Magnetic Action. 109 
On examining these results, the first obvious inference is, that 
the diminution of effect due to a greater length of wire is not 
owing to an accidental dissipation of the fluid; the compass, 
which was more than 400 feet from either extremity of the wire, 
being equally affected by the galvanic action, as those which 
were only 7 feet distant. Indeed, the central compass appears, 
in many cases, to have been more deflected than the others ; but 
this, I have little doubt, is due to errors in observation, or per- 
haps to the adjustment of the wire. It has been stated, that, in 
the greater series of experiments, the wire was only half an inch 
from the needle ; and, consequently, any little error in adj list- 
ing it, or any slight inflection of the wire just above the needle, 
would make a difference fully equal to any of the differences 
exhibited in the tabulated results. Moreover, although the four 
compasses employed were all as nearly alike as it was possible 
to get them, yet there might be slight differences in their action, 
which would still farther contribute to increase the other sources, 
of error. I »shall therefore assume, that each of the three com- 
passes employed in obtaining the results at B, C, D, were equal- 
ly affected, and shall take the mean of the six observations made 
with each distinct length of wire for a mean result, and the 
mean of the two deflections shewn by the standard compass in 
each case, for the mean standard measure, as in the following 
Table ; and then, assuming that the tangent of the mean angle 
of deflection is proportional to the tangent of the deflection 
shewn by the standard compass, I shall compute what the seve- 
ral mean deflections would have been, had the power of the bat- 
tery remained constant as at first, using 21° as the standard in 
the larger series of experiments, and 31° in the smaller. 
That is, let A and A' be two deflections shewn by the stand- 
ard compass under different powers of the battery, and d the 
mean deflection corresponding to the power A.' Then, as 
tan A : tan 
tan A : 
tan A' tan 
= tan 
tan a' 
the mean deflection that would be due to the power A'. 
In this way the angles in the fourth and seventh columns have 
been computed ; the former being all reduced to the power 
=: 21°, and the latter A = 31°. 
