1 6 8 D O C . 1 9 7 D E C E M B E R 1 9 1 9 you know, it is impossible to live today off the amount that I am receiving at the present time,[2] and I am steadily getting in worse straits, despite all my wife’s in- dustry in trying to cope with the deficit. I believe you can arrange that this bonus not encumber your institute’s science fund. Please have the bonuses dated retroac- tively to July 1st of this year. If the appointment in Potsdam is settled soon, your institute will obviously be relieved of this burden.[3] In the last few days I carried the calculations on globular star clusters further and have already written it down on paper for myself.[4] I hope that everything is cor- rect. Accordingly I assume that in star clusters, where a spherically symmetric field and an ellipsoidal one are superimposed, the surfaces of equal density are equipo- tential surfaces and calculate the “flattening” that the equipotential surfaces of globular red-giants must experience as a consequence of the flattened stars, namely, as a function of the ellipticity and the mass ratio of both systems. It turns out that, for the Hercules star cluster,[5] which is by far the best known, equidistant regions from the center would have to exhibit about 7% higher numbers of stars in the direction of the rotational axis than in the perpendicular direction for is = 26% (ρ = density) and the distance of the equipotential surfaces from the center is about 0.25 smaller in the direction of the ellipsoid’s rotational axis than perpendicular to it indeed, in the maximum case, the field of ellipsoidally distributed stars is decisive. Since, according to Shapley, a systematic asymmetry in the densities in the amount of 7% is certainly manifest for the star cluster “Mess. 15,” for ex., and with some certainty even for “Mess. 10,” with about 4% it can consequently be concluded that the ratio of the total masses must be , because flattening of the equipotential surfaces rises sharply as a function of μ from the 0 value and at μ = 1 already attains a value at which the asymmetry in the densities would be roughly 5%. Since giants make up about 1% of all stars in the cluster and the mean mass of strongly flattened stars in the sur- rounding system—predominantly spectral type A—may be about 2–5 solar masses, it follows as an average value for red giants: 200–500 solar masses.[6] From the general redshift of these giants, one obtains as densities of the individual stars roughly a mean of 0.0[7] solar densities, which does not seem implausible. I shall continue to consider the problem and might come to you on Wednesday before the colloquium[7] to show you everything. With best regards, yours, E. Freundlich P.S. Please excuse the printing paper.[8] dρ⎞ dr⎠ ------ ⎝ ⎛ Δr 1′ = ′ μ Mellipsoid- Msphere ------------------- 1 =