Perhaps an apology is due to the reader for my venturing to devote a chapter to my own efforts in the scientific line. If so, I scarcely know what apology to make, unless it is that one naturally feels interested in matters relating to his own work, and hopes to share that interest with his readers, and that it is easier for one to write such an account for himself than for any one else to do it for him.

Having determined to devote my life to the prosecution of exact astronomy, the first important problem which I took up, while at Cambridge, was that of the zone of minor planets, frequently called asteroids, revolving between the orbits of Mars and Jupiter. It was formerly supposed that these small bodies might be fragments of a large planet which had been shattered by a collision or explosion. If such were the case, the orbits would, for a time at least, all pass through the point at which the explosion occurred. When only three or four were known, it was supposed that they did pass nearly through the same point. When this was found not to be the case, the theory of an explosion was in no way weakened, because, owing to the gradual changes in the form and position of the orbits, produced by the attraction of the larger planets, these orbits would all move away from the point of intersection, and, in the course of thousands of years, be so mixed up that no connection could be seen between them. This result was that nothing could be said upon the subject except that, if the catastrophe ever did occur, it must have been many thousand years ago. The fact did not in any way militate against the theory because, in view of the age of the universe, the explosion might as well have occurred hundreds of thousands or even millions of years ago as yesterday. To settle the question, general formulÆ must be found by which the positions of these orbits could be determined at any time in the past, even hundreds of thousands of years back. The general methods of doing this were known, but no one had applied them to the especial case of these little planets. Here, then, was an opportunity of tracing back the changes in these orbits through thousands of centuries in order to find whether, at a certain epoch in the past, so great a cataclysm had occurred as the explosion of a world. Were such the case, it would be possible almost to set the day of the occurrence. How great a feat would it be to bring such an event at such a time to light!

I soon found that the problem, in the form in which it had been attacked by previous mathematicians, involved no serious difficulty. At the Springfield meeting of the American Association for the Advancement of Science, in 1859, I read a paper explaining the method, and showed by a curve on the blackboard the changes in the orbit of one of the asteroids for a period, I think, of several hundred thousand years,—"beyond the memory of the oldest inhabitants"—said one of the local newspapers. A month later it was extended to three other asteroids, and the result published in the "Astronomical Journal." In the following spring, 1860, the final results of the completed work were communicated to the American Academy of Arts and Sciences in a paper "On the Secular Variations and Mutual Relations of the Orbits of the Asteroids." The question of the possible variations in the orbits and the various relations amongst them were here fully discussed. One conclusion was that, so far as our present theory could show, the orbits had never passed through any common point of intersection.

The whole trend of thought and research since that time has been toward the conclusion that no such cataclysm as that looked for ever occurred, and that the group of small planets has been composed of separate bodies since the solar system came into existence. It was, of course, a great disappointment not to discover the cataclysm, but next best to finding a thing is showing that it is not there. This, it may be remarked, was the first of my papers to attract especial notice in foreign scientific journals, though I had already published several short notes on various subjects in the "Astronomical Journal."

At this point I may say something of the problems of mathematical astronomy in the middle of the last century. It is well known that we shall at least come very near the truth when we say that the planets revolve around the sun, and the satellites around their primaries according to the law of gravitation. We may regard all these bodies as projected into space, and thus moving according to laws similar to that which governs the motion of a stone thrown from the hand. If two bodies alone were concerned, say the sun and a planet, the orbit of the lesser around the greater would be an ellipse, which would never change its form, size, or position. That the orbits of the planets and asteroids do change, and that they are not exact ellipses, is due to their attraction upon each other. The question is, do these mutual attractions completely explain all the motions down to the last degree of refinement? Does any world move otherwise than as it is attracted by other worlds?

Two different lines of research must be brought to bear on the question thus presented. We must first know by the most exact and refined observations that the astronomer can make exactly how a heavenly body does move. Its position, or, as we cannot directly measure distance, its direction from us, must be determined as precisely as possible from time to time. Its course has been mapped out for it in advance by tables which are published in the "Astronomical Ephemeris," and we may express its position by its deviation from these tables. Then comes in the mathematical problem how it ought to move under the attraction of all other heavenly bodies that can influence its motion. The results must then be compared, in order to see to what conclusion we may be led.

This mathematical side of the question is of a complexity beyond the powers of ordinary conception. I well remember that when, familiar only with equations of algebra, I first looked into a book on mechanics, I was struck by the complexity of the formulÆ. But this was nothing to what one finds when he looks into a work on celestial mechanics, where a single formula may fill a whole chapter. The great difficulty arises from the fact that the constant action upon a planet exerted at every moment of time through days and years by another planet affects its motion in all subsequent time. The action of Jupiter upon our earth this morning changes its motion forever, just as a touch upon a ball thrown by a pitcher will change the direction of the ball through its whole flight.

The wondrous perfection of mathematical research is shown by the fact that we can now add up, as it were, all these momentary effects through years and centuries, with a view of determining the combined result at any one moment. It is true that this can be done only in an imperfect way, and at the expense of enormous labor; but, by putting more and more work into it, investigating deeper and deeper, taking into account smaller and smaller terms of our formulÆ, and searching for the minutest effects, we may gradually approach, though we may never reach, absolute exactness. Here we see the first difficulty in reaching a definite conclusion. One cannot be quite sure that a deviation is not due to some imperfection in mathematical method until he and his fellows have exhausted the subject so thoroughly as to show that no error is possible. This is hard indeed to do.

