D O C U M E N T 2 3 1 D E C E M B E R 1 9 2 0 3 3 3
Jeans contends, in particular, that describing it as an adiabatic gaseous sphere
doesn’t work at the edges of the cluster and that dm reflects the drop in den-
sity better.
Generally, the following applies for the conversion from the surface distribution
into the spatial one:
R = outer radius of the cluster
F(r) = surface density; f(r) = spatial density
F(r) =
If one sets
, ,
then one obtains the integral equation treated by Abel,
, for which Abel found the solution:
.
After partial integration and slight reformulation one finds
.
I hope this information suffices for you; otherwise please telephone me. Yours,
E. Freundlich
P. S. I almost forgot to give you the requested details concerning the American do-
nors. So, Mr.
Pagenstecher[3]
is father-in-law of Mr. von Estroff in Potsdam, where
I spoke to him during the summer. He is 82 years old and is very interested in all
new research. His daughter, Miss Pagenstecher, who also sent 100,000 marks, is
naturally more deeply interested than her elderly father. Do please write a letter to
Miss Pagenstecher that is directed at the father at the same time, and enclose a copy
of your booklet on relativity theory with a brief dedication. Please send the letter
and booklet to me over here; I will assemble everything for the mailing, along with
[my] letter.
Best regards, yours,
E. F.
a
1130
= N 1122 = a
1460
= N 2074 =
c r
3–
f h2 r2 + hd
R2 r2
––
+
R2 r2
–
2 f
d
2 r2 –
--------------------.
r
R
=
h
R2 r2
–=
x
R2 2
–=
F r h f
d
dx
------ - x = = =
h
x xd
h x –
-------------------
0
h
=
x
1
-- -
h hd
x h –
----------------- -
0
x
=
f
1
-- - r2 2 –
rd
d 1
r
-------- -
Fd
rd
rd
R
=