horizontal needle when under the influence of magnets. 363 
might so adjust the magnets, that I could make simultaneous 
observations on the same needle in three different positions, 
without altering the situations of the magnets, or of the centre 
of the needle. As I consider that these observations point to 
conclusions which cannot fairly be drawn from those made 
at several points, under different adjustments of the magnets, 
I shall omit giving those mentioned above. 
Previously to giving the observations themselves, I shall 
describe the principle on which I adjusted the magnets, and 
state what I considered would be the effects of certain changes 
in their distances from the centre of the needle, and in the 
angle which their axes made with the meridian, describing 
likewise the experiments, which proved the correctness of 
these conclusions : this will enable me the better to draw 
inferences from the observations. It is very evident that if 
the magnets are exactly in the meridian, at the same dis- 
tances from the centre of the needle, and in the same hori- 
zontal plane with it, whatever may be the directions of the 
resultants of all the forces acting on the needle in any par- 
ticular position of its ends, if that be changed for one 
diametrically opposite, the directions of the resultants will 
also be changed into others directly opposite ; so that for 
every position of stable equilibrium , where the resultants are 
in the directions from the centre towards the extremities of 
the needle, there will be a corresponding position of instable 
equilibrium , where the directions of the resultants are from 
the extremities of the needle towards its centre. Calling 
zero, the point of stable equilibrium for the north end, when 
the needle is free from every other action but terrestrial 
magnetism, 180° will be the point of instable equilibrium . If 