Taking up the question on the observational side, a source of difficulty and confusion at once presented itself. The motions of a heavenly body from day to day and year to year are mapped out by comparative observations on it and on the stars. The question of the exact positions of the stars thus comes in. In determining these positions with the highest degree of precision, a great variety of data have to be used. The astronomer cannot reach a result by a single step, nor by a hundred steps. He is like a sculptor chiseling all the time, trying to get nearer and nearer the ideal form of his statue, and finding that with every new feature he chisels out, a defect is brought to light in other features. The astronomer, when he aims at the highest mathematical precision in his results, finds Nature warring with him at every step, just as if she wanted to make his task as difficult as possible. She alters his personal equation when he gets tired, makes him see a small star differently from a bright one, gives his instrument minute twists with heat and cold, sends currents of warm or cold air over his locality, which refract the rays of light, asks him to keep the temperature in which he works the same as that outside, in order to avoid refraction when the air enters his observing room, and still will not let him do it, because the walls and everything inside the room, being warmed up during the day, make the air warmer than it is outside. With all these obstacles which she throws in his way he must simply fight the best he can, exerting untiring industry to eliminate their effects by repeated observations under a variety of conditions.

A necessary conclusion from all this is that the work of all observing astronomers, so far as it could be used, must be combined into a single whole. But here again difficulties are met at every step. There has been, in times past, little or no concert of action among astronomers at different observatories. The astronomers of each nation, perhaps of each observatory, to a large extent, have gone to work in their own way, using discordant data, perhaps not always rigidly consistent, even in the data used in a single establishment. How combine all the astronomical observations, found scattered through hundreds of volumes, into a homogeneous whole?

What is the value of such an attempt? Certainly if we measure value by the actual expenditure of nations and institutions upon the work, it must be very great. Every civilized nation expends a large annual sum on a national observatory, while a still greater number of such institutions are supported at corporate expense. Considering that the highest value can be derived from their labors only by such a combination as I have described, we may say the result is worth an important fraction of what all the observatories of the world have cost during the past century.

Such was, in a general way, the great problem of exact astronomy forty or fifty years ago. Its solution required extended coÖperation, and I do not wish to give the impression that I at once attacked it, or even considered it as a whole. I could only determine to do my part in carrying forward the work associated with it.

Perhaps the most interesting and important branch of the problem concerned the motion of the moon. This had been, ever since the foundation of the Greenwich Observatory, in 1670, a specialty of that institution. It is a curious fact, however, that while that observatory supplied all the observations of the moon, the investigations based upon these observations were made almost entirely by foreigners, who also constructed the tables by which the moon's motion was mapped out in advance. The most perfect tables made were those of Hansen, the greatest master of mathematical astronomy during the middle of the century, whose tables of the moon were published by the British government in 1857. They were based on a few of the Greenwich observations from 1750 to 1850. The period began with 1750, because that was the earliest at which observations of any exactness were made. Only a few observations were used, because Hansen, with the limited computing force at his command,—only a single assistant, I believe,—was not able to utilize a great number of the observations. The rapid motion of the moon, a circuit being completed in less than a month, made numerous observations necessary, while the very large deviations in the motion produced by the attraction of the sun made the problem of the mathematical theory of that motion the most complicated in astronomy. Thus it happened that, when I commenced work at the Naval Observatory in 1861, the question whether the moon exactly followed the course laid out for her by Hansen's tables was becoming of great importance.

The same question arose in the case of the planets. So from a survey of the whole field, I made observations of the sun, moon, and planets my specialty at the observatory. If the astronomical reader has before him the volume of observations for 1861, he will, by looking at pages 366-440, be able to infer with nearly astronomical precision the date when I reported for duty.

For a year or two our observations showed that the moon seemed to be falling a little behind her predicted motion. But this soon ceased, and she gradually forged ahead in a much more remarkable way. In five or six years it was evident that this was becoming permanent; she was a little farther ahead every year. What could it mean? To consider this question, I may add a word to what I have already said on the subject.

In comparing the observed and predicted motion of the moon, mathematicians and astronomers, beginning with Laplace, have been perplexed by what are called "inequalities of long period." For a number of years, perhaps half a century, the moon would seem to be running ahead, and then she would gradually relax her speed and fall behind. Laplace suggested possible causes, but could not prove them. Hansen, it was supposed, had straightened out the tangle by showing that the action of Venus produced a swinging of this sort in the moon; for one hundred and thirty years she would be running ahead and then for one hundred and thirty years more falling back again, like a pendulum. Two motions of this sort were combined together. They were claimed to explain the whole difficulty. The moon, having followed Hansen's theory for one hundred years, would not be likely to deviate from it. Now, it was deviating. What could it mean?

Taking it for granted, on Hansen's authority, that his tables represented the motions of the moon perfectly since 1750, was there no possibility of learning anything from observations before that date? As I have already said, the published observations with the usual instruments were not of that refined character which would decide a question like this. But there is another class of observations which might possibly be available for the purpose.

