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The condition that the family of surfaces φ(x, y, z, λ) = 0 may be one of an orthogonal triad

Published online by Cambridge University Press:  20 January 2009

F. E. Edwardes
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Cayley has shown that if the family of surfaces φ(x, y, z) = λ is one of an orthogonal triad, φ satisfies a differential equation of the third order. If, however, the parameter λ is involved implicitly in the equation of the family, the condition requires modification: for example, although

is one of an orthogonal triad, φ does not satisfy Cayley's equation.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , February 1911 , pp. 37 - 38
Copyright
Copyright © Edinburgh Mathematical Society 1911

References

* Proc. Edin. Math. Soc., vol. xxix.Google Scholar