Aslronomical and Nautical Collections. 129 



spheres is made to turn round its point of suspension ; which it 

 would be easy to verify by experiment. 



The example here considered, shows that it is not always possible 

 to destroy in every direction the deviations of a magnetic needle, 

 by adding a new body to the whole of those which have pccasioned 

 that deviation. Although we cannot assign, for bodies of all pos- 

 sible forms, such conditions as have been laid down for spherical 

 bodies, we may at least determine, for all cases, the number of 

 these conditions. When a system of bodies, magnetized by the 

 action of the earth, and mutually influencing each other, affects the 

 needle of a compass, it is necessary, in order that the horizontal 

 direction of the needle may be constantly annihilated, that the sys- 

 tem should correspond with equations belonging to the form and 

 disposition of these bodies, which, in the most general extent of 

 the problem, will be five in number. If among these bodies there is 

 a sphere of given diameter, but indeterminate in its position, we 

 may dispose of the three co-ordinates of its centre in such a manner, 

 as to satisfy these five equations, and thus reduce them to two 

 equations of condition; and, besides, there will be other conditions 

 which must be fulfilled, in order that the values of the unknown 

 quantities may be real. If the moveable body, instead of being a 

 sphere, is, for example, a circular plate, of a given diameter and 

 thickness, we may dispose of the three co-ordinates of its centre, 

 and of the two angles which serve to determine its direction ; we 

 shall thus have as many indeterminate quantities as there are equa- 

 tions to be satisfied, and there will only remain the conditions 

 necessary for the reality of the values of these five unknown quan- 

 tities. The use which has been made of this method, on board of 

 ships, having greatly diminished the deviations of the compass, it 

 must be inferred that, in the ordinary disposition of the masses of. 

 iron which are present, the conditions relative to this system of 

 bodies are nearly fulfilled ; but tve can never be certain that other 

 cases will not arise, in which the addition of a single body, of de- 

 terminate form and dimensions, would 7iot be sufficient to destroy 

 the deviations of the needle, or even to reduce them to moderate 

 /i?m75, especially if the dip should change very considerably in the 

 course of the voyage. 



Vol. XIX. K 



