328 Mr. W. Ellis on the Change of Rate produced in a Clock 



The last two columns of the preceding Table show, for the 

 maguets used, the mean effect of attraction and the mean effect 

 of repulsion. Confining our attention to these numbers, we 

 perceive how rapidly the change due to attraction accelerates as 

 the distance between the magnets is decreased, whilst that due 

 to repulsion advances only by small increments. This is, how- 

 ever, a natural result of the known action of magnets ; for when 

 the poles of two magnets are brought near together, each one 

 tends to develope or induce in the other an opposite magnetism, 

 which may combine with or act against the magnetism already 

 existing therein. So that when the poles are unlike, the total 

 force in action is the sum of two effects — one depending on the 

 permanent magnetisms, which is attractive^ the other on the 

 induced magnetisms, which is also attractive ; the total force is 

 consequently attractive and strong. But when the poles are 

 similar, the total force in action is the difference of two effects — 

 one (probably always the larger when the magnets are equal in 

 size and similar in constitution) depending on the permanent 

 magnetisms, which is repulsive, the other on the induced mag- 

 netisms, which is, as before, attractive; and under such condi- 

 tions the total force is repulsive but weak. Had, however, one 

 of the magnets been much larger than the other, it might have 

 happened, when similar poles were brought near together, that 

 the repulsive part of the force (depending on the permanent 

 magnetisms) might have been less than the attractive part 

 (depending on the induced magnetisms), giving not a total 

 repulsive force at all, but an attractive force which might be 

 weak or strong according to the relative difference in size and 

 constitution of the two magnets. 



If, in the two cases considered above, the effect of induction 

 in the one case, when the poles were unlike, may be considered 

 equal to its effect in the other case, when the poles were similar, 

 the half sum of the numbers contained in the last two columns 

 of the preceding Table (taken without regard to sign) will give 

 the change of rate due to the permanent magnetism ; and the 

 half difference (similarly without regard to sign) will give the 

 change due to the induced magnetism. Numbers formed in 

 this manner for all the different values of distance are given in 

 the following Table, P denoting the change due to permanent 

 magnetism (attractive, and increasing the gaining rate, for unlike 

 poles; repulsive, and decreasing the rate, for similar poles), I 

 denoting the change due to induced magnetism (always attrac- 

 tive and increasing the rate) : — 



