Astronomical and Nautical Collections. 327 
obstacle may be, it is found in the superficial particles as well as in 
the interior, so that there is no need of any external pressure, like 
that of the air, to prevent the further removal of the fluid; and 
this circumstance constitutes a material difference between the 
state of induced magnetism and that of the induced electricity of a 
conducting substance, 
If the coercive force of the magnetized body required also to be 
taken into consideration, it would then be sufficient for the magnetic 
equilibrium that the result of all the exterior and interior forces 
acting upon any point of the body should no where exceed the 
given magnitude of the coercive force, the effect of which would be 
similar to the friction of a machine. In this case the equilibrium 
might take place in an infinity of different manners ; but among all 
these possible states, there is one which is particularly remarkable, 
and in which bodies are said to be saturated with magnetism: a 
ease which may hereafter be made the subject of a separate me- 
moir; the present essay being intended to comprehend only the 
laws of bodies magnetized by induction only, and without any 
coercive force. 
The equations of magnetic equilibrium, formed in the way that 
has been described, are at first somewhat complicated; but by 
means of certain transformations, the triple’ integrals which they 
contain are reduced to double integrals, and the equations become 
much more simple, We then deduce this general consequence 
from them, that notwithstanding the boreal and austral fluids are 
distributed throughout the mass of a body magnetized by induction, 
the attractions and repulsions which it exercises externally are the 
same as if it were merely covered by a very thin stratum formed 
of the two fluids in equal quantities, and such that their total ac+ 
tion upon all the points within them should be equal to nothing, 
If the body contains an empty space within it, and if there are 
centres of magnetic force within this space and without the body, 
it must be considered as terminated by two thin strata, correspond- 
ing to the exterior and interior surface, and the action of these two 
Strata on any point of the substance, joined to that of all the given 
