VOIy. 6, 1920 
ASTRONOMY: H. SHAPLEY 
129 
'- = '- + K (3) 
f f D 
of the focal length of the intensifier and its position in the cone of light, 
a given intensifier will reduce the focal lengths of all telescopes in the same 
ratio when placed at a fixed distance in front of the normal focal plane. The 
one now in use at Mount Wilson is suitable without structural alteration 
for work at both the primary and secondary foci of the 60-inch and 100- 
inch reflectors, and with the 10-inch photographic refractor of 45 inches 
focus. Conditions analogous to those above hold for amplifying lenses. 
An interesting corollary of equation (2) is that no advantage accrues 
from having an intensifier of large aperture, unless, for the sake of ac- 
commodating a larger field, the increase in size can be made without in- 
creasing its focal length. Difficulties would obviously arise if the focal 
length of the intensifier were so short or so long that the distance of this 
secondary lens from the normal focus interfered with the photographic 
operations. Cf. equation (4) below. 
The distances IP = D and p'P = D — /' are important in the actual 
manipulation of an intensifier. In the formula for conjugate foci, 
7 = -^-' 
J U V 
we may put u = f\ v = — D, so that 
and from (2) 
/ = RD, D —f = D{1 — R). (4) 
That is, for any desired reduction of the effective focal length, the distance 
of the modified focus from the ordinary focal plane of the telescope is 
1 — R times the distance of the intensifier from that plane. Equations 
(2) and (4) define the arrangement of a given intensifier and the photo- 
graphic plate. 
As an illustration, let us suppose that in working with the 100-inch 
Hooker telescope the reduction desired is = V 3> and that the focal length 
of the intensifier employed is / = 3 inches; then D = 6 inches, D — f = 
4 inches. The primary focus of the Hooker reflector is Fi = 42.3 feet. 
From (1) the equivalent focal length is 14.1 feet, and we have, in effect, 
a 100-inch reflector with a focal ratio of 1.7 instead of 5. If we assume 
that not more than 25% of the light is lost in the intensifier, the theoretical 
gain of the telescope (limiting faintness) is a little more than two magni- 
tudes. 
For R = V2 the same intensifier should give a gain over normal photo- 
graphic power of approximately 1.25 magnitudes, and leaves the scale 
very slightly inferior to that of the 60-inch reflector. 
The most efficient intensifier for use with telescopes built for usual 
photographic purposes will be one that is adaptable to a large range of 
values of R; it should probably have a focal length between two and five 
