126 
*, C. Chree on the Law 
Table IX. gives the form taken by (28) for a number of 
combinations of distances. 
TABLE [X. 
| Vek ae Expression for P’. 
iy 4s 24 P +-4822Q x 1075 4 1790R x 107 
| 22-5 30 P+3086Q x 107° Eo 
225 40 P +2600Q x 1078 5d538R x 107 
25 35 P+2416Q x 107° 453R x 1078 
25 | 45 P+2094Q x 10-6 359R x 10-8 | 
26°25 35 P+2268Q x 10-8 396R x 10-8 | 
26°25 45 P+1945Q x 10-6 307R x 10-8 
30 40 P+1736Q x 10-6 232R x 10-8 | 
| 35 | 45 P+1310Q x 10-6 131R x 10-8 | 
3 
g 13. When Q ined R have w wali been diiced negligible, 
the consequent effect on H may be found as follows :— 
Assuming coefficients of higher terms negligible, we have 
H?=A(1+ Pr + Qr-* + Rr-), (29) 
where 7 is a distance of deflexion, and A is independent of 
P, Q, or R. Supposing 6H an increment to H, answering to 
increments dP, 6Q, and 6R, then 
28H/H=(7-786P + 7-46Q + 7-°6R)/(1 + Pr-? + Qr-44+ Rr-®), 
Unless 7 is unduly small, or the constants exceptionally 
large, we may replace the denominator on the right-hand 
side of the equation by unity. If, then, H has been originally 
determined from observations at 7; and 7, We have 
28H/H=7,-78P + 7,-46Q + 7-95 R = 77.~78P + 79-48Q + 727 SR, 
whence, eliminating 6P, 
26H/H = dQ7; eter? — ORr,—272-?(7, —? a 1?) Fy (30) 
If we now suppose H to be the value found when Q and R 
were neglected, H+6H to be the correct value when Q and 
Rare assigned their true values, then we have to substitute 
Q for 6Q and R for 6R in (80), and so find 
SO a ae ee 
2rere  2rere = + .- 9 as 
Here 6H is the correction which is necessary to the value 
of H obtained in the usual way by neglecting Q and R. It 
is assumed that the correction is but a small fraction of H. 
The result (31) may also be obtained by consideration of 
the quantities P and P’. 
sH/H =— 
