  The main purpose of the present paper is to show that a correction of one
mistake was crucial for Einstein's pathway to the first version of the 1915
general theory of relativity, but also might have played a role in obtaining
the final version of Einstein's 1915 field equations. In 1914 Einstein wrote
the equations for conservation of energy-momentum for matter, and established a
connection between these equations and the components of the gravitational
field. He showed that a material point in gravitational fields moves on a
geodesic line in space-time, the equation of which is written in terms of the
Christoffel symbols. By November 4, 1915, Einstein found it advantageous to use
for the components of the gravitational field, not the previous equation, but
the Christoffel symbols. He corrected the 1914 equations of conservation of
energy-momentum for matter. Einstein had already basically possessed the field
equations in 1912 together with his mathematician friend Marcel Grossman, but
because he had not recognized the formal importance of the Christoffel symbols
as the components of the gravitational field, he could "not obtain a clear
overview". Finally, considering the energy-momentum conservation equations for
matter, an important similarity between equations suggests that, this equation
could have assisted Einstein in obtaining the final form of the field equations
(the November 25, 1915 ones) that were generally covariant.
