326 Astronomical and Nautical Collections. 
the same magnetic element, they must be incomparably greater 
than the observed action of the element, and we can form no idea 
of their magnitude from that of the magnetic attractions or repul- 
sions which they occasion, since these effects are only derived from 
their difference. 
It is this distribution of the two magnetic fluids in magnetized 
bodies, such as it has been here described, that is to be the subject 
of the mathematical analysis contained in the sequel of this 
memoir, ; 
The first problem that was to be resolved was, to reduce to three 
rectangular directions the results ofall the attractions and repulsions 
of the magnetic elements of a magnetized body, of any imaginable 
form, upon a point either within or without its surface. By adding 
to these results, as belonging to any point within the body, those 
of the external magnetic forces which act on the body, we shal! 
have the whole forces which tend to separate the two fluids that are 
united at the point in question, And if the matter of the body op- 
poses no sensible resistance to the displacement of the fluids in 
each magnetic element, or, in other words, if there is no coercive 
force, it will be necessary, in order that there may be an equili- 
brium, that all the attractions and repulsions should destroy each 
other; since if any of them were uncompensated, they would pro- 
duce a new decomposition of the neutral fluid, which is never ex- 
hausted, and the magnetic state of the body would be changed. 
The sum of the results is therefore made equal to zero with respect 
to each of the three directions to which they are referred. The 
equations of equilibrium thus formed will always be possible; they 
will serve to determine, for each point of a magnetized body, the 
three unknown quantities which they comprehend; that is, the in- 
tensity of the action of a magnetic element on a given point, and 
the two angles which determine the corresponding direction of the 
line of polarity. At the extremities of each element these joint 
results will not vanish, they will produce pressures, from within 
each element, tending outwards, and counterbalanced by the 
obstacle of which the nature is unknown, but which opposes the 
passage of the fluid from one element to another. Whatever this 
