sun exert their attractive power. The chief of these disturbances take effect in alternately quickening and retarding the moon's pace, and therefore in accelerating or diminishing its right ascension among the stars. But the tilting of the planes of the two orbits in regard to each other besides contributing to this result also takes effect in raising or depressing the moon's position in latitude.

moon,

As many as forty distinct irregularities of the moon's movement have now been detected, tracked to their source by the sagacity of the astronomer and mathematician, and so exhaustively examined and discussed that they can henceforth be taken into account in astronomical forecasts. Some of the most recently discovered of these minor irregularities are invested with surpassing interest on account of the light they shed upon the magnificent impartiality and universality of the great gravitation-law. An error of eight seconds of positionthat is, of only the 225th part of the breadth of the moon's face-which recurs every nine years and three quarters, has, for instance, been traced to the influence of the pull of the protuberant mass of the earth's equator upon the varying in potential amount as the plane of the moon's orbit is inclined more or less to the plane of the earth's motion, between the extremes of 19 and 28 degrees. Another small irregularity of long period-namely, an alternate acceleration and retardation of the moon's movement to the extent of 23 seconds every 239 years, which was first detected by the present Astronomer Royal in 1846-was demonstrated by Professor P. A. Hansen, now of the Ducal Observatory of Gotha, to be due to an influence exerted by the planet Venus upon the earth. Venus retards the pace of the earth for 120 years, and then increases it for 120 years. So long as the slower rate prevails the earth is drawn in nearer to the sun. When the quicker speed prevails the earth moves off from the sun. But in both cases the moon goes with the earth, and consequently is first more energetically, and then less energetically, drawn by the sun. When most drawn by the sun its own pace is quickened, and when least drawn it is retarded. Professor Hansen believes that he has also referred another small irregularity of the long period of 273 years to the direct influence of the planet Venus upon the moon; but this has been since questioned, as will presently be seen.

So early as the year 1829 occasional letters from Professor Hansen, in the Astronomische Nachrichten,' indicated that he was at work upon the still untracked irregularities of the moon. In 1838, he published in Gotha a work entitled

Fundamenta Nova Investigationis Orbitæ veræ quam Luna 'perlustrat.' The last fruits of his investigations were the examinations of the influence of Venus in producing the two irregularities of long period which have been alluded to. These were completed shortly before the Schleswig-Holstein war. It then became known that a series of lunar tables which the Professor had been working upon very anxiously would have to be laid aside for some time, on account of the embarrassments brought upon the Danish Government, to which Hansen was then attached, by the war. Our own Astronomer Royal, however, very gallantly came to the rescue, and induced the British Government to undertake the charge of completing the calculations, and printing the tables. The calculations were finished at a cost of 3001. The tables were printed by the Board of Admiralty, and Professor Hansen paid a pleasant visit to Greenwich to pass his work through the press. It is upon record, as a characteristic trait of this distinguished astronomer, that when this welcome assistance was extended to his work he was calmly preparing to continue his elaborate and intricate computations singlehanded, and was only filled with concern at the contemplation of the long time that would have to elapse before his labour could be finished. By these tables errors of right ascension, which had notoriously been found to be as large as five-and-ahalf seconds when the tables of Burckhardt were employed by the computers, were at once reduced to two-and-a-half seconds. The gold medal of the Royal Astronomical Society was awarded to Professor Hansen in 1860 for this great service. In presenting the medal the President of the Astronomical Society spoke of the residual errors of the lunar theory as having been at last reduced to altogether insignificant limits, and of the great nautical problem of finding the longitude at sea as having been solved.

As Mr. Nasmyth, however, has pertinently remarked, 'the 'truths of Nature are for ever playing hide and seek with those 'who follow them.' At the very time when this eulogium was in process of delivery in the small crowded room in Somerset House, another astronomer was actually dealing with the remaining questions' with a still subtler refinement. Charles Eugène Delaunay had already made considerable progress with a work which was destined to throw even Hansen's admirable labours into the shade; and almost immediately after, the first volume of a large treatise on the Theory of the • Moon's Motion,' by Mons. Delaunay, appeared as a portion of the Memoirs of the Academy of Sciences of Paris, and the

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second volume followed in 1867. In these treatises an entire re-examination of all the perturbing influences that affect the moon's motions is effected, and the discussion of some of the most recondite of these influences is carried further than it ever had been before. The disturbing power is traced through 57 distinct operations, and the results are formulated into 461 distinct periodical terms. The mere details of the processes that are employed in this calculation are printed in 138 pages of the memoir. The gold medal of the Royal Astronomical Society was awarded to Mons. Delaunay, in 1870, for his 'Théorie de la Lune;' and in presenting the medal, Professor Adams, one of the greatest of living authorities on this branch of human knowledge, spoke of this great work as having been planned with admirable skill, and carried out with matchless perseverance, and as constituting an enduring scientific monument of which the age may well be proud.

