Mr Barlow’s Discoverks in Magnetism- 847 
of the compass, and A a constant co-efficient to be determined 
by experiment. 
This formula obtains while the directive power of the needle 
is constant. When the dip, and consequently the directive 
power, changes, it becomes 
m /c* n cosfd 
Tan A = -r-^ ( Sin 2a . cos Z 1 , 
Ad^ \ /cosfd'’ 
where d is the dip, A the place where the co-efficient was deter- 
mined, and d' the dip at the place of observation. 
The D in the above expression is to be understood to denote 
the external diameter of the ball or shell, and is equally appli- 
cable to either, the attraction being wholly independent of the 
mass ; the power of attraction being the same in the thinnest shell 
and the most solid hall. Mr Barlow indeed has found, that a tin 
spherical case ten inches in diameter, and whose weight does 
not exceed twenty-three ounces, has an equal power of attrac- 
tion with a solid iron ball of the same dimensions, weighing 
128 lb. 
This very curious and important fact, the discovery of which 
belongs exclusively to Mr Barlow, is another striking instance of 
the analogy between the electric and magnetic forces ; and the 
following deductions from the preceding laws, bring the analogy 
home again, nearly as strong, to the case of universal attraction. 
Since the tangents of deviation are as the cubes of the dia- 
meters of the attracting bodies, while the force of attraction is 
as the surface or squares of the diameters ; it follows, that the 
squares of the tangents of deviation are directly proportional to 
the cubes qfthe forces. 
The same inference may be drawn from the law of the dis- 
tances, if we assume the force to vary inversely as the squares 
of the distances. For the tangents being inversely as the cubes 
of the distances, and the forces inversely as the squares of the 
same, we shall have, as above, the squares of the tangents di- 
rectly as the cubes of the forces. 
By a due estimation of all the above deductions, Mr Barlow 
has been able to project an experiment of the most simple kind, 
whereby the amount of the influence of the guns of a vessel 
on her compass may be determined at any time, independent 
of any calculation, and in any part of the w^orld. This plan 
