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The Mechanical Integration of Differential Equations*

Published online by Cambridge University Press:  03 November 2016

D. R. Hartree
D. R. Hartree*
Affiliation:
University of Manchester
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Extract

In recent years there has been a great development in the design and use of machines for carrying out calculations of various kinds, and this is a technical advance of some importance, not only because of the saving of time and labour in calculations which would be carried out in any case, but still more because it makes it possible to carry out extensive calculations which would be too laborious and time-consuming to undertake without such mechanical or electrical aids.

Type
Research Article
Information
The Mathematical Gazette , Volume 22 , Issue 251 , October 1938 , pp. 342 - 364
Copyright
Copyright © Mathematical Association 1938

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Footnotes

*

Based on a paper read at the Annual Meeting of the Mathematical Association, January 1938.

References

References

[Note. This list is not intended to be exhaustive.]

General Articles on Integrating Mechanisms.

(1) SirThomson, W. (Lord Kelvin), Proc. Roy. Soc., Vol. 24, p. 269 (1876).Google Scholar
Thomson, W and Tait, P. G., Treatise on Natural Philosophy, Vol. 1, Appendix B′, Sections III, IV, V.Google Scholar
(2) Encyclopædia Britannica, 14th Edition, Article on Mathematical Instruments (Vol. 15); article on the Product Integraph (Vol. 18).Google Scholar
(3) Handbook of the Napier Tercentenary Exhibition (Edinburgh, 1914), edited by Horsburgh, E. M. (reprinted under the title Modern Instruments of Calculation), Section G, “Instruments of Calculation,” p. 181.Google Scholar
(4) Bush, V., Proc. 4th Internat. Congress of Appl. Mechanics (Cambridge, 1934), p. 3.Google Scholar
(5) Myers, D. M., Journ. Inst. Eng. Australia, Vol. 8, p. 423 (1936).Google Scholar
(6) Bush, V, Journ. Franklin Inst., Vol. 212, p. 447 (1931).CrossRefGoogle Scholar
(7) Hartree, D R., Nature, Vol. 135, p. 940 (1935).CrossRefGoogle Scholar
(8) The Engineer, Vol. 160, pp. 56, 82 (1935).Google Scholar
(9) Engineering, Vol. 140, p. 88 (1935).Google Scholar
(10) Hartree, D. R. and Porter, A., Mem. and Proc. Manchester Lit. and Phil. Soc., Vol. 79, p. 51 (1935) (Meccano model differential analyser).Google Scholar
(11) Massey, H. S. W and others, Journ. Roy. Irish Acad. (in press) (Small scale differential analyser).Google Scholar
(12) Hartree, D. R. and Nuttall, A. K., Journ. Inst. Elect. Eng. (in press).Google Scholar
(13) Morse, P. M. and Allis, W. P., Phys. Rev., Vol. 44, p. 269 (1933). (Scattering of electrons by helium atoms.)CrossRefGoogle Scholar
(14) Hartree, D. R., Phys. Rev., Vol. 46, p. 738 (1934);'CrossRefGoogle Scholar
Manning, M. F. and Millman, J., Phys. Rev., Vol. 49, p. 848 (1936). (Evaluation of atomic structures—mercury and tungsten.)CrossRefGoogle Scholar
(15) Lemaitre, G. and Vallarta, M. S., Phys. Rev., Vol. 49, p. 419 (1936); Vol. 50, p. 493 (1936). (Paths of electrified particles in the field of a magnetic dipole.)CrossRefGoogle Scholar
(16) Callender, A., Hartree, D. R. and Porter, A., Phil. Trans. Roy. Soc., Vol. 225, p. 415 (1936);Google Scholar
Hartree, D. R., Porter, A., Callender, A. and Stevenson, A. B., Proc. Roy. Soc., Vol. 161, p. 460 (1937). (Effect of time-lag in the behaviour of automatic control systems.)Google Scholar
(17) Hartree, D. R., Proc. Camb. Phil. Soc., Vol. 33, p. 223 (1937). (Calculations concerning boundary layer in the motion of a viscous fluid, and study of accuracy of the machine.)CrossRefGoogle Scholar
(18) Jackson, J. M. and Tyson, H., Mem. and Proc. Manchester Lit. and Phil. Soc., Vol. 81, p. 87 (1937). (Energy exchange between a gas and a solid at different temperatures.)Google Scholar
(19) Hartree, D. R. and Womersley, J. R., Proc Roy. Soc., Vol. 161, p. 353 (1937). (General theory of a method of applying the differential analyser to some forms of partial differential equations.)Google Scholar
(20) Hartree, D. R. and Porter, A., Journ. Inst. Elect. Eng. (in press). (Transients on an electrical transmission line.)Google Scholar