136 
Remarlcs on Professor Hansteen’s 
than those of Coulomb ; yet the mutual agreement of the two 
results, proceeding upon principles so different, tends strongly 
to confirm the accuracy of both ; and we may assert, without 
hesitation, that the magnetic force varies according to this law 
very nearly, and probably with absolute exactness. 
As to the degree of uncertainty which might arise from the 
undetermined value' of r, it is afterwards proved, that, at consi- 
derable distances, this circumstance has almost no effect. The 
value of r, therefore, or the ratio in which the magnetic force 
is distributed from the middle point of the axis towards both 
poles, cannot be ■''derived with any certainty from these experi- 
ments. Coulomb’s investigation of this second elementary law^ 
did not yield a very satisfactory result ; and the point cannot 
yet be considered as entirely determined. From comparing the 
second with the fourth column of the preceding table, Mr tlan^ 
Steen seems inclined to think that r—% or that the absolute m- 
tensity of any magnetic particle situated in the axis^ is propor- 
tional to the square of its distance from the middle point of that 
axis. It must be owned, that this conclusion does not differ 
very widely from the facts established in the foregoing experi- 
ments ; yet it seems likely that the function of the distance, 
which expresses the value of r, may be much more complicated 
than Mr Hansteen supposes : indeed, the culminating points of 
Van Swinden, which occur in every magnetic bar of great length, 
shew clearly that the curve denoting the intensities, must cut its 
axis more than once ; and as this cannot happen to any species 
of parabola, we are forced to conclude, that the absolute force 
of a given magnetic particle is not proportional to any power of 
its distance from the middle of the axis. 
The third elemeyitary law of magnetism, or the ratio in which 
the intensity is distributed among the particles of a section per-, 
pendicular to the axis, has not been more accurately fixed than 
the second. On this head, Mr Hansteexi observes : It is the 
more difficult to overcome the present obstacle, because, in all 
probability, the law assumes different modifications according to 
the different figures of the section. When the magnet is cylin- 
drical, it seems likely that all such particles of the section as lie 
at the same distance from the centre or axis of the cylinder, 
have the same intensity; so that any section may be represented 
