12*8 
ASTRONOMY: H. SHAPLEY 
Proc. N. a. S. 
H \- 
duce the effective focal length of the telescope, thus giving high speed and 
reducing the scale on the photograph. 
In studies where the important thing is scale, an intensifying lens does 
not help; further, if a large field is desired, the intensifiers now available 
are unsatisfactory. But for the problems mentioned above, where scale 
and field are of second importance to limiting magnitude, the intensifying 
device is efficiently and inexpensively adaptable. 
For example, by using such a device at the primary focus of the 100- 
M 
\ ^ 
inch, so as to reduce the scale to that of the 60-inch, the exposure time 
needed to give a required density in the photograph of a nebula should be 
less than one-half that otherwise necessary, even after allowing for a reason- 
able loss of light in the lens system of the intensifier. 
Several lenses have been experimented with successfully in combination 
with various telescopes during the last six months. I am indebted to 
Mr. BeniofF, who was associated with me in the early plans and experi- 
ments, for assistance in adapting the different intensifiers. 
Let 
Fi be the focal length of the objective (mirror) of linear aperature A, MP 
f be the focal length of the intensifier of linear aperture a, Ip 
f be the apparent focal length of the intensifier in the converging beam, Ip' 
F be the equivalent focal length of the combination, 
d be the distance between the objective and intensifier, MI 
D = Fi — J be the distance from the focus of the objective to the in- 
tensifier, IP 
R = F/Fi be the reduction of focal length and linear scale of the field. 
From the relation giving the focal length of a combination of lenses we 
derive, 
Fif FJ 
Fi+f-d f + D' 
(1) 
R = (2) 
f + D 
Equation (2) shows that for a given intensifier the reduction depends 
only on the distance of the intensifying element from the normal focal 
point, P, of the telescope. Since the reduction is independent of the aper- 
tures and the focal length of the objective (mirror), being a function only 
