11 6 
Mr. Christie on the mutual action of 
or, if <p be the angular distance of d s from the point vertically 
over the pole of the magnet, by 
4 m i r d <f> 
P 3 
The force on d s, or r dq>, in the direction of a tangent to the 
ring, that which urges it in the direction of the rotation of the 
magnet, will therefore be represented by 
4 m i r 9 sin. tp dp 
P 4 
The intensity i, is, as I have before mentioned, greater than 
that due to the distance p : let us then suppose that it is the 
intensity corresponding to a position of the magnet at a very 
small distance a behind its position at the instant at which we 
are estimating the force of the magnet on ds. Considering u 
as a right line, the distance between this point and ds will be 
{ ^ ,2 + ( r s ^ n - <?>— «) 2 +^(i — c ° s - <?> y } 
or { c ,2 -f 2r l (i — cos. <p) — 2 reo sin. (p } K 
where c' represents the vertical distance between the pole of 
the magnet and the middle horizontal section of the ring, or 
c + p in the first set of experiments. We shall therefore 
have, being a constant multiplier, 
i — ^ 
c' 4 2r J (i - cos. <p) — 2 r u sin. 
or, since u is extremely small, 
fj., , 2 fjL,r u sin. <p 
l = — j - -J- *7 5 } a , 
c' + 2 r 9 (i — cos. (p) -j c' + 2 r 9 (i — cos. <p) > 
very nearly. 
If then, according to what I have before stated, r\ p repre- 
sents that portion of the ring, behind the magnet, whose 
action is destroyed by the action of the part in advance , the 
