*For an account of the precursors of Eotvos and of the latter's experiments, see [W2]. For a descrip-
tion of improved results of more recent vintage, see the papers by Dicke and collaborators [Rl] and
by Braginskii and Panov [B4].THE EINSTEIN-GROSSMANN COLLABORATION 217Eotvos experiments for the first time in EG, concluding that 'the physical identity
of gravitational and inertial mass. .. possesses a high degree of probability.'*
After these prefatory remarks, I turn to Grossmann's contribution to EG. 'Ein-
stein grew up in the Christoffel-Ricci tradition,' Christian Felix Klein wrote in
his history of mathematics in the nineteenth century [K3]. This masterwork
explains how from a mathematical point of view general relativity may be consid-
ered as one of the culmination points in a noble line of descendance starting with
the work of Carl Friedrich Gauss, moving on to Georg Friedrich Bernhard Rie-
mann, and from there to Elwin Bruno Christoffel, Gregorio Ricci-Curbastro,
Tullio Levi-Civita, and others. I hope my readers will derive the same enjoyment
as I did in reading these original papers as well as Klein's history. I would further
recommend the essays by Dirk Struik on the history of differential geometry [S7].
I restrict my own task to explaining how Einstein 'grew up.' The two principal
references in Grossmann's contribution to EG are the memoir 'On the Transfor-
mation of Homogeneous Differential Forms of the Second Degree' by Christoffel
[Cl], written in Zurich in 1869, and the comprehensive review paper of 1901 on
the 'absolute differential calculus' [R2] by Ricci and his brilliant pupil Levi-
Civita.
Grossman's contribution consists of a lucid exposition of Riemannian geometry
and its tensor calculus. In addition, he gives mathematical details in support of
some of Einstein's arguments. He begins with a discussion of the invariance of the
line element (Eq. 12.1) under the transformation
Then follow the definitions of tensors, the principal manipulations of tensor alge-
bra (as in [ W3]), the use of the metric tensor to relate covariant and contravariant
tensors, and the description of covariant differentiation ('Erweiterung'). Recall
that the covariant derivative V^ of a contravariant vector V is given by
where the affine connection ('Christoffel Drei-Indizes Symbol') FJ, is a nontensor
given by [W4]