OF ARTS AND SCIENCES. 



121 



of continuity will be observed in the changes of dip in the needle 

 while it moves over the bar. If the needle is placed so that its hori- 

 zontal axis is at right angles to the axis of the large magnet, then 

 there is a remarkable breach of continuity in the sequences of dip. 

 While moving from one end of the bar to the middle, the needle will 

 be vertical all the time. Suddenly, on passing the middle point, it 

 makes half a revolution, so as to bring the end which before pointed 

 to the zenith towards the nadir. Here, then, in the changes of dip in 

 a needle thus exposed, the law of continuity is not observed. If we 

 substitute for the large magnet the magnetism of the earth, we have 

 the same result. A dipping-needle, placed so that the axis on which it 

 turns is in the magnetic meridian, keeps a vertical position while it is 

 carried from the earth's magnetic poles to the earth's magnetic equator. 

 As it crosses the magnetic equator, its two poles suddenly exchange 

 positions with each other. 



" There is one view to be taken of these facts which does not require 

 us to believe that the law of continuity is disturbed. In both cases, the 

 needle is constrained by its axis ; for this axis is put in such a position 

 that the whole force of nature is decomposed into two others, one of 

 which is destroyed by the axis. If we take the action of the free 

 force, the law of continuity prevails both in regard to the direction and 

 the amount of the force. Still, this example will show that in the 

 motions of a machine, or in any case where the forces of nature are 

 artificially modified, it is not always safe to assume, in unqualified terms, 

 the applicability of the law of continuity. 



" A case can be supposed in which the force of gravity will be found 

 in the same predicament. We cannot make the experiment, but it is 

 not diflicult to imagine what the result would be if the experiment were 

 tried. I suppose a small tunnel to be cut from any point on the 

 earth's surface to the centre, and so on to the opposite hemisphere. A 

 plumb-line, if brought to the extremity of this opening, would point to 

 the earth's centre ; and, if let down into the opening, would still do so, 

 though with diminished force. If it continued to move along the tunnel, 

 at the instant of passing the earth's centre of gravity its direction 

 would suddenly change 180 degrees. In this case, the law of continuity 

 is observed so far as the intensity of the earth's gravity is concerned, 

 but it is broken in regard to the direction of the force. This must 

 necessarily be the case under the influence of central forces, unless 

 there is combined with them anollier force, like the projectile force, 



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