By John Henry Constantine Whitehead

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14a n ) we have, if p

852, also p. 1083. 22 ON LINEAR CONNECTIONS T h e associated space at each point can be identified with the sub-space spanned in the tangent space b y the vectors £«, but the essential feature which distinguishes the theory of a linear connection from that of an affine connection is retained: namely that the frame of reference m a y be changed in each associated space independently of coordinate transformations. 7. Integral sub-spaces. 1) dZ« + Z U £ < * * ' - 0. 1 n 1 m I t will be convenient to say that a set of numbers (x , • • • , x ; Z , • • • , Z ) determine, on the one hand a point x in the underlying'manifold Vn, together with a point Z in the linear space associated with x, and on the other hand a point in a space oim+n dimensions, which we shall denote b y Sn+m.

Let Hjk be the components of D in a coordinate system x, in which the i i l equations to G are x =