D O C . 5 2 G E O M E T R Y A N D E X P E R I E N C E 4 0 5

[29]In Einstein 1917b (Vol. 6, Doc. 43), sec. 4, the cosmological term was added to the field equa-

tions of general relativity to allow a spatially closed static model of the universe. This term can be

interpreted as a constant correction of the energy-momentum tensor. (See Einstein 1918d [Doc. 3] and

Felix Klein to Einstein, 16 June 1918 [Vol. 8, Doc. 566], note 13.) In the Newtonian approximation,

this correction leads to an additional constant negative density of gravitating mass.

[30]See Einstein 1921f (Doc. 56), note 2, for Einstein’s attempt to realize this idea.

[31]With “Können” begins the part that was added to the version in the Sitzungsberichte. The manu-

script for this part is not continuous with the first and is written on the verso of a technical proposal,

probably from 1918, since it extols the usefulness of an invention for the war effort and mentions

“recent measurements” performed in January 1918. This makes it plausible to assume that Einstein

reused an earlier manuscript for the second part, most probably a version of a lecture that he gave on

15 May 1919 at the Prussian Academy of Sciences about Einstein 1919a (Doc. 17), in which he also

spoke about the visualization of the relations in spherical space (see Doc. 17, note 1, for a summary

of the lecture). However, since Einstein 1919a itself does not treat the visualization of spherical space,

it is possible that the manuscript was originally part of a manuscript for a printed version of the lecture

of 15 May 1919 or of an earlier draft of Einstein 1919a. Einstein had discussed the visualization of

spherical space earlier in Einstein 1917a (Vol. 6, Doc. 42), pp. 72–76.

[32]In Einstein 1917a (Vol. 6, Doc. 42), p. 72, Einstein refers to Helmholtz (Helmholtz 1884) and

Poincaré (Poincaré 1902) as having presented these ideas with unsurpassable clarity.

[33]The spherical model of the universe was introduced in Einstein 1917b (Vol. 6, Doc. 43). See the

discussion on pp. 11–13 of the document.

[34]In the manuscript, “in den Gesetzen der relativen Lagerung der Kugeln” is deleted and replaced

by “beim Messen mit Massstäben.”

[35]Both Erwin Freundlich and Felix Klein had noted that not only the spherical, but also the elliptic

geometry is a possible solution of Einstein’s cosmological equations (see Einstein to Erwin Freun-

dlich, 18 February 1917 or later [Vol. 8, Doc. 300], and Einstein to Felix Klein, 26 March 1917 [Vol.

8, Doc. 319]).