395 
induced in iron bodies by rotation. 
If (sl be the angle which, in consequence of these forces, the 
magnetic particle makes with the axis or line of the dip, 
that is, its angle of deviation towards the west, we shall have 
Tan. Q? = \ ( 1 ) 
Let now x be the latitude of the plate's centre ; R the radius 
of the circle in which the centre of the plate is made to move, 
that is, its distance from the centre of the needle ; p, half the 
distance between the poles in the iron plate : then 
a =Rcos. X, b =Rsin. X; 
a^j. = R cos. X + p sin. ip, = R sin. x + p cos. \I/ ; 
Oy =R cos. X — p sin. i[/, by = R sin. x — pcos. 
S 7-® = R* — 2 R r sin. x, N 7* = R® + + 2 R r sin. x ; 
Si/* = R* + r®-|-p* — 2 Rp sin. (vj/ -f- — 2r (Rsin. x — p cos.\|/); 
Nv* =z=R® + — 2 Rp sin. (\j/ 4- x) + 2r(Rsin.x — pcos.\|/); 
S(T* =R* + r*+p*+2 Rp sin. (\(/ + x) — 2 r(R sin.x + p cos. ■v!/); 
N (T* =: R* 4 ” r* 4 " p* 4 " 2 Rp sin. 4 “ 4 ” ^ ^ sin. x 4 " P cos. \f/). 
Substituting these values in the expressions for X and Z, ex- 
panding the several fractions, and neglecting the terms in 
the series after the third, on account of r and p being small 
compared with R, the equation ( 1 ) will become. 
2 / p C ) 
3 sin. X cos. X + -t— { 3 <in. (-4/ + X) . cos. x — sin. \ 
Tan. <p'= ^ L (2 ) 
I 3 sin. ('V + x) . sin. x — cos. | 
mR^ iff 
— 4- 3 sin.* X — I + TT — 
F r ^ ' F r 
If we call the angle of deviation of the magnetic particle 
when the plate revolves in the opposite direction, that is, its 
upper edge from west to east, we shall have 
Tan. (p = 
2 / p f . .7 
3 sin. X cos. X — -p— • j 3 sin. (4 — . cos. x — sin. 4 
2.ff { . 
-p-jT I 3 sm. (4 _x) . sin. x -f cos. 4 
3 F 
m R 3 
-JV + 3 sin.* X — I 
(s) 
MDCCCXXV. 
