LINES OF TERRESTRIAL MAGNETIC FORCE — MOVING RECTANGLES. 145 
best. The difference in the extreme case is less than might have been expected, and 
shows that there is no practical objection in this respect to the method proposed of 
experimenting with the lines of magnetic force. 
3197 . In order to obtain for the present an expression of the power of the earth’s 
magnetic force by this rectangle, observations were made on both sides of zero, as 
already reeomrnended (3182.). Nine moderately quick direct revolutions (i. e. as the 
hands of the clock) gave as the average of many experiments 23°-87, and nine reverse 
revolutions gave 23°'37 ; the mean of these is 23°*62 for the nine revolutions of the 
rectangle, and therefore 2°’624 per revolution. Now the six quick revolutions (3196.) 
gave 15°‘66, which is 2°‘61 per revolution, and the twelve quick revolutions gave 
31°'33, which is also 2°‘61 per revolution; and these results of 2°'624, 2°'61, and 
2°'61, are very much in accordance, and give great confidence in this method of 
investigating magnetic forces*. 
3198. A rectangle was prepared of the same length (4 feet) of the same wire, but 
the sides were respeetively 8 and 16 inches (fig. 6), so that g Fio- 7 
when revolving the intersecting parts should be only 8 inches in 
length instead of 12. The area of the rectangle was necessarily 
128 square inches instead of 144. This rectangle showed the 
same differenee of quick and slow rotations as before (3196.). 
When nine direct revolutions were made, the result was 20°'87 swing. Nine reverse 
revolutions gave an average of 20°'25 swing ; the mean is 20°’56, or 2°‘284 per revolu- 
tion. A third rectangle was prepared of the same length and kind of wire, the sides 
of which were respectively 8 and 16 inches long (fig. 7), hut now so revolved that 
the intersecting parts were 1 6 inches, or twice as long as before ; the area of the rect- 
angle remained the same, i.e. 128 inches. The like effect of slow and quick revolu- 
tions appeared as in the former cases (3196. 3198.). Nine direct revolutions gave as 
the average effect 20°’75 ; and nine reverse revolutions produced 21°*375 ; the mean is 
21°'06, or 2°'34 per revolution. 
3199. Now 2°‘34 is so near to 2°'284, that they may in the present state of the 
investigation be considered the same. The little difference that is evident, was, I 
suspect, occasioned by centrifugal power throwing out the middle of the longer in- 
tersecting parts during the revolution. The coincidence of the numbers shows, that 
the variation in the arrangement of the rectangle and in the length of the parts of 
the wires intersecting the lines of magnetic force, have had no influence in altering 
the result, which, being dependent alone on the number of lines of force intersected, 
is the same for both ; for the area of the rectangles is the same. This is still further 
shown by comparing the results with those obtained with the square. The area in 
L 
r 
* sin ^.^=3111 7-83 =sm 7 49-8=-1362343 
2 
sinl^=sm 11-81 = sin 11 48-6=-2047069 
sinl^=sinl5-665 = sinl5 40 =*2700403 
2 
MDCCCLII. U 
1^^^3 ^_.q227057 
6 
20470 .^ = -0227474 
9 
27Q04^=.q225034 
12 
