HISTORY OF PHYSICAL ASTRONOMY.

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tlie celestial bodies in their orbits (supposed circular) varies according tothe inverse square of the distance.

It is impossible too much to admire the conduct of Halley in regard tothe part lie took in the publication of the Principia . Indeed we mayreasonably doubt whether that immortal work would ever have beenwritten at all, if it had not been for his enlightened zeal in the cause ofscience; for Newton himself appears to have been imbued much morestrongly with the love of pondering in secret over his discoveries, than hewas urged by the equally natural feeling of communicating them to others.This disposition of mind was fostered by a lively recollection of the an-noyance he had suffered from the publication of his researches in Optics ,and the consequent dread he entertained of having his tranquillity againdisturbed by a controversy with envious rivals. Halley, therefore, besidesdiscovering the only individual living who could unfold the physicaltheory of the celestial motions, is entitled to the credit of having per-suaded him to communicate his discoveries to the world. Nor was thisall; for, as has been already hinted, he defrayed the expense of publish-ing* * * § the Principia , at a time too when his finances could ill afford suchan outlay j-; and also undertook the revision of it in its progress throughthe press. Posterity has retained a grateful recollection of those princeswho at different periods of history have distinguished their reign by amunificent patronage of learning and science; but, among all those whohave thus contributed indirectly to the progress of knowledge, there isnone who exhibits such a bright example of disinterestedness and self-sacrificing zeal as the illustrious superintendent of the first edition of thePrincipia . It is pleasing to reflect that Halley received such a noble re-ward for his exertions in the splendid discovery with which his name isimmortally associated, and to which he was mainly conducted by Netv-ton’s researches on comets.

The Principia was published in 1687, and was dedicated to theP.oyal Society. At the beginning of it was inserted a Latin poem inhexameter verse by Halley, in honour of Newton’s discoveries. The con-cluding line runs thus :—

“ Nee fas est propius mortali attingere divos; ” J

“ an eulogium,” says the severe Delambre, “ which no one has charged withexaggeration.” §

The whole work is divided into three books. The first book treats ofmotion in free space; the second is occupied chiefly with questions re-lating to resisted motion; the third is upon the system of the world.

The first book is divided into fourteen sections, and contains ninety-eight propositions, besides a number of corollaries, lemmas, and scholia.In the first section, Newton explains the geometry which he employs inhis subsequent investigations. It is termed by him the method of primeand ultimate ratios, and is essentially the same as the differential calculus.In the second section he enters upon the subject of centripetal forces,demonstrating Kepler’s theorem of areas, and investigating the law of the

* It must be understood that Halley was subsequently reimbursed for the expensesconnected with the publication of the Principia by the sale of the copies of the work.

+ He was brought up in affluent circumstances, but in 1684 his father died, after com-pletely wasting his fortune.

t Nor is it lawful for mortals to approach nearer the Deity.

§ Histoire de l’Astronomie de Dixhuitieme Siecle, p. 2.