The author of the elaborate and masterly calculations which were thus spoken of by Professor Adams was appointed Director of the Paris Observatory just about the period when he received the medal. Shortly after this his time was entirely occupied in his efforts to preserve the delicate and costly instruments of the Observatory from injury during the siege of Paris by the Germans. He had scarcely resumed the routine of his official duties after the close of the Franco-German war, when he was snatched from the sphere of his distinguished labours by the upsetting of a pleasure-boat in the Bay of Cherbourg. His death from this lamentable accident occurred on the 5th of August, 1872. The third volume of his Theory of the 'Moon,' which would have contained his tables of the moon's movements, perfected by his own especial method of handling, has not been published. Sir George Airy speaks of the Lunar Theory of Delaunay, as a glorious work, almost superhuman in its labour, and perfect beyond others in the detailed exhi'bition of its results; ' and adds that every term in the book is more complete than it has been made by any preceding writer; but that some terms to which great interest would have attached have been lost for the present by the untimely death of the author.

Yet again, however, there is light upon the horizon, and promise that the gap which has been left by the premature death of Mons. Delaunay will be filled in by no incompetent hand. On January 9 a paper was read at a meeting of the Royal Astronomical Society by the Astronomer Royal, in which he announced that he had himself taken up the garment which had fallen from the shoulders of Mons. Delaunay, and

that he had commenced a lunar theory, in which he intended to avail himself of certain of Delaunay's fundamental expressions, and then to proceed by a new method of his own which would have the great advantage that every co-efficient throughout the process would be expressed by simple numbers, and so allow much of the labour to be carried through by mere computers of average training and skill. Sir George Airy has printed the details of this method with sufficient fulness and completeness to enable the work to be carried through by other hands, if, unfortunately, he should not be able to finish it himself. Both Mons. Delaunay and the Astronomer Royal reject one of the corrections based upon Professor Hansen's view of the action of Venus upon the moon; and after this rejection it appears that there is still a discrepancy between theory and observation, which oscillates through a long period between a retardation of 6.79 seconds and an acceleration of 4.93 seconds, which has not been traced, but which Sir George believes his method will eliminate.

Before concluding the narrative of this marvellous episode of sustained intellectual effort, it may be as well to remark that the successful observation of the transit of Venus at the close of the current year may be expected to furnish a last touch to the perfection of the lunar theory. It is anticipated that after this observation the uncertain quantity of 300,000 miles which stands at this time as a possible error in the estimate of the sun's distance, will be reduced to about 50,000 miles. If this anticipation is fulfilled, the more exact and reliable measure of the sun's distance, so secured, will have a material effect in perfecting the method of determining terrestrial longitudes, and of so giving a finer and firmer grasp upon the last residual irregularities of the moon.

Mr. Proctor's book deals largely with the question of these irregularities of the moon's movement, and it does so with a method that he has made very much his own by the ready and copious facility with which he conceives pictorial illustrations of geometrical subjects. In recent years Mr. Proctor has been almost as fertile in the production of popular works on astronomical subjects as Mr. Anthony Trollope has been in the matter of popular novels. The Sun'; Other Worlds than Ours'; The Moon'; Saturn and its Systems'; 'The Orbs around us'; Essays on Astronomy'; A New Star Atlas," and The Universe and the Coming Transits,' are some of the instances of this fecundity, which have been all produced within something like an eighth of the time that has been occupied by Mr. Nasmyth in preparing his monograph on the moon. geometrical part of Mr. Proctor's book comprises about 160

The

pages, and these pages are illustrated by a series of sixty-five clever geometrical designs, which look, many of them, like the elaborate and beautiful figures produced by amateur turners who delight in eccentric chucks. In reference to this part of his book, and in explanation of his own purpose in regard to it, Mr. Proctor says:

'I propose to endeavour in this place to present the subject in a merely popular, yet exact manner. I wish the reader to see, not merely how the law of gravity accounts for the more obvious features of the moon's motion, but also how her peculiarities of motion-her perturbations are explained by the law of attraction. On the one hand the Scylla of too great simplicity is to be avoided, lest the reader should be left with the impression that the evidence for the law of gravity is not so complete as it actually is; on the other hand the Charybdis of complexity must be escaped from, lest the general reader be deterred altogether from the investigation of a subject which is not only extremely important, but in reality full of interest. I invite the general student to notice in the first instance that the whole of the following line of argument must be attentively followed. If a single paragraph be omitted, or slurred over, what follows will forthwith become perplexing. But I believe I can promise him that with this sole proviso he will meet with no difficulties of an important nature.'

The reader of these pages of geometrical demonstration is certainly safe from the rock that Mr. Proctor speaks of. After the clever ingenuity in the construction of such illustrations which has been alluded to, the next characteristic of Mr. Proctor's work is unquestionably sufficiency and accuracy in matters of scientific detail. In this particular he stands almost without a rival among copious writers on popular science. Whether the reader is also as safe from the whirlpool of the mid-passage it is not equally easy to say; but if he does find himself ultimately sucked into the Charybdis of complexity, the untoward result will at least be more due to the unalterable and unavoidable intricacy of the channel than to inefficiency in the sailing directions. The plain and unreserved truth of the matter is that any reader who can follow to the end this neat and clever piece of consecutive geometrical reasoning, must possess a certain amount of mathematical aptitude, and must have had some measure of technical training. The accomplished geometrician's idea of the purely popular' unfortunately varies considerably in some particulars from the idea of the same attribute that is entertained by the general run of fairly educated men. If the reader succeed in mastering this explanation of a very complicated subject, without foundering in the midway whirlpool, he will have good reason to be satisfied with the result of his adventurous voyage.

The most original, and perhaps most successful part of Mr.