330 Astronomical and Nautical Collections. 
must be sufficient to prevent the transmission of the maenetic 
action; so that a strong magnet being placed on one side of such 
a plate, and at a great distance from its extremities, a small piece 
ofiron placed on the opposite side would neither be attracted nor 
repelled ; and on this side they would not adhere to the plate of 
iron, while they might adhere strongly to the ide next the magnet, 
although the thickness of the plate, or the distance between these 
surfaces, might be very inconsiderable. [It is to be presumed that 
this corollary is demonstrated in the original memoir; for it is by 
no means self evident that the remoter portion of the supposed 
infinite sphere would be without all effect, notwithstanding its in- 
finite distance, especially as it has been before observed that the 
thickness of a stratum of electricity would be the same in every 
part of the spherical surface. ] 
The most simple case, to which the formulas of this memoir can 
be applied, is that of a hollow sphere, magnetized by the action of 
the earth, that is to say, by the action of a force of which the ori- 
gin is very remote, and which may be considered, for this reason, 
as constant in magnitude and in direction throughout the extent of 
a magnetized body of ordinary dimensions. In this case, the in- 
tegrations are capable of being expressed in a finite form: the 
equations of magnetic equilibrium are completely resolved, and we 
obtain from them all that is required to be known, either with re- 
gard to the direction of the lines of polarity, and to the intensity 
of the magnetism, in the solid part of the sphere; or with regard 
to the action which it exerts externally upon any point given in 
position. This memoir contains the expression of the three ortho- 
gonal component forces of this external action, whence it was easy 
to infer, by adding them to the terrestrial force, as resolved in a 
similar manner, the true directions of the horizontal needle, and of 
the dipping needle, as well as the duration of their oscillations ina 
given position, which will afford the simplest manner of comparing 
the theory withexperiment. Although the magnetism is not confined 
to the exterior surface of the hollow sphere, and although its intensity 
may be determined for any point of the solid shell, yet the magnitude 
of the three component forces produced by it is WHOLLY INDEPEN= 
