618 LAMONT: MAGNETIC RESULTS 
From the values of yp! and g' we obtain 
p= + 0:0679 
g = — 0°8286 ; 
and hence if the distance is equal to four times the length of the 
magnet, 
gee’ 
OES 11400" 
The error becomes much greater still if the deflecting bar is 
placed south and north. 
Thus we see that the third member must not be neglected in 
the development. 
In regard to the series of deflections given by M. Gauss, the 
errors of observation are too considerable (most of them exceed 
siz of the whole amount) for it to have been possible to prove 
anything thereby; they merely show that the deviations from 
the assumed law are not greater than the probable errors of ob- 
servation *, 
2. The law which Mr. Lloyd has assumed, after Biot, for the 
distribution of magnetism in the bar appears by no means ex- 
perimentally confirmed. M. Muncke has related, in Gehler’s 
Physical Dictionary (Art. Magnetism), a number of experiments, 
which all show that the magnetism increases from the middle but 
very slowly, and rapidly towards the extremities; no single ex- 
periment indicates a uniform increase towards both ends. The 
latter hypothesis gives the magnetic centre too far from the ends, 
whereby the calculated values of p and g are too small. In the 
above-mentioned series of experiments 
p was found = + 0°0679 
g was found = — 08286. 
* In the expressions given by M. Gauss, 
tan v = 0-086870 R~* — 0:002185 R~* 
tan v' = 0043435 R—* + 0-002449 R~, 
the coefficients of R~° are already imperfect, as the members multiplied by 
sin 2v and sin *v' are neglected, namely, 
30 ae = sin 2v, and — = = ¥ sin vw. 
Under the here very nearly correct assumption that M = M! and M; = Msg’, 
we shall have to add 
To the first expression + 0°052775 sin 2v R7° 
To the second expression — 0°012245 sin 2x) R7 5, 
The corrections of the greatest values of v and v’ given by M. Gauss would 
amount according to this to + 2'"7 and — 1'"'8, 
