VALUE OE THE BRITISH ASSOCIATION UNIT OF RESISTANCE. 
237 
scale vertically below the axis of the telescope, A the point of the scale which appears 
to coincide with the cross wire when the needle is at rest, and B the apparent 
extremity of the throw. 
Now the scale was carefully set so as to be at right angles to 0 M, and the distance 
0 A was always small compared with O B. 
Also 
v OA— 2 , AB=^>, AMB=2/3, OM=ct. 
£ 
a a 
Z T) 
Hence if we neglect squares of - and fourth powers of - and - 
angle AMO = - 
and 
Therefore 
Also 
hence 
and 
tan (2 / 8+-)= /,+ 
' a a 
s i n ^— JlJ i _ii _ Pi. 
Sm 2~4«l i QO " 
32 a~a? 
tan ( 2 0 “b ~ i — - 
a a 
tan 0=~ — — 
2 a 4a 2 a s 
tan 6 2q [ 11 qr — Sq 2 (p — q)z 
’. /3 ~p\ ^ 32 1 
sm ^ 1 L 
Now the values of p, q, z , and a were such that 
therefore write with sufficient accuracy 
(p-q> 
was about ‘0001, we may 
tan 6 
sm = 
1 Ipr — 8 < 7 2 \ 
3 3 ) 
p and q being the scale values of the throw and deflection. 
To observe these quantities accurately the following adjustments are necessary. 
The scale should be parallel to the mirror when at rest. 
The coils of the galvanometer should be north and south so that their plane may be 
parallel to the magnetic axis of the needle. 
The telescope should be placed so that its axis and the normal to the mirror, when 
at rest, may be in the same vertical plane. If this is the case the division of the scale 
which appears to coincide with the vertical cross- wire will be that just below the axis 
