$64 Analysis of ' Mr Barlow's Essay on Magnetic Attractions . 
The next object was to determine the law for the distance, 
with which view the same series of experiments were performed 
at four different distances, viz. 1$, 15, 18, and $0 inches ; and 
applying to these results the method of minimum square , the 
author obtained, in the most satisfactory manner, the following 
conclusion ; viz. that all other things being the same, the tan- 
gents of the angle of deviation are reciprocally proportional to 
the cubes of the distance. And, lastly, by using balls of differ- 
ent diameters, he found the tangents of deviation proportional 
to the cubes of the diameters. The general formula for ex- 
pressing the deviation under every circumstance is therefore, 
D 3 f • 
A = A — 1 sin. $ a cos. 1. 
d 3 { 
where A is the angle of deviation, D the diameter of the base, 
d the distance, a the latitude, l the longitude of position, and A 
a constant factor to be found by experiment. 
But the most remarkable discovery of the author still re- 
mains to be noticed. We have stated that he found the tan- 
gents of the angles of deviation to be proportional to the cubes 
of the diameters, whence it was natural to conclude, that they 
were proportional to the masses ; and he had, in fact, come to 
this conclusion, when he fortunately made trial of a ten-inch 
shell, and found that it gave precisely the same deviations as 
the solid ball of the same dimensions. This led to a new course 
of experiments on balls, plates, and shells of iron, of various 
thicknesses ; and he thus ascertained that the attracting power 
of iron bodies, for the magnet, resides wholly in their surfaces, 
and that it is independent of their masses, provided their thick- 
nesses exceed a certain quantity, (probably about ^th of an 
inch.) 
Lastly, as the laws we have been enumerating were all de- 
duced from experiments on balls and shells, he was next desir- 
ous of ascertaining whether they obtained equally on irregular 
masses ; and, with this view, a series of experiments were made 
on an iron $4-pounder, mounted on a traversing carriage and 
platform, which, together with its iron trucks, &c. weighed 58 
cwt, on which the laws were still found to be the same as on 
the most regular body ; and hence it followed that they might 
be made immediately applicable to the correction of the local 