Millions of stars, visible with large telescopes, are scattered over the heavens; tens of thousands are bright enough to be seen with small instruments, and several thousand are visible to any ordinary eye. The moon, in her monthly course around the heavens, often passes over a star, and of course hides it from view during the time required for the passage. The great majority of stars are so small that their light is obscured by the effulgence of the moon as the latter approaches them. But quite frequently the star passed over is so bright that the exact moment when the moon reaches it can be observed with the utmost precision. The star then disappears from view in an instant, as if its light were suddenly and absolutely extinguished. This is called an occultation. If the moment at which the disappearance takes place is observed, we know that at that instant the apparent angle between the centre of the moon and the star is equal to the moon's semi-diameter. By the aid of a number of such observations, the path of the moon in the heavens, and the time at which she arrives at each point of the path, can be determined. In order that the determination may be of sufficient scientific precision, the time of the occultation must be known within one or two seconds; otherwise, we shall be in doubt how much of the discrepancy may be due to the error of the observation, and how much to the error of the tables.

Occultations of some bright stars, such as Aldebaran and Antares, can be observed by the naked eye; and yet more easily can those of the planets be seen. It is therefore a curious historic fact that there is no certain record of an actual observation of this sort having been made until after the commencement of the seventeenth century. Even then the observations were of little or no use, because astronomers could not determine their time with sufficient precision. It was not till after the middle of the century, when the telescope had been made part of astronomical instruments for finding the altitude of a heavenly body, and after the pendulum clock had been invented by Huyghens, that the time of an occultation could be fixed with the required exactness. Thus it happens that from 1640 to 1670 somewhat coarse observations of the kind are available, and after the latter epoch those made by the French astronomers become almost equal to the modern ones in precision.

The question that occurred to me was: Is it not possible that such observations were made by astronomers long before 1750? Searching the published memoirs of the French Academy of Sciences and the Philosophical Transactions, I found that a few such observations were actually made between 1660 and 1700. I computed and reduced a few of them, finding with surprise that Hansen's tables were evidently much in error at that time. But neither the cause, amount, or nature of the error could be well determined without more observations than these. Was it not possible that these astronomers had made more than they published? The hope that material of this sort existed was encouraged by the discovery at the Pulkowa Observatory of an old manuscript by the French astronomer Delisle, containing some observations of this kind. I therefore planned a thorough search of the old records in Europe to see what could be learned.

The execution of this plan was facilitated by the occurrence, in December, 1870, of an eclipse of the sun in Spain and along the Mediterranean. A number of parties were going out from this country to observe it, two of which were fitted out at the Naval Observatory. I was placed in charge of one of these, consisting, practically, of myself. The results of my observation would be of importance in the question of the moon's motion, but, although the eclipse was ostensibly the main object, the proposed search of the records was what I really had most in view. In Paris was to be found the most promising mine; but the Franco-Prussian war was then going on, and I had to wait for its termination. Then I made a visit to Paris, which will be described in a later chapter.

At the observatory the old records I wished to consult were placed at my disposal, with full liberty not only to copy, but to publish anything of value I could find in them. The mine proved rich beyond the most sanguine expectation. After a little prospecting, I found that the very observations I wanted had been made in great numbers by the Paris astronomers, both at the observatory and at other points in the city.

And how, the reader may ask, did it happen that these observations were not published by the astronomers who made them? Why should they have lain unused and forgotten for two hundred years? The answer to these questions is made plain enough by an examination of the records. The astronomers had no idea of the possible usefulness and value of what they were recording. So far as we can infer from their work, they made the observations merely because an occultation was an interesting thing to see; and they were men of sufficient scientific experience and training to have acquired the excellent habit of noting the time at which a phenomenon was observed. But they were generally satisfied with simply putting down the clock time. How they could have expected their successors to make any use of such a record, or whether they had any expectations on the subject, we cannot say with confidence. It will be readily understood that no clocks of the present time (much less those of two hundred years ago) run with such precision that the moment read from the clock is exact within one or two seconds. The modern astronomer does not pretend to keep his clock correct within less than a minute; he determines by observation how far it is wrong, on each date of observation, and adds so much to the time given by the clock, or subtracts it, as the case may be, in order to get the correct moment of true time. In the case of the French astronomers, the clock would frequently be fifteen minutes or more in error, for the reason that they used apparent time, instead of mean time as we do. Thus when, as was often the case, the only record found was that, at a certain hour, minute, and second, by a certain clock, une Étoile se cache par la lune, a number of very difficult problems were presented to the astronomer who was to make use of the observations two centuries afterward. First of all, he must find out what the error of the clock was at the designated hour, minute, and second; and for this purpose he must reduce the observations made by the observer in order to determine the error. But it was very clear that the observer did not expect any successor to take this trouble, and therefore did not supply him with any facilities for so doing. He did not even describe the particular instrument with which the observations were made, but only wrote down certain figures and symbols, of a more or less hieroglyphic character. It needed much comparison and examination to find out what sort of an instrument was used, how the observations were made, and how they should be utilized for the required purpose.

