DITTON (Humphrey)
, an eminent mathematician, was born at Salisbury, May 29, 1675. Being an only son, and his father observing in him an extraordinary good capacity, determined to cultivate it with a good education. For this purpose he placed him in a reputable private academy; upon quitting of which, he, at the desire of his father, though against his own inclination, engaged in the profession of divinity, and began to exercise his function at Tunbridge in the county of Kent, where he continued to preach some years; during which time he married a lady of that place.
But a weak constitution, and the death of his father, induced Mr. Ditton to quit that profession. And at the persuasion of Dr. Harris and Mr. Whiston, both eminent mathematicians, he engaged in the study of mathematics, a science to which he had always a strong inclination. In the prosecution of this science, he was much encouraged by the success and applause he received: being greatly esteemed by the chief professors of it, and particularly by Sir Isaac Newton, by whose interest and recommendation he was elected master of the new Mathematical School in Christ's Hospital; where he continued till his death, which happened in 1715, in the 40th year of his age, much regretted by the philosophical world, who expected many useful and ingenious discoveries from his assiduity, learning, and penetrating genius.
Mr. Ditton published several mathematical and other tracts, as below.—1. Of the Tangents of Curves, &c. Philos. Trans. vol. 23.
2. A Treatise on Spherical Catoptrics, published in the Philos. Trans. for 1705; from whence it was copied and reprinted in the Acta Eruditorum 1707, and also in the Memoirs of the Academy of Sciences at Paris.
3. General Laws of Nature and Motion; 8vo, 1705. Wolfius mentions this work, and says, that it illustrates and renders easy the writings of Galileo, Huygens, and the Principia of Newton. It is also noticed by La Roche, in the Memoires de Literature, vol. 8, pa. 46.
4. An Institution of Fluxions, containing the first Principles, Operations, and Applications, of that admirable Method, as invented by Sir Isaac Newton; 8vo, 1706. This work, with additions and alterations, was again published by Mr. John Clarke, in the year 1726.
5. In 1709 he published the Synopsis Algebraica of John Alexander, with many additions and corrections.
6. His Treatise on Perspective was published in 1712. In this work he explained the principles of that art mathematically; and besides teaching the methods then generally practised, gave the first hints of the new | method afterward enlarged upon and improved by Dr. Brook Taylor; and which was published in the year 1715.
7. In 1714, Mr. Ditton published several pieces, both theological and mathematical; particularly his Discourse on the Resurrection of Jesus Christ; and The New Law of Fluids, or a Discourse concerning the Ascent of Liquids, in exact Geometrical Figures, between two nearly contiguous Surfaces. To this was annexed a tract, to demonstrate the impossibility of thinking or perception being the result of any combination of the parts of matter and motion: a subject much agitated about that time. To this work also was added an advertisement from him and Mr. Whiston, concerning a method for discovering the longitude, which it seems they had published about half a year before. This attempt probably cost our author his life; for although it was approved and countenanced by Sir Isaac Newton, before it was presented to the Board of Longitude, and the method has been successfully put in practice, in finding the longitude between Paris and Vienna, yet that Board then determined against it: so that the disappointment, together with some public ridicule (particularly in a poem written by Dean Swift), affected his health, so that he died the ensuing year, 1715.
In an account of Mr. Ditton, prefixed to the German translation of his Discourse on the Resurrection, it is said that he had published, in his own name only, another method for finding the longitude; but which Mr. Whiston denied. However, Raphael Levi, a learned Jew, who had studied under Leibnitz, informed the German editor, that he well knew that Ditton and Leibnitz had corresponded upon the subject; and that Ditton had sent to Leibnitz a delineation of a machine he had invented for that purpose; which was a piece of mechanism constructed with many wheels like a clock, and which Leibnitz highly approved of for land use; but doubted whether it would answer on shipboard, on account of the motion of the ship.
DIVERGENT Point. See Virtual Focus.
Divergent, or Diverging Lines, in Geometry, are those whose distance is continually increasing.— Lines which diverge one way, converge the other way.
Divergent, or Diverging, in Optics, is particularly applied to rays which, issuing from a radiant point, or having, in their passage, undergone a refraction, or reflexion, do continually recede farther from each other.
In this sense the word is opposed to convergent, which implies that the rays approach each other, or that they tend to a centre, where they intersect, and, being continued, go on diverging. Indeed all intersecting rays, or lines, diverge both ways from the centre, or point of intersection.
Concave glasses render the rays diverging; and convex ones, converging.—Concave mirrors make the rays converge; and convex ones, diverge.—It is demonstrated in Optics, that as the diameter of a pretty large pupil does not exceed 1/5 of a digit; diverging rays, flowing from a radiant point, will enter the pupil as parallel, to all intents and purposes, if the distance of the radiant from the eye amount to 40,000 feet. See Focus, Light, and Vision.
Diverging Hyperbola, is one whose legs turn their convexities toward each other, and run out quite contrary ways. See Hyperbola.
Diverging Parabola. See Diverging Parabola.
