followed. As regards the perturbations of the nodes and inclinations, indeed, nothing equally luminous can ever be substituted for his explanation. But as respects the other disturbances, the point of view chosen by Newton has been abandoned for another, which it is somewhat difficult to perceive why he did not, himself, select. By a different resolution of the disturbing forces from that adopted by him, and by the aid of a few obvious conclusions from the laws of elliptic motion which would have found their place, naturally and consecutively, as corollaries of the seventeenth proposition of his first book (a proposition which seems almost to have been prepared with a special view to this application), the momentary change of place of the upper focus of the disturbed ellipse is brought distinctly under inspection; and a clearness of conception introduced into the perturbations of the excentricities, perihelia, and epochs which the author does not think it presumption to believe can be obtained by no other method, and which certainly is not obtained by that from which it is a departure. It would be out of keeping with the rest of the work to have introduced into this part of it any algebraic investigations; else it would have been easy to show that the mode of procedure here followed leads direct, and by steps (for the subject) of the most elementary character, to the general formulæ for these perturbations, delivered by Laplace in the Mécanique Céleste.*

The reader will find one class of the lunar and planetary inequalities handled in a very different

* Livre ii. chap. viii. art. 67.

manner from that in which their explanation is usually presented. It comprehends those which are characterized as incident on the epoch, the principal among them being the annual and secular equations of the moon, and that very delicate and obscure part of the perturbational theory (so little satisfactory in the manner in which it emerges from the analytical treatment of the subject), the constant or permanent effect of the disturbing force in altering the disturbed orbit. I will venture to hope that what is here stated will tend to remove some rather generally diffused misapprehensions as to the true bearings of Newton's explanation of the annual equation.*

If proof were wanted of the inexhaustible fertility of astronomical science in points of novelty and interest, it would suffice to adduce the addition to the list of members of our system of no less than eight new planets and satellites during the preparation of these sheets for the press. Among them is one whose discovery must ever be regarded as one of the noblest triumphs of theory. In the account here given of this discovery, I trust to have expressed myself with complete impartiality; and in the exposition of the perturbative action on Uranus, by which the existence and situation of the disturbing planet became revealed to us, I have endeavoured, in pursuance of the general plan of this work, rather to exhibit a rational view of the dynamical action, than to convey the slightest idea of the conduct of those masterpieces of analytical skill which the researches of Messrs. Leverrier and Adams exhibit.

* Principia, lib. i. prop. 66. cor. 6.

1

To the latter of these eminent geometers, as well as to my excellent and esteemed friend the Astronomer Royal, I have to return my best thanks for communications which would have effectually relieved some doubts I at one period entertained had I not succeeded in the interim in getting clear of them as to the compatibility of my views on the subject of the annual equation already alluded to, with the tenor of Newton's account of it. To my valued friend, Professor De Morgan, I am indebted for some most ingenious suggestions on the subject of the mistakes committed in the early working of the Julian reformation of the calendar, of which I should have availed myself, had it not appeared preferable, on mature consideration, to present the subject in its simplest form, avoiding altogether entering into minutiae of chronological discussion.

J. F. W. HERSCHEL.

Collingwood, April 12, 1849.

PREFACE

ΤΟ

THE FIFTH EDITION.

THE rapid progress of science renders it necessary frequently to revise and bring up elementary works to the existing state of knowledge, under penalty of their becoming obsolete. In former editions of this work, this has been done, so far as it could be done without incurring the necessity of an almost total typographical reconstruction. But Astronomy, within the last few years, has been enriched by so many and such considerable additions, that it has been considered preferable (another edition being called for), not indeed to recast the general plan of the work, but to incorporate these in it in due order and sequence, thereby materially enlarging the volume, and giving it in many respects the air of a new work, The articles thus introduced are distinguished from those of the former editions between which they have been inserted by the addition to the last current number of an italic letter- thus, between Arts.

394. and 395. will be found inserted 394. a, 394. b, and 394. c. The enclosure of any passage in brackets [] indicates its having been introduced in the Fourth Edition. The index references in this as in former editions, being to the articles and not to the pages, are thus preserved. Together with these recent accessions to our knowledge, I have taken the opportunity of introducing several things which might justly have been noted as deficient in the former editions, as, for instance, the account of the methods by which the mass of the Earth has been determined, and that of the successful treatment, and it is presumed final subjugation, of those rebellious ancient Solar Eclipses which have so much harassed astronomers. A brief account of M. Foucault's remarkable pendulum experiments, and of that beautiful instrument, the gyroscope, is introduced: as are also notices of Professor Thomson's speculations on the origin of the Sun's heat, and his estimate of its average expenditure, as well as of some curious views of M. Jean Reynaud *, on the secular variation of our climates, supplementary to those put forward in former editions of this work. I could have wished that its nature and limits would have permitted some account of Mr. Cooper's magnificent contributions to sidereal astronomy, in his catalogue of upwards of 60,000 previously unregistered ecliptic stars; of Mr. Bishop's ecliptic charts and those of M. Chacornac; of Mr. Carrington's elaborate circumpolar catalogue; and of Mr. Jones's immense work on the zodiacal light, forming the third volume of the account of the

* Misprinted Regnault in p. 235.