Generally the star which the moon hid was mentioned, but not in all cases. If it was not, the identification of the star was a puzzling problem. The only way to proceed was to calculate the apparent position of the centre of the moon as seen by an observer at the Paris Observatory, at the particular hour and minute of the observation. A star map was then taken; the points of a pair of dividers were separated by the length of the moon's radius, as it would appear on the scale of the map; one point of the dividers was put into the position of the moon's centre on the map, and with the other a circle was drawn. This circle represented the outline of the moon, as it appeared to the observer at the Paris Observatory, at the hour and minute in question, on a certain day in the seventeenth century. The star should be found very near the circumference of the circle, and in nearly all cases a star was there.

Of course all this could not be done on the spot. What had to be done was to find the observations, study their relations and the method of making them, and copy everything that seemed necessary for working them up. This took some six weeks, but the material I carried away proved the greatest find I ever made. Three or four years were spent in making all the calculations I have described. Then it was found that seventy-five years were added, at a single step, to the period during which the history of the moon's motion could be written. Previously this history was supposed to commence with the observations of Bradley, at Greenwich, about 1750; now it was extended back to 1675, and with a less degree of accuracy thirty years farther still. Hansen's tables were found to deviate from the truth, in 1675 and subsequent years, to a surprising extent; but the cause of the deviation is not entirely unfolded even now.

During the time I was doing this work, Paris was under the reign of the Commune and besieged by the national forces. The studies had to be made within hearing of the besieging guns; and I could sometimes go to a window and see flashes of artillery from one of the fortifications to the south. Nearly every day I took a walk through the town, occasionally as far as the Arc. As my observations during these walks have no scientific value, I shall postpone an account of what I saw to another chapter.

One curious result of this work is that the longitude of the moon may now be said to be known with greater accuracy through the last quarter of the seventeenth century than during the ninety years from 1750 to 1840. The reason is that, for this more modern period, no effective comparison has been made between observations and Hansen's tables.

Just as this work was approaching completion I was called upon to decide a question which would materially influence all my future activity. The lamented death of Professor Winlock in 1875 left vacant the directorship of the Harvard Observatory. A month or two later I was quite taken by surprise to receive a letter from President Eliot tendering me this position. I thus had to choose between two courses. One led immediately to a professorship in Harvard University, with all the distinction and worldly advantages associated with it, including complete freedom of action, an independent position, and the opportunity of doing such work as I deemed best with the limited resources at the disposal of the observatory. On the other hand was a position to which the official world attached no importance, and which brought with it no worldly advantages whatever.

I first consulted Mr. Secretary Robeson on the matter. The force with which he expressed himself took me quite by surprise. "By all means accept the place; don't remain in the government service a day longer than you have to. A scientific man here has no future before him, and the quicker he can get away the better." Then he began to descant on our miserable "politics" which brought about such a state of things.

Such words, coming from a sagacious head of a department who, one might suppose, would have been sorry to part with a coadjutor of sufficient importance to be needed by Harvard University, seemed to me very suggestive. And yet I finally declined the place, perhaps unwisely for myself, though no one who knows what the Cambridge Observatory has become under Professor Pickering can feel that Harvard has any cause to regret my decision. An apology for it on my own behalf will seem more appropriate.

On the Cambridge side it must be remembered that the Harvard Observatory was then almost nothing compared with what it is now. It was poor in means, meagre in instrumental outfit, and wanting in working assistants; I think the latter did not number more than three or four, with perhaps a few other temporary employees. There seemed little prospect of doing much.

On the Washington side was the fact that I was bound to Washington by family ties, and that, if Harvard needed my services, surely the government needed them much more. True, this argument was, for the time, annulled by the energetic assurance of Secretary Robeson, showing that the government felt no want of any one in its service able to command a university professorship. But I was still pervaded by the optimism of youth in everything that concerned the future of our government, and did not believe that, with the growth of intelligence in our country, an absence of touch between the scientific and literary classes on the one side, and "politics" on the other, could continue. In addition to this was the general feeling by which I have been actuated from youth—that one ought to choose that line of activity for which Nature had best fitted him, trusting that the operation of moral causes would, in the end, right every wrong, rather than look out for place and preferment. I felt that the conduct of government astronomy was that line of activity for which I was best fitted, and that, in the absence of strong reason to the contrary, it had better not be changed. In addition to these general considerations was the special point that, in the course of a couple of years, the directorship of the Nautical Almanac would become vacant, and here would be an unequaled opportunity for carrying on the work in mathematical astronomy I had most at heart. Yet, could I have foreseen that the want of touch which I have already referred to would not be cured, that I should be unable to complete the work I had mapped out before my retirement, or to secure active public interest in its continuance, my decision would perhaps have been different.

On September 15, 1877, I took charge of the Nautical Almanac Office. The change was one of the happiest of my life. I was now in a position of recognized responsibility, where my recommendations met with the respect due to that responsibility, where I could make plans with the assurance of being able to carry them out, and where the countless annoyances of being looked upon as an important factor in work where there was no chance of my being such would no longer exist. Practically I had complete control of the work of the office, and was thus, metaphorically speaking, able to work with untied hands. It may seem almost puerile to say this to men of business experience, but there is a current notion, spread among all classes, that because the Naval Observatory has able and learned professors, therefore they must be able to do good and satisfactory work, which may be worth correcting.

