Proceedings of the London Mathematical Society, Volume 20

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London Mathematical Society, 1889 - Electronic journals
"Papers presented to J. E. Littlewood on his 80th birthday" issued as 3d ser., v. 14 A, 1965.

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Page 365 - A-%J3 is a positive quantity becomes unnecessary, " provided we either suppose the medium to extend all through boundless space, or give it a fixed containing vessel as its boundary...
Page 10 - It seems to me that the only objects of the abstract sciences or of demonstration are quantity and number, and that all attempts to extend this more perfect species of knowledge beyond these bounds are mere sophistry and illusion.
Page 398 - ... given circle is equidistant from two given straight lines : describe another circle which shall touch these two straight lines and shall cut off from the given circle a segment containing an angle equal to a given angle. 319.
Page 426 - ... daughter of his former partner, Charles W. Prentiss), and two children. EDWIN P. GREEN. Edwin P. Green died at his home in Akron, Ohio, on Sunday, December 23, 1894. He was born in Gaysville Village, in the town of Stockbridge, Windsor County, Vermont, March 10, 1828. His boyhood and youth were passed on his father's farm? and his early education was acquired in the district school of his native village. Later he attended the Bradford Academy, and subsequently himself taught in the schools of...
Page 10 - ... and to substitute for such flat three-dimensional space a curved three-dimensional space, say, of constant positive or negative curvature. In regarding the physical space of our experience as possibly non-Euclidian, Riemann's idea seems to be that of modifying the notion of distance, not that of treating it as a locus in four-dimensional space. I have just come to speak of four-dimensional space. What meaning do we attach to it ? or can we attach to it any meaning? It may be at once admitted...
Page 350 - FRS ; a theorem in the calculus of linear partial differential operations, by Major Macmahon, RA ; on crystalline reflection and refraction, by AB Basset, FRS ; on some rings of circles connected with a triangle and the circles (Schoute's system) that cut them at equal angles, by W.
Page 245 - FRS, President, in the chair. — The following communications were made : — On the deformation of an elastic shell, by Prof.
Page 379 - J m + n [ m + na*) It will be seen that, in order to give rise to this discrepancy, it is not necessary to suppose the introduction of surface forces more powerful than are actually required to maintain the deformation. This instance is sufficient to show that the potential energy of deformation cannot, in general, be expressed in terms of extensions and changes of curvature of the middle surface, when it is necessary to include terms of order h2, without further information as to the manner in which...

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