Popular Science Monthly/Volume 6/December 1874/The Transit of Venus

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THE TRANSIT OF VENUS.
By Prof. S. P. LANGLEY,

OF THE ALLEGHANY OBSERVATORY.

ON the 8th day of the present month, at a little before nine in the evening of our time, the planet Venus will be first seen entering upon the face of the sun, from that side of the earth on which it is then day, and to observe the event astronomers will have made their way from all the principal countries of the civilized world. The spectacle in itself offers nothing that is imposing; to the naked eye, indeed, nothing of it will be visible, and all that the best telescope can discern will be a small, black, circular spot moving across the upper part of the solar disk, during some four and a half hours. The interest of the occasion, as all know, lies in the rare opportunity it offers for obtaining the sun's distance from the earth; but, as it is not so well understood why this distance is wanted, why it has not been found before, and what Venus has to do with determining it now, it is proposed here to attempt to answer such questions, as fully as it can be done in general and untechnical terms, and in a single article.

The exact object to be obtained can be better understood after considering what we know about the relations of the sun and planets, and what we have yet to learn. We know already, then, with almost entire exactness, the relative distances from the sun of every planet (the earth included), so that, if we wished to make a map of the solar system, on which the position of each member should be laid down with great precision, we have already all the means at hand to do it. Let us suppose such a map to be drawn, in which circles around a central point represent the planetary orbits. Then the planets being ranged in a line from the sun, and the distance of Venus from it being let us say five inches, that of the earth will be seven, and that of Mars over ten, whence we observe that Venus is our nearest neighbor, and her distance from the sun two and a half times ours from her.

As round numbers are given only for simplicity, and as we could in fact draw such a map, with the actual elliptic orbits, in which no error would exist which a microscope could detect, it may be asked, "What more can be wanted?"

But there is a most important want unsupplied: our map has no scale, and we do not know how much an inch on it represents in actual distance. Our case, then, is like that of a person with an accurate chart of his country before him, from which he wants to find his distance from the capital. If it have no scale attached, or an erroneous one (and the latter is our own case), he cannot measure a single distance upon it.

If, however, he can ascertain the actual number of miles between any two points of the map, he will plainly know what an inch on it stands for, and thus be able to construct the lacking scale; and so we, if we can measure the distance between any two primary planets, or between any one of them (such as the earth) and the sun, have got at the same time the means of determining all the dimensions of the solar system.

A determination of the distance of any remote object, which we can see but cannot reach, whether celestial or terrestrial, the sun or a mountain-top, requires that we should know either its size and the angle it fills to the eye, or else how much the direction in which we see it changes, as we change our own position by a known amount. Thus, in the latter case, a surveyor, who wishes to determine his distance from an inaccessible object of unknown size, sends an assistant to hold up a staff at the end of a line measured on the ground by a chain. First he notes, with an instrument for the purpose, the direction in which the object is seen as compared with that of the staff, and then, the assistant and observer changing places, the latter notes again the direction from the second point of view, and this will enable him to calculate the distance desired. That first found by direct measurement with the chain is called the "base-line," and it ought to be considerable when the object is far away, since in that case its direction will not, evidently, be much altered, without a corresponding alteration in the observer's position. This difference of direction, caused by a changed point of view, is called by astronomers parallax; nearly the only professional term with which the reader need be troubled, but one which should be clearly understood.

The principle involved in the method is probably familiar to him already, but it is here recalled, to point out how its application must be modified in finding the distance of the sun. As the earth sweeps round that far-distant controller of her path, we can send no messenger in advance along our orbit to distinguish the place we shall move to later; we can leave no mark behind to denote the point in the void of space the earth has quitted. Our motion round the sun is therefore no help in finding its distance, and we may, in fact, for the sake of simplicity in illustration, treat the earth as standing still in its orbit, since the essential difficulty is thus nowise heightened. This difficulty, arising from the want of a proper base-line, is similar in degree and kind to that a surveyor would labor under, if he were called on to measure the distance of an object of unknown size at least half a mile away, without moving from his place. Success under such circumstances may well seem, not so much difficult as impossible; yet this is a fair simile of the apparent impracticability of measuring the distance of the sun without stepping beyond the limits of our little earth, a body so small by comparison with the sun's remoteness that, to an observer at that distance, a three-cent piece, held one hundred and fifty yards from the eye, would completely cover our globe and hide it from his view.

