169 



computation unless we know the law of the force exerted on each 

 other by two elements of free magnetism, or, in other words, with 

 which, according as they are of the same or different denominations, 

 they repel or attract each other. Tobias Mayer had already conjec- 

 tured this law to be the same with that of general gravitation, i. e. that 

 the force is in the inverse ratio of the square of the distance. Coulomb 

 and Hansteen have endeavoured experimentally to confirm this conjec- 

 ture ; and the fact is now completely established by the experiments 

 detailed in Professor Gauss's forthcoming memoir. This law, however, 

 only relates to the elementary effect ; for the computation of the total 

 effect of a magnetic body on another, as soon as the nature of the 

 distribution of free magnetism in these bodies is accurately known, 

 becomes a problem purely mathematical, and consequently remains 

 dependent on their casual individual nature ; but the greater the 

 distance, the less the influence of this individuality becomes ; and if 

 the distance be very great, we may, ceteris paribus, assume (as indeed 

 follows from the above principle,) the total effect to be inversely pro- 

 portional to the cube of the distance. The product of this cube into 

 the fraction which expresses the ratio of the effect of the first needle, 

 and of the terrestrial magnetism on the second needle, will therefore, 

 as the distances continually increase, tend to a determined limit. A 

 proper combination of observations at several judiciously selected 

 distances will, being mathematically treated, make us acquainted with 

 that limit, from which may be deduced the ratio of those two quan- 

 tities the product of which was derived from the observed times of 

 vibration. The combination of both results will then obviously give 

 those two quantities themselves. 



The experiments for comparing the effects of the magnetism of the 

 earth, and of the first needle on the second, suspended by a thread, 

 may be conducted in two different ways ; inasmuch as the latter may 

 be observed either in a state of motion or of rest. The former is best 

 effected by placing the first needle in the magnetic meridian of the 

 second, whereby the time of a vibration of the latter is either increased 

 or diminished, according as poles of the same or of different names 

 are opposed to each other. The comparison of the time of vibration 

 thus changed, with that occasioned by terrestrial magnetism alone, 

 or rather, the comparison of an increased with a diminished one (under 

 opposite directions of the first needle), will then readily lead to the 

 ratio sought. The second mode is that of placing the first needle in such 

 a manner that the direction of its influence on the second makes an 

 angle with the magnetic terrestrial meridian ; when the angle of de- 

 viation from the meridian, in a state of equilibrium, will equally lead to 

 the knowledge of the ratio sought. And here, too, it is more advan- 

 tageous to compare with each other two opposite deviations, under op- 

 posite positions of the first needle. The most advantageous position 

 of this needle is along a straight line drawn through the middle of the 

 second and perpendicular to the magnetic meridian. The first mode 

 agrees upon the whole with that proposed some years ago by Poisson ; 

 but the experiments, as far as we. have any record of them, made by 

 some natural philosophers with a view to apply that mode, have either 



