VALUE OF THE BRITISH ASSOCIATION UNIT OF RESISTANCE. 
239 
Let A 0 B (fig. 5) be the scale, 0 M the normal to the mirror, draw A' 0 B' at 
right angles to 0 M. 
Then AO A'=y; let A and B be the observed extremities of the throw or 
deflection; 6 its value in angular measure; let M A, M B, cut A' B in A' and B', and 
let p be the true scale value of the deflection, then 
A / 0 = 0B'=_p 
AOM=MOB=2<9 
0 L) perpendicular to M A, M B respectively. 
00 = 0 A' cos COA'=OA cos CO A 
p cos 2 6—p x cos (2d+y) 
p cos 2 ^=j> 2 (cos 26—y) 
2 P=(Pi+lh) cos y—(Pi—Pz ) tan sin 7 
Now p 1 was always very nearly equal to p. 2 , and 2 9 and y are both small. 
Hence very approximately indeed we have 
Similarly 
Thus, by observing deflections right and left and taking the mean, we get a value 
for the ratio of which is independent of an error in the azimuth of the scale, much 
greater than anything possible in the actual experiments. 
If the magnet be not parallel to the mirror the angle turned through by the mirror 
is still that turned through by the magnet; the fact that the magnet and mirror were 
very nearly parallel afforded a ready means of setting the plane of the coils in the 
magnetic meridian. 
Ih +lh 
P~ o 
cos y 
'h + c h 
2- 2 
cos y 
Draw 0 C, 
Then 
Thus 
Similarly 
Therefore 
