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XVI.—On Triple Systems of Surfaces and Non-Orthogonal Curvilinear Coordinates

Published online by Cambridge University Press:  15 September 2014

C. E. Weatherburn
C. E. Weatherburn
Affiliation:
Canterbury College, Christchurch, New Zealand
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Extract

The properties of “triply orthogonal” systems of surfaces have been examined by various writers and in considerable detail; but those of triple systems generally have not hitherto received the same attention. It is the purpose of this paper to discuss non-orthogonal systems, and to investigate formulæ in terms of the “oblique” curvilinear coordinates u, v, w which such a system determines.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 46 , 1927 , pp. 194 - 205
Copyright
Copyright © Royal Society of Edinburgh 1927

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References

page 194 note * “On Congruences of Curves,” Proc. Lond. Math. Soc., 1926.

page 196 note * See the author's Elementary Vector Analysis, Art. 46.

page 197 note * See the author's Advanced Vector Analysis, Art. 3.

page 198 note * Elementary Vector Analysis, Art. 47.

page 199 note * Advanced Vector Analysis, Art. 7.

page 200 note * “On Differential Invariants in Geometry of Surfaces, etc.,” § 4, Quarterly Journal of Mathematics, vol. 1, pp. 230–269 (1925)Google Scholar.

page 201 note * Usually denoted by E, F, G.

page 201 note † See the author's Differential Geometry, Art. 26, or Forsyth, Differential Geometry, Art. 28.

page 202 note * See § 6 of a recent paper by the author entitled “On Congruences of Curves,” Proc. Lond. Math. Soc., 1926.

page 202 note † Ibid., § 7.

page 203 note * “On Congruences of Curves,” § 5.

page 203 note † Ibid., § 9.