planets. Centrifugal motion would constantly impel the planets to fly off in a straight line from the sun; but they are kept in their orbits by the pressure of an outer sphere, consisting of denser particles which are beyond the action of the vortices.

Newton had demolished this theory. He had shown that the planets are held in their orbits by the force of gravity, which is always drawing them towards the sun, combined with a transverse impulse, which is always projecting them at tangents to their orbits. Bentley takes up Newton's great discovery, and applies it to prove the existence of an Intelligent Providence. Let us grant, he says, that the force of gravity is inherent to matter. What can have been the origin of that other force-the transverse impulse? This impulse is not uniform, but has been adjusted to the place of each body in the system. Each planet has its particular velocity, proportioned to its distance from the sun and to the quantity of the solar matter. It can be due to one cause alone—an intelligent and omnipotent Creator.

This view has the express sanction of Newton. His letters to Bentley - subsequent in date to the Lectures -repeatedly confirm it. "I do not know any power in nature," Newton writes, "which would cause this transverse motion without the divine arm." . . . "To make this system, with all its motions, required a cause which understood and compared together the quantities of matter in the several bodies of the sun and planets, and the gravitating powers resulting from thence; the several distances of the primary planets from the sun, and of the secondary ones from Saturn, Jupiter, and the Earth; and the velocities with which these planets could revolve about those quantities of matter in the central bodies; and to com

pare and adjust all these things together, in so great a variety of bodies, argues that cause to be, not blind and fortuitous, but very well skilled in mechanics and geometry."

The application of Newton's discoveries which Bentley makes in the Boyle Lectures was peculiarly welcome to Newton himself. "When I wrote my treatise about our system," he says to Bentley, "I had an eye upon such principles as might work with considering men for the belief of a Deity; and nothing can rejoice me more than to find it useful for that purpose. But if I have done the public any service this way, it is due to nothing but industry and patient thought."

The correspondence between Bentley and Newton, to which the Boyle Lectures gave rise, would alone make them memorable. It has commonly been supposed that Bentley first studied the Principia with a view to these Lectures. This, as I can prove, is an error. The Library of Trinity College, Cambridge, contains the autographs of Newton's four letters to Bentley, and of his directions for reading the Principia; also a letter to Wotton from John Craig, a Scottish mathematician, giving advice on the same subject, for Bentley's benefit. Now, Craig's letter is dated June 24, 1691; Bentley, then, must have turned his mind to the Principia six months before the Boyle Lectures were even founded. We know, further, that in 1689 he was working on Lucretius. I should conjecture, then, that his first object in studying Newton's cosmical system had been to compare it with that of Epicurus, as interpreted by Lucretius; to whom, indeed, he refers more than once in the Boyle Lectures. Craig gives an alarming list of books which must be read before the Principia can be understood, and represents the study as most arduous. Newton's own directions to Bentley are simple and en

th

couraging: "at ye first perusal of my Book," he concludes, "it's enough if you understand ye Propositions W some of ye Demonstrations wch are easier than the rest. For when you understand ye easier, they will afterwards give you light into ye harder." At the bottom of the paper Bentley has written, in his largest and boldest character, "Directions from Mr. Newton by his own Hand." There is no date. Clearly, however, it was Craig's formidable letter which determined Bentley on writing to Newton. The rapidity with which Bentleyamongst all his other pursuits-comprehended the Principia proves both industry and power. Some years later, his Lectures were searched for flaws by John Keill, afterwards Savilian Professor of Astronomy at Oxford, and the principal agent in introducing Newton's system there. The Phalaris controversy was going on, and Keill wished to damage Bentley. But he could find only one real blot. Bentley had missed Newton's discovery-mentioned, but not prominent, in the Principia-that the moon revolves about her own axis. Keill's only other point was a verbal cavil, refuted by the context. Better testimony to Bentley's accuracy could scarcely have been borne.

The last Lecture was given on December 5, 1692. The first six had already been printed. But before publishing the last two-which dealt in more detail with Newton's principles-Bentley wished to consult Newton himself. He therefore wrote to him, at Trinity College, Cambridge. It was in the autumn of that year that Newton had finished his Letters on Fluxions. He was somewhat out of health, suffering from sleeplessness and loss of appetite; perhaps (as his letters to Locke suggest) vexed by the repeated failure of his friends to obtain for him such a provision as he desired. But he at once answered Bentley's

letter with that concise and lucid thoroughness which makes his style a model in its kind. His first letter is dated Dec. 10, 1692, and addressed to Bentley "at the Bishop of Worcester's House, in Park Street in Westminster." On the back of it Bentley has written: "Mr Newton's Answer to some Queries sent by me, after I had preach't my 2 last Sermons; All his answers are agreeable to what I had deliver'd before in the pulpit. But of some incidental things I do Téxεv [suspend judgment]. R. B." Three other letters are extant which Newton wrote at this time to Bentley-the last on Feb. 25, 1693. He probably wrote others also; there are several from Bentley to him in the Portsmouth collection.

In the course of these four letters, Newton approves nearly all the arguments for the existence of God which Bentley had deduced from the Principia. On one important point, however, he corrects him. Bentley had

conceded to the atheists that gravity may be essential and inherent to matter. "Pray," says Newton, "do not ascribe that notion to me; for the cause of gravity is what I do not pretend to know, and therefore would take more time to consider of it." In the last letter, about five weeks later, Newton returns to this topic, and speaks more decidedly. The notion of gravity being inherent to matter "is to me," he says, "so great an absurdity, that I believe no man, who has in philosophical matters any competent faculty of thinking, can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers."

One of the most interesting points in these letters is to see how a mind like Bentley's, so wonderfully acute in

certain directions, and logical in criticism even to excess, is corrected by a mathematical mind. Thus Bentley, in writing to Newton, had argued that every particle of matter in an infinite space has an infinite quantity of matter on all sides, and consequently an infinite attraction every way; it must therefore rest in equilibrium, all infinites being equal. Now, says Newton, by similar reasoning we might prove that an inch is equal to a foot. For, if an inch may be divided into an infinite number of parts, the sum of those parts will be an inch; and if a foot may be divided into an infinite number of parts, the sum of those parts must be a foot; and therefore, since all infinites are equal, those sums must be equal; that is, an inch must be equal to a foot. The logic is strict; what, then, is the error in the premises? The position, Newton answers, that all infinites are equal. Infinites may be considered in two ways. Viewed absolutely, they are neither equal nor unequal. But when considered under certain definite restrictions, as mathematics may consider them, they can be compared. "A mathematician would tell you that, though there be an infinite number of infinite little parts in an inch, yet there is twelve times that number of such parts in a foot." And so Bentley's infinite attracting forces must be so conceived as if the addition of the slightest finite attracting force to either would destroy the equilibrium.

Johnson has observed that these letters show "how even the mind of Newton gains ground gradually upon darkness" a fine remark, but one which will convey an incorrect impression if it is supposed to mean that Bentley's questions had led Newton to modify or extend any doctrine set forth in the Principia. Bentley's present object in using the Principia was to refute atheism.