of Action between Magnets. 119 
When we observe at a single distance, as (21) shows, an 
error of 1 part in 10,000 in r entails an error of 1°5 parts in 
10,000 in H, whatever » may be. 
This relation is so simple that it is often convenient to 
make it the point of departure when considering the effect 
of errors in the distance when P, or P and Q, are retained, 
applying multipliers answering to the ratios considered above. 
The following results for specified cases will serve for 
illustration. 
TABLE I. 
Distances one, two, three of the following: 22°5, 30,40 cms. 
Observations at 
For 
given : ‘ ; 5 < 
error | Single distance. | Two distances. Three distances. 
SS SS SSS ee 
22'5 30 | 40 22°5 & 30 | 29:5 & 40 | 30 & 40 | 22°5, 30 & 40 cms. | 
ees Os ee pee Se Lye | 
225...) 1 |...|..| —129 | —0-46 fe +0-60 
SA Lng for 229. | ae —1:29 —2-94 
ipo | 1 ly | ETE. | 42-29 43:34 
| 
The Table is to be interpreted as follows :— 
If a certain error in the value accepted for the distance 
22°5 cms. produces an error of e* x 1 in the value of H when 
P and Q are negligible, and observations are made at 22°5 cms. 
only, then if observations are taken at two distances, and 
combined in the usual way, the error is —1°29e or —O0°46e, 
according as the distances are 22°5 and 30, or 22°5 and 
40 ems., while if P and Q are eliminated from observations 
at 22°5, 30, and 40 cms. the error is +0°60e. As a concrete 
instance, suppose a correction of +003 cm. necessary to the 
value assigned the 30 cms. distance, the local value of H 
being -186 c.c.s. Then the value deduced for H by employ- 
ing the erroneous value for the 30 cms. requires to be 
diminished by 
(3/2) x (0:003/30) x °186 =2°79y (where ly=1 x 10-* ¢.G.s.), 
when observations at 30 cms. suffice, P and Q being negligible. 
When, however, & only is negligible, the value requires to be 
diminished by 2°29 x 2°79, or 6:4, when observations are 
made at 22°5 and 30 cms., 
increased by 1°29 x 2°79, or 3°6y, when observations are 
made at 30 and 40 cms. 
* When we observe at a single distance the errors in the values accepted 
for the distance and calculated for H are really opposite in sign. 