I found my new office in a rather dilapidated old dwelling-house, about half a mile or less from the observatory, in one of those doubtful regions on the border line between a slum and the lowest order of respectability. If I remember aright, the only occupants of the place were the superintendent, my old friend Mr. Loomis, senior assistant, who looked after current business, a proof-reader and a messenger. All the computers, including even one copyist, did their work at their homes.

A couple of changes had to be made in the interest of efficiency. The view taken of one of these may not only interest the reader, but give him an idea of what people used to think of government service before the era of civil service reform. The proof-reader was excellent in every respect except that of ability to perform his duty. He occupied a high position, I believe, in the Grand Army of the Republic, and thus wielded a good deal of influence. When his case was appealed to the Secretary of the Navy, apellant was referred to me. I stated the trouble to counsel,—he did not appear to see figures, or be able to distinguish whether they were right or wrong, and therefore was useless as a proof-reader.

"It is not his fault," was the reply; "he nearly lost his eyesight in the civil war, and it is hard for him to see at all." In the view of counsel that explanation ought to have settled the case in his favor. It did not, however, but "influence" had no difficulty in making itself more successful in another field.

Among my first steps was that of getting a new office in the top of the Corcoran Building, then just completed. It was large and roomy enough to allow quite a number of assistants around me.

Much of the work was then, as now, done by the piece, or annual job, the computers on it very generally working at their homes. This offers many advantages for such work; the government is not burdened with an officer who must be paid his regular monthly salary whether he supplies his work or not, and whom it is unpleasant and difficult to get rid of in case of sickness or breakdown of any sort. The work is paid for when furnished, and the main trouble of administration saved. It is only necessary to have a brief report from time to time, showing that the work is actually going on.

I began with a careful examination of the relation of prices to work, making an estimate of the time probably necessary to do each job. Among the performers of the annual work were several able and eminent professors at various universities and schools. I found that they were being paid at pretty high professional prices. I recall with great satisfaction that I was able to reduce the prices and, step by step, concentrate all the work in Washington, without detriment to the pleasant relations I sustained with these men, some of them old and intimate friends. These economies went on increasing year by year, and every dollar that was saved went into the work of making the tables necessary for the future use of the Ephemeris.

The programme of work which I mapped out, involved, as one branch of it, a discussion of all the observations of value on the positions of the sun, moon, and planets, and incidentally, on the bright fixed stars, made at the leading observatories of the world since 1750. One might almost say it involved repeating, in a space of ten or fifteen years, an important part of the world's work in astronomy for more than a century past. Of course, this was impossible to carry out in all its completeness. In most cases what I was obliged practically to confine myself to was a correction of the reductions already made and published. Still, the job was one with which I do not think any astronomical one ever before attempted by a single person could compare in extent. The number of meridian observations on the sun, Mercury, Venus, and Mars alone numbered 62,030. They were made at the observatories of Greenwich, Paris, KÖnigsberg, Pulkowa, Cape of Good Hope,—but I need not go over the entire list, which numbers thirteen.

The other branches of the work were such as I have already described,—the computation of the formulÆ for the perturbation of the various planets by each other. As I am writing for the general reader, I need not go into any further technical description of this work than I have already done. Something about my assistants may, however, be of interest. They were too numerous to be all recalled individually. In fact, when the work was at its height, the office was, in the number of its scientific employees, nearly on an equality with the three or four greatest observatories of the world.

One of my experiences has affected my judgment on the general morale of the educated young men of our country. In not a single case did I ever have an assistant who tried to shirk his duty to the government, nor do I think there was more than a single case in which one tried to contest my judgment of his own merits, or those of his work. I adopted the principle that promotion should be by merit rather than by seniority, and my decisions on that matter were always accepted without complaint. I recall two men who voluntarily resigned when they found that, through failure of health or strength, they were unable to properly go on with their work. In frankness I must admit that there was one case in which I had a very disagreeable contest in getting rid of a learned gentleman whose practical powers were so far inferior to his theoretical knowledge that he was almost useless in the office. He made the fiercest and most determined fight in which I was ever engaged, but I must, in justice to all concerned, say that his defect was not in will to do his work but in the requisite power. Officially I was not without fault, because, in the press of matters requiring my attention, I had entrusted too much to him, and did not discover his deficiencies until some mischief had been done.

Perhaps the most eminent and interesting man associated with me during this period was Mr. George W. Hill, who will easily rank as the greatest master of mathematical astronomy during the last quarter of the nineteenth century. The only defect of his make-up of which I have reason to complain is the lack of the teaching faculty. Had this been developed in him, I could have learned very much from him that would have been to my advantage. In saying this I have one especial point in mind. In beginning my studies in celestial mechanics, I lacked the guidance of some one conversant with the subject on its practical side. Two systems of computing planetary perturbations had been used, one by Leverrier, while the other was invented by Hansen. The former method was, in principle, of great simplicity, while the latter seemed to be very complex and even clumsy. I naturally supposed that the man who computed the direction of the planet Neptune before its existence was known, must be a master of the whole subject, and followed the lines he indicated. I gradually discovered the contrary, and introduced modified methods, but did not entirely break away from the old trammels. Hill had never been bound by them, and used Hansen's method from the beginning. Had he given me a few demonstrations of its advantages, I should have been saved a great deal of time and labor.

