of Action between Magnets. 123 
(i.) Observation at single distance 7,, P and Q negligible, 
6B/H == ent udu, 3.0). (24) 
(ii.) Observations at two distances 7, 72, Q negligible, 
§H/H=3{r/ cot u, 8%, —7,” cot u2duz}/(7227—7;7) ; - (25) 
{iii.) Observations at three distances 7, 73, 73, neither P nor Q 
negligible, 
1 oe Bit chia 
6H/H = oA {rf (re—r37) cot u, du +794 (r3?—717) Cot uy Suz 
2 9 
+ 73'(7y7—7r2") cot uz du3} 3. . . (26) 
where A is given by (19), and the suffixes distinguish the 
three distances. 
These formule are deducible from the formule for the 
effects on H of errors in the distances (e.g. (16)) by writing 
cot uw, du, for 36r,/r; Ke. Thus the way in which error in 
an angle modifies the value of H according as observations 
are made at one, or at two, or at three distances, is exactly the 
same as in the corresponding case of error in a distance, and 
Tables I. and II. apply equally to the case of errors in angles. 
A complication arises, however, when we come to consider 
the absolute size of the error in H. This depends partly on 
the size of the angle, i.e. on the strength of the deflecting 
magnet. The stronger this magnet, the larger the deflexion- 
angle, and the smaller the effect of a given error in reading 
or graduation. Tables VI., VII., and VIII. give some 
numerical results for two different values of H, and two dif- 
ferent strengths of collimator magnet. The error in the 
angle is supposed to be 1’, the consequent error in H is given 
in terms of ly as unit. The sign + or — "ls attached 
according as the corrections to be applied to the angle and 
to H agree or differ in sign. It should be noticed that the 
value of a deflexion-angle is usually based on four readings, 
so that it would require an error of 4’ in a single reading to 
produce an error of 1’ in the angle. 
TaBLE VI. 
Error of 1' in deflexion-angle. Effect on H (unit 1y). 
Observation at a single distance, P and Q negligible. 
H m Distances 22-5 25 26°25); 30 | 35 40 | 45 cms. | 
C.G.S. C.G.S. Sign ...... — “= ae | - = = ae dy 
- jac Baie! 28 | 36 | 62/103 | 157 | 225 
pnt PEL eS 27 44 | 54 | 85/140 211 | 301 
379 {1000 100 146 172 | 263 | 423 634 | 906 
TD) he de 141 201 234 | 354 | 56-7 848 | 1208 
