Page:Memoirs of Royal Astronomical Society Volume 01.djvu/535

512 extraction of the roots of numbers and approximates to the roots of equations, may in a more advanced state of improvement rise to the approximate solution of algebraic equations of elevated degrees. I refer to solutions of such equations proposed by, and more recently by other analysts, which involve operations too tedious and intricate for use, and which must remain without efficacy, unless some mode be devised of abridging the labour or facilitating the means of its performance. In any case this engine tends to lighten the excessive and accumulating burden of arithmetical application of mathematical formulæ, and to relieve the progress of science from what is justly termed by the author of this invention, the overwhelming incumbrance of numerical detail.

For this singular and pregnant discovery, I have the authority of the Astronomical Society of London to present to Mr., its Gold medal, which accordingly I now do, as a token of the high estimation in which it holds his invention of an engine for calculating mathematical and astronomical tables.

The greatest step which has been made in the astronomy of comets, since the verification of 's comet, which reappeared in 1759, has been the identifying of 's comet, at once determined by the evidence of its frequent appearance within short periods, and already confirmed by its rediscovery in a distant hemisphere.

It is scarcely to be doubted, that other, many other, like bodies, moving through very eccentric orbits, in short periods, belong to our solar system. Though 's comet has not been again observed since 1770, it is not therefore to be despaired of. More extended, more diffused diligence may yet detect it, if in truth it has not ceased to be capable of becoming luminous. Nor is it an over-sanguine expectation, which counts upon more discoveries of the like nature. It is not likely that 's should be solitary of its kind; the only one revolving in a short period; or the only visible one.