128 Dr. C. Chree on the Law 
where a, 6 are the radii of the outer and inner surfaces of 
the deflecting magnet, while a’, b' are the corresponding radii 
for the deflected magnet. The value of P when the a, d, 
a’, b’ terms are neglected I shall denote by P(A, 2). 
Similarly, Q(A, /), R(A, A’) will represent those parts of 
the complete expressions for Q and R which remain when the 
areas of the cross sections are neglected. Complete ex- 
pressions for () and R would contain terms involving a, 0, 
a’, b', but the influence of Q and R on the value of the 
deflecting couple is ordinarily so small that it seems desir- 
able to avoid the complication which the retention of these 
small terms would entail. Omitting them, we have in terms 
of X and 2X’ 
Q(A, ’) = (3/8) (8A4*— 407A? + 150"), | GB 4) 
R(A, X’) = (1/4) (160° — 168A40? + 21 0a2A/4 — 35") |” 
Table X. gives the numerical value of the contribution to 
P from the terms in a, }, a’, b’, in some actual cases. The 
diameters 2a, &ec. are in cms. 
TABLE X. 
Qa. | 2b. | Qa’. | 2b". (8/4){3(a2+b")— 2(a?+8%)} 
ee _———— 
Jones's magnets :— | 
| | 
Magnetometer i. 1:00 | 735 “76 | “50 | —11 | 
a ii] “O75 h)-742 | i ae} —-09 
! 3 iii.) -955| ‘665 | -73 | °435 —"10 ) 
Cooke magnets ...... 1:02 | °76 ‘70 | 52 —'18 | 
Dover Ahad ee -f 1035 | °82 ‘20° “bib —'12 | 
Bittathe 0,000 1iia 0:98 | ‘77 | ‘15 | -40 —18 | 
The Jones’s magnets—a very old form—are more variable 
in diameter than recent patterns, but absolute uniformity can 
hardly be claimed for any pattern, and in most cases the 
tube-walls are not quite uniform in thickness. Most collimator 
magnets, in fact, have shallow screws cut on the inner 
surface at the ends, a circumstance introducing some slight 
additional uncertainty, both as to the values of } and as to 
the degree of accuracy of Bérgen’s formula. : 
According to the figures in Table X. the contribution to P 
from the terms in a, ), &. is negative in each case. It 
would be reduced numerically by a reduction in the wall 
thickness of the mirror magnets—keeping their external 
diameters unchanged or slightly increasing them—which 
would have the further recommendation of making these 
magnets more nearly than at present exact copies of the 
collimator magnets on a uniformly reduced scale. 
