77 
the particles of magnetic bodies, ^c. 
&, or ill which the torsion of the wire is 9 ; and v the velocity 
of a point in the disc at the distance i from the axis of rota¬ 
tion ; a, fi and v being in degrees to the radius i. We have 
therefore, v dv = 7n [u — d9, 
v~= m (2 ccd — 6 ^), 
and t = -4— . vers. — . 
^/m a. 
Let the values of t and 9 , when v becomes 0, or the disc 
begins to turn back, be t^ and 61, then we shall have 
2 « — 9 ,- = 0 , and a = i . 
also, 4 = . TT , and = tt . ^ . 
The mean value of t, from the experiments is 269'83 seconds, 
or very nearly 270 seconds ; so that -v/w = ^ • y • 
We have therefore — = vers (2°. y); whence 
e 
" =- r\ 
vers. (z° . — j ■ 
The corresponding values of 6 and t, contained in the pre¬ 
ceding table, being substituted in this formula, will give the 
folloi\Tng values of or of the relative forces with which 
the magnets urged the disc when revolving at different 
distances from the axis. 
Table II. 
Distance of the axes ^ 
of the magnets from 1 — 
the axis of rotation J 
Inches 
4-2 
Inches 
S-7 
Inches 
3-2 
Inches 
2-7 
Inches 
2-2 
Inches 
1-7 
ct 
a 
» 
a 
ct 
a 
p =« 
tC o . 
> < 
r 360 
720 
1080 
1440 
1800 
698-8 
688-0 
6762 
1229-1 
1213-6 
1221-8 
1203-5 
1196-0 
1168-8 
1642-3 
1531-6 
1538-3 
1528-9 
1518-9 
1512-0 
1498-2 
1494-4 
1493-5 
1589-2 
1500-0 
1491-0 
1457-0 - 
1423-6 
1440-0 
1409-4 
1132-1 
1122-0 
1112-3 
1104-7 
1098-7 
I 1 00-4 
641-0 
632-0 
620-9 
® 2-5 
o 
2160 
'H:2 fi 
2520 
^2880 
> »* 
— a 
— 2 
K = 
659-0 
1156-3 
1394-3 
I 106-0 
600-5 
Mean values of a . 
680-5 
1198-4 
1528-7 
1463-1 
1110-9 
623-6 