The part assigned to Hill was about the most difficult in the whole work,—the theory of Jupiter and Saturn. Owing to the great mass of these "giant planets," the inequalities of their motion, especially in the case of Saturn, affected by the attraction of Jupiter, is greater than in the case of the other planets. Leverrier failed to attain the necessary exactness in his investigation of their motion. Hill had done some work on the subject at his home in Nyack Turnpike before I took charge of the office. He now moved to Washington, and seriously began the complicated numerical calculations which his task involved. I urged that he should accept the assistance of less skilled computers; but he declined it from a desire to do the entire work himself. Computers to make the duplicate computations necessary to guard against accidental numerical errors on his part were all that he required. He labored almost incessantly for about ten years, when he handed in the manuscript of what now forms Volume IV. of the "Astronomical Papers."

A pleasant incident occurred in 1884, when the office was honored by a visit from Professor John C. Adams of England, the man who, independently of Leverrier, had computed the place of Neptune, but failed to receive the lion's share of the honor because it happened to be the computations of the Frenchman and not his which led immediately to the discovery of the planet. It was of the greatest interest to me to bring two such congenial spirits as Adams and Hill together.

It would be difficult to find a more impressive example than that afforded by Hill's career, of the difficulty of getting the public to form and act upon sane judgments in such cases as his. The world has the highest admiration for astronomical research, and in this sentiment our countrymen are foremost. They spend hundreds of thousands of dollars to promote it. They pay good salaries to professors who chance to get a certain official position where they may do good work. And here was perhaps the greatest living master in the highest and most difficult field of astronomy, winning world-wide recognition for his country in the science, and receiving the salary of a department clerk. I never wrestled harder with a superior than I did with Hon. R. W. Thompson, Secretary of the Navy, about 1880, to induce him to raise Mr. Hill's salary from $1200 to $1400. It goes without saying that Hill took even less interest in the matter than I did. He did not work for pay, but for the love of science. His little farm at Nyack Turnpike sufficed for his home, and supplied his necessities so long as he lived there, and all he asked in Washington was the means of going on with his work. The deplorable feature of the situation is, that this devotion to his science, instead of commanding due recognition on the public and official side, rather tended to create an inadequate impression of the importance of what he was doing. That I could not secure for him at least the highest official consideration is among the regretful memories of my official life.

Although, so far as the amount of labor is concerned, Mr. Hill's work upon Jupiter and Saturn is the most massive he ever undertook, his really great scientific merit consists in the development of a radically new method of computing the inequalities of the moon's motion, which is now being developed and applied by Professor E. W. Brown. His most marked intellectual characteristic is the eminently practical character of his researches. He does not aim so much at elegant mathematical formulÆ, as to determine with the greatest precision the actual quantities of which mathematical astronomy stands in need. In this direction he has left every investigator of recent or present time far in the rear.

After the computations on Jupiter and Saturn were made, it was necessary to correct their orbits and make tables of their motions. This work I left entirely in Mr. Hill's hands, the only requirement being that the masses of the planets and other data which he adopted should be uniform with those I used in the rest of the work. His tables were practically completed in manuscript at the beginning of 1892. When they were through, doubtless feeling, as well he might, that he had done his whole duty to science and the government, Mr. Hill resigned his office and returned to his home. During the summer he paid a visit to Europe, and visiting the Cambridge University, was honored with the degree of Doctor of Laws, along with a distinguished company, headed by the Duke of Edinburgh. One of the pleasant things to recall was that, during the fifteen years of our connection, there was never the slightest dissension or friction between us.

I may add that the computations which he made on the theory of Jupiter and Saturn are all preserved complete and in perfect form at the Nautical Almanac Office, so that, in case any question should arise respecting them in future generations, the point can be cleared up by an inspection.

In 1874, three years before I left the observatory, I was informed by Dr. Henry Draper that he had a mechanical assistant who showed great fondness for and proficiency in some work in mathematical astronomy. I asked to see what he was doing, and received a collection of papers of a remarkable kind. They consisted mainly of some of the complicated developments of celestial mechanics. In returning them I wrote to Draper that, when I was ready to begin my work on the planetary theories, I must have his man,—could he possibly be spared? But he came to me before the time, while I was carrying on some investigations with aid afforded by the Smithsonian Institution. Of course, when I took charge of the Nautical Almanac Office, he was speedily given employment on its work. His name was John Meier, a Swiss by birth, evidently from the peasant class, but who had nevertheless been a pupil of Professor Rudolph Wolf at Zurich. Emigrating to this country, he was, during the civil war, an engineer's mate or something of that grade in the navy. He was the most perfect example of a mathematical machine that I ever had at command. Of original power,—the faculty of developing new methods and discovering new problems, he had not a particle. Happily for his peace of mind, he was totally devoid of worldly ambition. I had only to prepare the fundamental data for him, explain what was wanted, write down the matters he was to start with, and he ground out day after day the most complicated algebraic and trigonometrical computations with untiring diligence and almost unerring accuracy.

