| RefNo | AP/31/17 |
| Level | File |
| Title | Unpublished paper, 'On the universal law of attraction including that of gravitation as a particular case of approximation deducible from the principle that equal and similar particles of matter move similarly relatively to each other' by John Kinnersley Smythies |
| Creator | Smythies; John Kinnersley (1808-1892); British barrister; inventor |
| Date | 1849 |
| Description | After stating the general object of his investigations and explaining the notation he employs, Smythies enters upon some preliminary geometrical inquiries. He gives the equation between the six right lines drawn between four points in a plane, the solidity of a tetrahedron in terms of its edges, the equation between the cosines of the six angles made by four right lines meeting in a point, and the equation between ten right lines drawn between five points, with some formulae of verification. Giving some general rules for the transformation and consolidation of series, he transforms the last equation into one involving the solidities of tetrahedrons, and shows how the sign of each tetrahedron in that equation is determined by its position relatively to the least solid including them all, and then gives the equation between all the right lines drawn between n points. Having shown that the result of differentiating the product of n variables, m times successively may be derived from the mth power of the sum of the n variables, developed by the polynomial theorem by substituting for every power of each variable its differential of an order numerically the same as the power; and applied the theorem to find the differential of the mth order of the equation between ten right lines drawn between five points, Smythies gives the first four successive differentials of the same equation in another form.
Includes a letter from Smythies addressing an error in the paper.
Subject: Physics / Mathematics
Received 30 May 1849. Read 14 June 1849. Communicated by Thomas Flower Ellis.
Whilst the Royal Society declined to publish this paper in full, an abstract of the paper was published in volume 5 of Abstracts of the Papers Printed in the Philosophical Transactions of the Royal Society of London [later Proceedings of the Royal Society] as 'On the universal law of attraction, including that of gravitation, as a particular case of approximation deducible from the principle that equal and similar particles of matter move similarly, relatively to each other'. |
| Extent | 46p |
| Format | Manuscript |
| PhysicalDescription | Ink on paper |
| Digital images | View item on Science in the Making |
| AccessStatus | Open |
| RelatedMaterial | DOI: 10.1098/rspl.1843.0193 |
Fellows associated with this archive
| Code | PersonName | Dates |
| NA3305 | Ellis; Thomas Flower (1796 - 1861) | 1796 - 1861 |