xvi.] THE METHOD OF MEANS. 365 



Newton showed that uniform spheres of matter have this 

 property, and this truth proved of the greatest importance 

 in simplifying his calculations. But it is after all a purely 

 hypothetical truth, because we can nowhere meet with, nor 

 can we construct, a perfectly spherical and homogeneous 

 body. The slightest irregularity or protrusion from the 

 surface will destroy the rigorous correctness of the assump- 

 tion. The spheroid, on the other hand, has no invariable 

 centre at which its mass may always be regarded as con- 

 centrated. The point from which its resultant attraction 

 acts will move about according to the distance and posi- 

 tion of the other attracting body, and it will only coincide 

 with the centre as regards an infinitely distant body whose 

 attractive forces may be considered as acting in parallel 

 lines. 



Physicists speak familiarly of the poles of a magnet, and 

 the term may be used with convenience. But, if we attach 

 any definite meaning to the word, the poles are not the 

 ends of the magnet, nor any fixed points within, but the 

 variable points from which the resultants of all the forces 

 exerted by the particles in the bar upon exterior magnetic 

 particles may be considered as acting. The poles are, in 

 short, Centres of Magnetic Forces ; but as those forces are 

 never really parallel, these centres will vary in position 

 according to the relative place of the object attracted. 

 Only when we regard the magnet as attracting a very 

 distant, or, strictly speaking, infinitely distant particle, do 

 its centres become fixed points, situated in short magnets 

 approximately at one-sixth of the whole length from each 

 end of the bar. We have in the above instances of centres 

 or poles of force sufficient examples of the mode in which 

 the Fictitious Mean or Average is employed in physical 



The Precise Mean Result, 



We now turn to that mode of employing the mean 

 result which is analogous to the method of reversal, but 

 which is brought into practice in a most extensive manner 

 throughout many branches of physical science. We find 

 the simplest possible case in the determination of the lati- 

 tude of a place by observations of tbft Pole-star. Tycho 



