Action of a Galvanic Coil on an external small Magnet. 441 



73. I come now to the consideration of a circumstance which 

 bears in an especial manner on the relation of the hydrodynami- 

 cal theory to the theory of Ampere, and on the proof of the a 

 priori character of the former. It is made evident by the inves- 

 tigations of Ampere and of physicists who have adopted his 

 views, that the formula for the mutual action between two 

 galvanic elements, which he constructed with so much labour 

 and ingenuity, does not apply, without some additional hypo- 

 thesis, to the action of a galvanic element on a magnetic 

 element. (I understand a magnetic element to be the magne- 

 tism of an indefinitely small magnetized needle.) This is true 

 also of the formula, consisting of a single term, which I have 

 employed for the solution of the problems discussed in arts. 

 69-72. The hydrodynamical theory assigns as the reason for 

 this inapplicability of the formula, that a galvanic element 

 differs essentially from a magnetic element in respect of the 

 mode in which the circulation of the currents takes place in the 

 two cases, this condition being fulfilled in galvanism by means 

 of conductors forming a complete circuity whilst in magnetism, 

 as is explained in art. 12, the circulation results from the reaction 

 of the inertia of the fluid against the impulses of the magnet. 

 The theory has, in fact, shown that two elements of galvanic 

 currents are capable by their composition of producing forces 

 which vary inversely as the square of the distance between the 

 rheophore-elements to which they belong, and are proper for 

 causing motions of translation of these elements, but that a 

 stream pertaining to a galvanic element (as also one pertaining 

 to a magnetic element) can give to an elementary magnet, by 

 composition with its streams, only amotion of rotation, the force 

 producing this effect varying approximately as the inverse cube 

 of the distance between the elements. 



74. This theory therefore accounts for the introduction into 

 Ampere's theory of an additional hypothesis, having the effect of 

 changing the law of action of a galvanic element from the inverse 

 square to the inverse cube, when, in place of acting on an ele- 

 ment of a rheophore, it acts upon a small magnetic needle. The 

 case is analogous to that of the action of a large magnet on a 

 small one (considered in arts. 21-23), in which the law of the 

 inverse cube results from the empirical hypothesis of a mutual 

 action, attractive and repulsive, according to the law of the in- 

 verse square, between the two magnetisms named by the Astro- 

 nomer Royal red and blue. There is, however, this distinction 

 between the two cases — that whereas the hydrodynamical theory 

 does not indicate the existence of two magnetic forces varying 

 inversely as the square of the distance, but simply the action by 

 pressure, according to the law of the inverse cube, of a single 

 fluid (the sether), the same theory accounts for the mutual action, 



