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Published online by Cambridge University Press: 20 January 2009
The following pages have been written in consequence of reading some paragraphs by Reye, in which he obtains, from a quartic surface, a chain of contravariant quartic envelopes and of covariant quartic loci. This chain is, in general, unending; but Reye at once foresaw the possibility of the quartic surface being such that the chain would be periodic. The only example which he gave of periodicity being realised was that in which the quartic surface was a repeated quadric. It is reasonable to suppose that, had he been able to do so, he would have chosen some surface which had the periodic property without being degenerate; in the present note two such surfaces are signalised.
page 73 note 1 Journal für Math. 82 (1877), 198.Google Scholar
page 74 note 1 The proof of the invariance of | μ | and of the contravariance of R, which has been given in Proc. Royal Soc. Edinburgh, A 61 (1941), 157, for the case of p = 2, can be carried over, with the few necessary verbal changes, to furnish a proof for any value of p.Google Scholar
page 75 note 1 Trans. American Math. Soc. 4 (1903), 65–85.CrossRefGoogle Scholar
page 75 note 2 The proof which Reye gives (p. 200) of this result in space of three dimensions is easily extended to give the corresponding result in space of any number of dimensions.
page 77 note 1 Burnside, : The Theory of Groups (Second Edition, Cambridge, 1911), 371, Ex. 6.Google Scholar
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