In the article titled “Clusters of Galaxies in a Weyl Geometric Approach to Gravity” [1], there was an error in equation () that led to a wrong relation between the acceleration due to the scale connection () and the acceleration arising from the scalar field energy density (). The correction of () has consequences for the model. It makes a new run of the data evaluation based on the corrected dynamical equations necessary. The new results are given in updated Tables 3 and 4 and Figures 16. The overall picture of the empirical test does not change, although now three rather than two galaxy clusters agree with the model only in the range. To facilitate controlling the correction, a detailed derivation of the corrected equation is given in Appendix.

Minor Corrections. “15” should be changed to “14” in the following two sections. In the abstract, the number should be corrected in the phrase “the total mass for 15 of the outlier reduced ensemble of 17 clusters seems to be predicted correctly (in the sense of overlapping 1σ error intervals).” In paragraph 6 of Introduction, it should be corrected in the sentence “For 15 of the 17 main reference clusters the empirical and the theoretical values for the total mass agree in the sense of overlapping 1σ error intervals.” Equations (), (), and () should read as follows.

Major Corrections, Section  2. Equation () should read as follows: The paragraph following equation (), including the old equation (), has to be cancelled. The correction of () entails the following modifications in the equations of Section : In the comment below equation (59) “three quarters” and “one quarter” should be replaced with “one-half” and the inline formula below equation (62) should be replaced with .

Major Corrections, Sections  3–5. The modifications of the equations in Section lead to the following changes in Section : This makes a new run of the data evaluation necessary, now based on the corrected dynamical equations. The new results are given in updated Tables 3 and 4 and Figures 26. In the evaluation on p. 16, right column, first two sentences of the first paragraph should be replaced with the following: For 5 clusters A85, A2255, and A2589 and the outliers A2029 and A2065, the error intervals of empirical data and model data do not overlap. For the first three of them (A85, A2255, and A2589) the model predictions are consistent with the empirical data within doubled error intervals ( range).

In page 20, right column (Section ), 20, at the middle of the second paragraph “15 clusters” should be replaced with “14 clusters,” and “Two clusters  …” should be substituted by “Three clusters  …” at the beginning of the last phrase.

Appendix

Energy Component of the Scalar Field

In scalar field (Einstein) gauge , and . Similarly Moreover, leads to Thus Following () and () of the main article and using (, the Hubble parameter at present), the energy momentum of the scalar field, becomes In the static case the first two terms of vanish and the total energy component of the scalar field turns into Assuming conditions under which the terms of cosmological orders of magnitude and those of order can be neglected, we arrive at like in the corrected equation . In the central symmetric case () implies . In spherical coordinates and Because of the approximation is justified.