290 Dr. Tyndall on the Laws of Magnetism. 



We here see that the experimental substantiation of the de- 

 duction is as complete as could be desired. 



32. One important omission, which has been the source of 

 considerable error, occurs in the first utterance of the law by 

 its discoverers*. It is essential to its validity that a ^ fixed 

 distance' shall separate the magnet from the attracted mass. 

 Were the distance 0, we should have the case embraced by our 

 first proposition, which, however, as we have seen, leads to a 

 totally different law. The error, as observed at the commence- 

 ment of this paper, lies in the assumption, that the law which 

 was true for a fixed distance is also true for contact. Lenz and 

 Jacobi obseiTC a certain caution in expressing themselves on this 

 subject, which would lead one to suppose that they also doubted 

 the applicability of the law to the case of contact. In the course 

 of their memoir the following significant remark occm's : — " For 

 the present, at least, we will grant the limitation, that the magnet 

 and submagnet are not in immediate contact, but stand about a 

 line apart." Physicists generally, however, appear to have 

 assimied that the law was meant to be of universal application. 

 M. Miiller, for example, in the memoir already alluded to, writes 

 as follows : — " Lenz and Jacobi assumed that the lifting power 

 of the magnet must be proportional to the square of the deve- 

 loped magnetism, which assumption is beyond all doubt correct." 

 Under the term 'lifting power' [Tragh-aft] is here meant the 

 attraction between the magnet and the submagnet when they 

 are in contact ; and for this particular case, as proved in § 2, 

 the assumption is untenable. M. Miillei-'s experiments on lift- 

 ing power were made with an electro-magnet of the horse-shoe 

 form. This is a point on which Lenz and Jacobi have expressed 

 themselves very explicitly, as the following extract from their 

 memoir testifies t- "^'All our precautions, however, served only 

 to prove, that when currents of equal power were applied, the 

 results were tolerably coincident. But to the expected result they 

 did not lead us ; and we could only arrive at the conclusion, 

 that, by strong magnetizing, the lifting power — we do not say 

 the law of attraction — of two electro-magnets, or of a horse-shoe 

 magnet and its submagnet, is a ])ha:;nomeiaon far too complicated 

 to be referred to any such simple law as the square of the strength 

 of the current, or the strength itself." This veiy difficulty of 

 ai'riving at anything like a safe result in the case of contact 

 seems to have suggested the expedient of placing a distance of 

 jijth of an inch between the submagnet and the magnet. 



33. If m be the strength of a magnetic ])ole referred to any unit, 



and m' the strength of a second pole referred to the same unit, 



the mutual action of the two poles at the unit of distance will 



be expressed by the product mm' , the said product being negative 



* Poggendorff' s Annalen, vol. xlvii. p. 403, t Ibid. p. 411. 



