LINES OF MAGNETIC FORCE — GALVANOMETER INDICATIONS. 
141 
that, whilst observing the place attained at the end of a swing which is retained only 
for an instant, some degree of error must creep in ; and that that error must be 
greatest, in the first number, where it falls altogether upon the unit of comparison 
than in the other observations, where only one-half or one-third of it is added to a 
half or a third of the whole result. Thus, if we halve the arc for two introductions 
of the pole, it gives 15°'625 ; if we take the third of that for three introductions, it 
gives 15°'6l ; — numbers which are almost identical, so that if the first number was 
increased by only 0°'6, the proportion would be as 1, 2 and 3, The reason why the 
fourth, which is 14°'625, is less, may perhaps be referred to the cause already assigned, 
namely, the declination distance of the needle from the coil when that impulse was 
given (3186.). 
3188. In order to avoid in some degree this case, and to compare the degrees at 
the beginning of the scale, which are most important for the comparison of future 
experiments with one another, I took one of the bars of the compound magnet em- 
ployed above (3184.). The results were as follows : — 
o 
One introduction 8 
Two introductions 15'75 
Three introductions 23'87 
Four introductions 31-66 
which numbers are very closely as 1, 2, 3 and 4. If we divide as before, we have 8°, 
7°'87, 7°'95, 7°‘91 ; so that if only O'OO be subtracted from the first observation, or 8°, 
it leaves that simple result*. 
3189. Hence it appears, that in this mode of applying and measuring the magnetic 
powers, the number of degrees of swing deflection are for small arcs nearly propor- 
tional to the magnetic force which has been brought into action on the moving wireT. 
sin -= sin 4 = ’0697565 
2 
sin sin 7’875 = sin 7 5V5 = ’1370123 
2 
sin =sinll’935 = sinll56’l=-2068019 
sin sin 15’83 = sin 15 49’8=-2727840 
■0697565 
1370123 
2 
2068019 
= •0685061 
= •0689340 
2727840 
= •0681960 
t Mr. Christie has recalled my attention to a paper in the Philosophical Transactions, 1833, p. 95, in which 
he has investigated, atp. lll,6cc., the effect of what may be called magneto-electric impulses in deflecting the 
magnetic needle. He found that the velocity of the projection of the needle, which is a measure of the force 
acting upon it at the instant of its moving, will be proportional to the sine of half the arc of swing. My state- 
ment, therefore, would as a general expression be erroneous ; but for small arcs the results as given by it are 
not far from the truth. The error does not interfere with the general reasoning and conclusions of the paper ; 
and as the numbers are the results of experiment, which, though made with a first and therefore rough appa- 
ratus, were still made with some care, and are expressed simply as deflections, I prefer their appearance as they 
are rather than in an altered state. Mr. Christie has been so kind as to give me the true expression of force 
for many of the cases, and I have inserted the results as foot-notes where the cases occur. — Jan. 26, 1852. 
