Page:A biographical dictionary of eminent Scotsmen, vol 7.djvu/189

him to think of the most simple and elegant means of explaining those difficult propositions, which were hitherto only accessible to men deeply versed in the modern analysis. In doing this, he was pursuing the object which, of all others, he most ardently wished to attain, viz., the application of geometry to such problems as the algebraic calculus alone had been thought able to resolve. His solution of Kepler's problem was the first specimen of this kind which he gave to the world; and it was impossible to have produced one more to the credit of the method which he followed, or of the abilities with which he applied it." This solution appeared in the second volume of the Essays of the Philosophical Society of Edinburgh, for the year 1756. To quote again the words of the eminent biographer: "Whoever examines it, will be astonished to find a problem brought down to the level of elementary geometry, which had hitherto seemed to require the finding of fluents, and the reversion of series; he will acknowledge the reasonableness of whatever confidence Mr Stewart may be hereafter found to place in those simple methods of investigation, which he could conduct with so much ingenuity and success; and will be convinced, that the solution of a problem, though the most elementary, may be the least obvious; and though the easiest to be understood, may be the most difficult to be discovered." In pursuance of his principle of introducing the forms of ancient demonstration, as applicable to those more complicated parts of the science, called the mixed mathematics, for which they had been considered unqualified, he published, in 1761, his "Tracts, Physical and Mathematical, containing an Explanation of several important Points in Physical Astronomy; and a New Method of ascertaining the Sun's distance from the Earth, by the Theory of Gravitation." "In the first of these," says his biographer, "Mr Stewart lays down the doctrine of centripetal forces, in a series of propositions, demonstrated, (if we admit the quadrature of curves,) with the utmost rigour, and requiring no previous knowledge of the mathematics, except the elements of plain geometry, and conic sections. The good order of these propositions, added to the clearness and simplicity of the demonstrations, renders this tract the best elementary treatise of physical astronomy that is anywhere to be found." It was the purpose of the three remaining tracts to determine the effect of those forces which disturb the motions of a secondary planet; and, in particular, to determine the distance of the sun, from its effect in disturbing the motions of the moon. Owing to the geometrical method which he adopted, and likewise to the extreme distance of the sun, which makes all the disturbances he produces on the motion of the moon, very near to that point at which increase of distance to infinity would not change their force, he could only proceed on a system of approximation; and in applying the principles of his plan to a practical calculation of the sun's distance, which he published in 1763, entitled, "Distance of the Sun from the Earth, determined by the Theory of Gravitation, together with several other things relative to the same subject," he was found to have made a very considerable error. He found the distance of the sun to be equal to 29,875 semi-diameters of the earth, or about 118,541,428 English miles. About five years afterwards, there appeared a pamphlet from the pen of Mr Dawson of Sudbury, called "Four Propositions, intended to point out certain Errors in Dr Stewart's Investigation, which had given a result much greater than the truth." This was followed by a second attack from Mr Lauden, who, like Price in arithmetic, accomplished the difficult task of be- coming an enthusiast in mathematics, and, by means of exaggerating errors, and commenting on their atrocity, astonished the world with a specimen of controversial mathematics. The biographer thus states the sources of the mistakes which called forth these animadversions: "As in arithmetic, we neglect those