But a dark side of the picture showed itself very suddenly and unexpectedly in a few years. For the most selfish reasons, if for no others, I desired that his peace of mind should be undisturbed. The result was that I was from time to time appealed to as an arbitrator of family dissensions, in which it was impossible to say which side was right and which wrong. Then, as a prophylactic against malaria, his wife administered doses of whiskey. The rest of the history need not be told. It illustrates the maxim that "blood will tell," which I fear is as true in scientific work as in any other field of human activity.

A man of totally different blood, the best in fact, entered the office shortly before Meier broke down. This was Mr. Cleveland Keith, son of Professor Reuel Keith, who was one of the professors at the observatory when it was started. His patience and ability led to his gradually taking the place of a foreman in supervising the work pertaining to the reduction of the observations, and the construction of the tables of the planets. Without his help, I fear I should never have brought the tables to a conclusion. He died in 1896, just as the final results of the work were being put together.

High among the troublesome problems with which I had to deal while in charge of the Nautical Almanac, was that of universal time. All but the youngest of my readers will remember the period when every railway had its own meridian, by the time of which its trains were run, which had to be changed here and there in the case of the great trunk lines, and which seldom agreed with the local time of a place. In the Pennsylvania station at Pittsburg were three different times; one that of Philadelphia, one of some point farther west, and the third the local Pittsburg time. The traveler was constantly liable to miss a train, a connection, or an engagement by the doubt and confusion thus arising.

This was remedied in 1883 by the adoption of our present system of standard times of four different meridians, the introduction of which was one of the great reforms of our generation. When this change was made, I was in favor of using Washington time as the standard, instead of going across the ocean to Greenwich for a meridian. But those who were pressing the measure wanted to have a system for the whole world, and for this purpose the meridian of Greenwich was the natural one. Practically our purpose was served as well by the Greenwich meridian as it would have been by that of Washington.

The year following this change an international meridian conference was held at Washington, on the invitation of our government, to agree upon a single prime meridian to be adopted by the whole world in measuring longitudes and indicating time.

Of course the meridian of Greenwich was the only one that would answer the purpose. This had already been adopted by several leading maritime nations, including ourselves as well as Great Britain. It was merely a question of getting the others to fall into line. No conference was really necessary for this purpose, because the dissentients caused much more inconvenience to themselves than to any one else by their divergent practice. The French held out against the adoption of the Greenwich meridian, and proposed one passing through Behring Strait. I was not a member of the conference, but was invited to submit my views, which I did orally. I ventured to point out to the Frenchmen that the meridian of Greenwich also belonged to France, passing near Havre and intersecting their country from north to south. It was therefore as much a French as an English meridian, and could be adopted without any sacrifice of national position. But they were not convinced, and will probably hold out until England adopts the metric system, on which occasion it is said that they will be prepared to adopt the Greenwich meridian.

One proceeding of the conference illustrates a general characteristic of reformers. Almost without debate, certainly without adequate consideration, the conference adopted a recommendation that astronomers and navigators should change their system of reckoning time. Both these classes have, from time immemorial, begun the day at noon, because this system was most natural and convenient, when the question was not that of a measure of time for daily life, but simply to indicate with mathematical precision the moment of an event. Navigators had begun the day at noon, because the observations of the sun, on which the latitude of a ship depends, are necessarily made at noon, and the run of the ship is worked up immediately afterward. The proposed change would have produced unending confusion in astronomical nomenclature, owing to the difficulty of knowing in all cases which system of time was used in any given treatise or record of observations. I therefore felt compelled, in the general interest of science and public convenience, to oppose the project with all my power, suggesting that, if the new system must be put into operation, we should wait until the beginning of a new century.

"I hope you will succeed in having its adoption postponed until 1900," wrote Airy to me, "and when 1900 comes, I hope you will further succeed in having it again postponed until the year 2000."

The German official astronomers, and indeed most of the official ones everywhere, opposed the change, but the efforts on the other side were vigorously continued. The British Admiralty was strongly urged to introduce the change into the Nautical Almanac, and the question of doing this was warmly discussed in various scientific journals.

One result of this movement was that, in 1886, Rear-Admiral George H. Belknap, superintendent of the Naval Observatory, and myself were directed to report on the question. I drew up a very elaborate report, discussing the subject especially in its relations to navigation, pointing out in the strongest terms I could the danger of placing in the hands of navigators an almanac in which the numbers were given in a form so different from that to which they were accustomed. If they chanced to forget the change, the results of their computations might be out to any extent, to the great danger and confusion of their reckoning, while not a solitary advantage would be gained by it.

There is some reason to suppose that this document found its way to the British Admiralty, but I never heard a word further on the subject except that it ceased to be discussed in London. A few years later some unavailing efforts were made to revive the discussion, but the twentieth century is started without this confusing change being introduced into the astronomical ephemerides and nautical almanacs of the world, and navigators are still at liberty to practice the system they find most convenient.

