Mean displacements of lines towards the less refrangible end of the spectrum are certainly revealed by statistical investigations of the fixed stars ; but up to the present the examination of the available data does not allow of any definite decision being arrived at, as to whether or not these displacements are to be referred in reality to the effect of gravitation.  The results of observation have been collected together, and discussed in detail from the standpoint of the question which has been engaging our attention here, in a paper by E. Freundlich entitled “Zur Prüfung der allgemeinen Relativit¨aut;ts-Theorie” (Die Naturwissenschaften, 1919, No. 35, p. 520:  Julius Springer, Berlin).

At all events, a definite decision will be reached during the next few years.  If the displacement of spectral lines towards the red by the gravitational potential does not exist, then the general theory of relativity will be untenable.  On the other hand, if the cause of the displacement of spectral lines be definitely traced to the gravitational potential, then the study of this displacement will furnish us with important information as to the mass of the heavenly bodies. [5][A]

  Notes

*) Especially since the next planet Venus has an orbit that is almost an exact circle, which makes it more difficult to locate the perihelion with precision.

The displacentent of spectral lines towards the red end of the spectrum was definitely established by Adams in 1924, by observations on the dense companion of Sirius, for which the effect is about thirty times greater than for the Sun.  R.W.L. —­ translator

APPENDIX IV

The structure of space according to the general theory of relativity (supplementary to section 32)

Since the publication of the first edition of this little book, our knowledge about the structure of space in the large (” cosmological problem “) has had an important development, which ought to be mentioned even in a popular presentation of the subject.

My original considerations on the subject were based on two hypotheses: 

(1) There exists an average density of matter in the whole of space which is everywhere the same and different from zero.

(2) The magnitude (” radius “) of space is independent of time.

Both these hypotheses proved to be consistent, according to the general theory of relativity, but only after a hypothetical term was added to the field equations, a term which was not required by the theory as such nor did it seem natural from a theoretical point of view (” cosmological term of the field equations “).

Hypothesis (2) appeared unavoidable to me at the time, since I thought that one would get into bottomless speculations if one departed from it.