28^ Mr Barlow’s Discovery of the Mathematical Laws 
tide of the vertical wire. The distance being now made con- 
stant, and the length of the wire varied, he found still the same 
result, viz. that every particle of the galvanic wire acts on every 
particle of the magnetic needle, with a power varying inversely 
as the square of the distance, the power of the battery being 
maintained at the same degree of intensity ; which latter condi- 
tion was insured, by means of a mechanical contrivance, for low- 
ering gi-adually the combination of plates, into the vessel con- 
taining the dilute acid, and a standard compass fixed opposite 
the other vertical branch of the conducting rectangle. 
Having established this point, the needle was now passed suc- 
cessively, at different distances, round the wire, and the law of 
deviation ascertained, as the same depended upon the azimuth 
of the needle with respect to the wire, and which law is thus 
given by the author : “ Let A represent the deviation of the 
needle at the north point ; and <p the angle of the , azimuth from 
the north, and ^ the deviation of that azimuth ; then ' 
cot A X sin (p. 
This formula, although so extremely simple, is sufficient to 
explain all the peculiarities of action observed between the 
needle and the wire, by merely attending to the changes of 
signs which take place io cos p and sin <p in the four quadrants, 
and to the distinct cases which follow from considering cot A, as 
greater than, equal to, or less than unity. In the two latter cases 
tan ^ will become infinite, and the needle will revolve on its pi- 
vot during its rotation round the wire, which cannot take place 
if cot A be greater than unity, that is, if the deviation at the 
north be less than 45°. In all these cases, and in a long series 
of computed and observed deviations, Mr Barlow has found the 
most complete and satisfactory coincidences, and comparing to- 
gether the experimental and theoretical laws of action, he has 
drawn the following general conclusions, viz. That every par- 
ticle of the galvanic fluid in the conducting wire, acts on every 
particle of the magnetic fluid in a magnetized needle, by a force 
which varies inversely as the square of the distance ; but that 
this action is neither to attract nor to repel either pole of the 
imagnetic particles, but a tangential force, which is reciprocal be- 