In 1894 I had succeeded in bringing so much of the work as pertained to the reduction of the observations and the determination of the elements of the planets to a conclusion. So far as the larger planets were concerned, it only remained to construct the necessary tables, which, however, would be a work of several years.

With the year 1896 came what was perhaps the most important event in my whole plan. I have already remarked upon the confusion which pervaded the whole system of exact astronomy, arising from the diversity of the fundamental data made use of by the astronomers of foreign countries and various institutions in their work. It was, I think, rather exceptional that any astronomical result was based on entirely homogeneous and consistent data. To remedy this state of things and start the exact astronomy of the twentieth century on one basis for the whole world, was one of the objects which I had mapped out from the beginning. Dr. A. M. W. Downing, superintendent of the British Nautical Almanac, was struck by the same consideration and animated by the same motive. He had especially in view to avoid the duplication of work which arose from the same computations being made in different countries for the same result, whereby much unnecessary labor was expended. The field of astronomy is so vast, and the quantity of work urgently required to be done so far beyond the power of any one nation, that a combination to avoid all such waste was extremely desirable. When, in 1895, my preliminary results were published, he took the initiative in a project for putting the idea into effect, by proposing an international conference of the directors of the four leading ephemerides, to agree upon a uniform system of data for all computations pertaining to the fixed stars. This conference was held in Paris in May, 1896. After several days of discussion, it resolved that, beginning with 1901, a certain set of constants should be used in all the ephemerides, substantially the same as those I had worked out, but without certain ulterior, though practically unimportant, modifications which I had applied for the sake of symmetry. My determination of the positions and motions of the bright fixed stars, which I had not yet completed, was adopted in advance for the same purpose, I agreeing to complete it if possible in time for use in 1901. I also agreed to make a new determination of the constant of precession, that which I had used in my previous work not being quite satisfactory. All this by no means filled the field of exact astronomy, yet what was left outside of it was of comparatively little importance for the special object in view.

More than a year after the conference I was taken quite by surprise by a vigorous attack on its work and conclusions on the part of Professor Lewis Boss, director of the Dudley Observatory, warmly seconded by Mr. S. C. Chandler of Cambridge, the editor of the "Astronomical Journal." The main grounds of attack were two in number. The time was not ripe for concluding upon a system of permanent astronomical standards. Besides this, the astronomers of the country should have been consulted before a decision was reached.

Ultimately the attack led to a result which may appear curious to the future astronomer. He will find the foreign ephemerides using uniform data worked out in the office of the "American Ephemeris and Nautical Almanac" at Washington for the years beginning with 1901. He will find that these same data, after being partially adopted in the ephemeris for 1900, were thrown out in 1901, and the antiquated ones reintroduced in the main body of the ephemeris. The new ones appear simply in an appendix.

As, under the operation of law, I should be retired from active service in the March following the conference, it became a serious question whether I should be able to finish the work that had been mapped out, as well as the planetary tables. Mr. Secretary Herbert, on his own motion so far as I know, sent for me to inquire into the subject. The result of the conference was a movement on his part to secure an appropriation somewhat less than the highest salary of a professor, to compensate me for the completion of the work after my retirement. The House Committee on Appropriations, ever mindful of economy in any new item, reduced the amount to a clerical salary. The committee of conference compromised on a mean between the two. It happened that the work on the stars was not specified in the law,—only the tables of the planets. In consequence I had no legal right to go on with the former, although the ephemerides of Europe were waiting for the results. After much trouble an arrangement was effected under which the computers on the work were not to be prohibited from consulting me in its prosecution.

Astronomical work is never really done and finished. The questions growing out of the agreement or non-agreement of the tables with observations still remain to be studied, and require an immense amount of computation. In what country and by whom these computations will be made no one can now tell. The work which I most regretted to leave unfinished was that on the motion of the moon. As I have already said, this work is complete to 1750. The computations for carrying it on from 1750 to the present time were perhaps three fourths done when I had to lay them aside. In 1902, when the Carnegie Institution was organized, it made a grant for supplying me with the computing assistance and other facilities necessary for the work, and the Secretary of the Navy allowed me the use of the old computations. Under such auspices the work was recommenced in March, 1903.

So far as I can recall, I never asked anything from the government which would in any way promote my personal interests. The only exception, if such it is, is that during the civil war I joined with other professors in asking that we be put on the same footing with other staff corps of the navy as regarded pay and rank. So far as my views were concerned, the rank was merely a pro forma matter, as I never could see any sound reason for a man pursuing astronomical duties caring to have military rank.

In conducting my office also, the utmost economy was always studied. The increase in the annual appropriations for which I asked was so small that, when I left the office in 1877, they were just about the same as they were back in the fifties, when it was first established. The necessary funds were saved by economical administration. All this was done with a feeling that, after my retirement, the satisfaction with which one could look back on such a policy would be enhanced by a feeling on the part of the representatives of the public that the work I had done must be worthy of having some pains taken to secure its continuance in the same spirit.

I do not believe that the men who conduct our own government are a whit behind the foremost of other countries in the desire to promote science. If after my retirement no special measures were deemed necessary to secure the continuance of the work in which I had been engaged, I prefer to attribute it to adventitious circumstances rather than to any undervaluation of scientific research by our authorities.