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The present paper contains solutions of the tensor generalisation of Laplace's Equation. The results obtained are summarised in the two theorems enunciated in § 1. They apply only to the case when the Riemannian space forming the background of the theory is flat. In the concluding paragraph a special case is considered, and it is shown that the present theory is closely connected with Whittaker's well known general solution of the ordinary Laplace's Equation.
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page 181 note 1 Whittaker, and Watson, , “Modern Analysis” (1920), § 18.3.
page 181 note 2 Some properties of this function have been investigated in earlier papers, particularly (i) Proc. London Math. Soc., 31 (1930), 225 ; (ii) ibid., 32 (1931), 87. These will be referred to as papers 1 and 2 respectively.
page 182 note 1 ∂ω∂τ is in general a function of τ as well as of the x's, so τ must be eliminated in order that the solution should be expressed as a function of the x's only.
page 182 note 2 See, for example, Veblen, “Invariants of Quadratic Differential Forms” Camb.). Math. Tract. No. 24) (1927), 95.
page 183 note 1 This in fact follows at once from equations (1) and (10) of paper 2.
page 183 note 2 Paper 1, § 2, where ω denotes twice the function here represented by ω.
page 186 note 1 See Bateman, , “Electrical and Optical Wave Motion” (1915), 115.
page 187 note 1 Since u is an arbitrary constant, the function ƒ of the two arguments 
and u, is (regarded as a function of x, y, z), an arbitrary function of the former argument only ; that is, of ∂ω∂τ only.
page 188 note 1 Whittaker, and Watson, , loc. cit.
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