Royal Society, 495 



80 desirable to confirm his deductions relative to the action of iron 

 shells and balls on the compass needle, which he found to be as the 

 f power of the surface, whatever the weight and thickness of the 

 iron. 



The author now proceeds to notice the investigations of Hawks- 

 bee, Brook Taylor, Muschenbroek and others, and thinks the inqui- 

 ries of these philosophers have not been sufficiently considered or 

 appreciated ; that instead of the results exhibiting anomalies and 

 discrepancies, they are really necessary consequences of the more 

 elementary laws of induction, and perfectly explicable upon the fun- 

 damental principles of magnetism. He endeavours to show, that by 

 the changes in the law of the induction, as already stated, laws of 

 force will arise perfectly coincident with the results arrived at by 

 Hawksbee, Brook Taylor and others ; that is to say, the law of force 

 may appear to be as the f power of the distance inversely, as found 

 by Brook Taylor; or as the f power inversely, as found by Martin ; 

 or in the inverse duplicate ratio of the distance, as observed by 

 Lambert ; or as the simple distance inversely, as determined by Mus- 

 chenbroek in several cases; or it may be as the cubes of the di- 

 stances inversely, as stated by Newton. Examples are given in 

 which these several laws were found to obtain. 



In examining the laws of magnetic repulsion, similar results are 

 arrived at. The inductive forces here, however, are subversive of 

 the existing polar arrangements ; hence the apparent repulsion : so 

 long as the existing magnetic polarities remain unchanged, the law 

 of force will be generally as the second power of the distance in- 

 versely ; when the distances are small, it will be inversely as the 

 simple distance ; when the inductive actions subvert the existing 

 polarities, then the law of force appears irregular and subject to no 

 regular variation, as observed in all the early experiments wiih re- 

 pellent poles. 



The author is led to conclude, that the apparent law of attractive 

 force will be found to depend in certain cases on the distances at 

 which the force operates, as referred to the total distance or limit of 

 action. Taken between f ths and fths of the limit of action, the 

 force may be inversely as the third powers or cubes of the distances ; 

 taken between f ths and f ths of the limit of action, it may be in the 

 inverse sesquiduplicate ratio, or f power of the distances ; between 

 -i-rd and fths as the squares of the distances inversely. From the 

 ith to -i- of the limit of action it may be as the f power of the 

 distance inversely ; within less than itli, it will be generally as the 

 simple distance inversely. 



On a further review of these laws of magnetism, it is evident that 

 the immediate effect of an increase or decrease of distance, is an in- 

 crease or decrease of the effective magnetism on which the total or 

 reciprocal force depends. Thus taking the cases just quoted, it will 

 be seen that the total force is always as the square of the induction, 

 whatever be the resulting law of the attraction. Hence the force 

 may as well be taken as the square of the quantity of effective 

 magnetism directly, as some power of the distance inversely. 



2L2 



