page 93 note 1 Whittaker, E. T., Proc. Roy. Soc. (A) 149 (1935), 384–395.
page 93 note 2 Ruse, H. S., Proc. Edin. Math. Soc. (2) 4 (1935), 144–158.
page 93 note 3 A form of Gauss's theorem inapplicable to such a fundamental case is not satisfactory. We cannot apply Ruse's form of the theorem to this case with λi = θi, because the special conditions which he imposes on λi require p = 0, as we can see from inspection of equation (5.7) with g i = 0
page 94 note 1 Temple, G., Proc. Roy. Soc. (A) 154 (1936), 354–363.
page 94 note 2 CfSynge, J. L., “A criticism of the method of expansion in powers of the gravitational constant in general relativity,” to appear shortly in Proc. Roy. Soc. (A).
page 95 note 1 Prof Barnes, C. has drawn my attention to Maxwell's remarks regarding this point: J. C. Maxwell, Mattel- and Motion (London, 1894), 85.
page 95 note 2 CfSynge, J. L., Annals of Mathematics 35 (1934), 705–713, for a simple proof by a method applicable also to the deviation of geodesic null-lines.
page 97 note 1 Eisenhart, L. P., Riemannian Geometry (Princeton, 1926), 113.
page 99 note 1 For this form, see Synge, J. L., “Integral electromagnetic theorems in general relativity” (Proc. Roy. Soc. A, 157 (1936), 434–443), equation (2.25).
page 100 note 1 Eisenhart, L. P., Riemannian Geometry (Princeton, 1926), 96.
page 101 note 1 CfEisenhart, L.P., Riemannian Geometry (Princeton 1926), 113.
page 101 note 2 It is possible to adopt two definitions of the energy tensor, differing by a factor c 2. That here employed reduces for a stream of unstressed matter to T ij = pθi θj, where θi is a unit vector and p is energy-density, not mass-density. This form is to be preferred, because in general relativity energy should be regarded as the more primitive concept, from which mass is a convenient conventional derivative.
page 102 note 1 Synge, J. L., Trans. Roy. Soc. Canada, Sect. III, 28 (1934), 163, where however a factor c 2 enters because there the concept of mass was taken as fundamental.
page 102 note 2 The factor c 2 is present in the denominator on the right hand side of (3.20) because we have used proper time s instead of the usual time in our definition of acceleration, so that our X i is the usual force (comparable to that of Newtonian mechanics) divided by c 2.