Within such narrow bounds we must work, or not work at all, and the reader, if he have not, from what he has just read, gained a definite conception of the principle on which all such distance measurement rests, may find aid in a very simple experiment. If any small object, such as a pencil, be held in front of the eyes as near as it can be conveniently seen, we may easily note the point on the opposite side of the room which it appears to cover, as viewed first by the right eye and then by the left. Though itself unmoved, it will appear to shift its place on the wall, when the latter is distant, in a notable degree, owing both to the difference of direction under which either eye views it, and the remoteness of the background, and the amount of this shifting will diminish progressively as it is carried directly away from the eyes, owing to its being now seen more nearly in the same direction by both, and to its approach to the wall. The change of direction due to the distance from the eyes only, but, this being constant, the amount of its displacement on the wall is due only to the distance of the latter, as is easily proved by walking toward it.

The distance of the wall might. conceivably be reckoned without going to it, by preparing tables which should show how this distance was proportioned to the apparent motion of the pencil on it, since one of these things evidently depends on the other, or which should tell the distance of the pencil, by the difference of direction under which we saw it. Such are the trigonometrical tables in common use, which give the distance when this change of direction and place is known. But this change as viewed by one eye or the other is the parallax of the pencil, the known distance between the eyes being a little "baseline," which plays the same part as the surveyor's longer one; and now, if we suppose ourselves in possession of tables which give the distance of any object, directly its parallax is known, we may substitute the earth for the head, two observers as far apart on it as they can get for the eyes, the sun's face for the wall, and Venus for the pencil, with a better idea of the way in which her coming between us and the sun will help to find how far off it is.

By the sun's horizontal parallax is meant that particular amount of change in its direction which would be noted by our two observers if they were half the diameter of the earth apart (as in Fig. 1, where the observer at A sees V in the direction A B, the one at C in the direction C D, and where the difference of these directions is A V C, the angle under which the earth's radius would be seen from V). At the

PSM V06 D229 Horizontal parallax.png
Fig. 1.—Horizontal Parallax.

risk of needless repetition, the reader is again asked to keep in mind that, finding an object's distance and finding its parallax are convertible terms: that when the latter is large it is easily got, and implies a short distance; that when small, it is found with difficulty, and implies great distance, and that the solar horizontal parallax is almost immeasurably small—less, whatever it is, than an angle of 9.', or than that which would be filled by a human hair over five feet from the eye. It was an error of one-thirtieth part of this last—an error less, that is, than a literal hair's-breadth seen fifty yards off—which caused the mistake of 3,000,000 miles, now known to have been made in measuring the sun's distance in 1769; and, if the reader has heard such a mistake cited to the discredit of astronomy, he is now in a position to judge of the justice of the reproach. It may be added, in the words of Sir John Herschel: "Moreover, this error has been detected, and the correction applied, and the detection and correction have originated with the friends, and not the enemies, of science."

If we briefly review the history of human effort at this problem, we find it occupying the mind of the ancient philosophy as well as the modern. Ptolemy, following Hipparchus, estimated, by an unreliable method, the solar parallax at 3.', or its distance at 1,210 semi-diameters of the earth; and this grossly erroneous value remained unimproved to the time of Kepler, with whose age modern astronomy begins. Kepler having, by life-long study, discovered a means of obtaining the proportionate distances of the planets from the sun, saw clearly that this led to a new method of finding its absolute distance; since, whatever it is, it stands in a known relation to that of Venus and Mars, either of which is easier found, owing to the comparative nearness of these planets, when in a line with the earth and sun. Venus, at this time, commonly passes above or below the sun, and in either case is lost in the surrounding brightness. Kepler left the suggestion, therefore, of the use of the latter's transit, for the benefit of the future generation in which it should occur. The parallax even of Mars turned out to be, with the means of that day, immeasurably small; but he reached from this the conclusion that the sun's still unknown distance was, at any rate, not less than 13,000,000 miles.

To see how it is that transits are so rare, we may consider the annexed diagram (Fig. 2), where the outer circle shows the orbit of the earth, and her positions in March, June, September, and December. The orbit of Venus, lying within this, would need to be represented by a ring, inclined to the plane in which the earth moves; that part of Venus's path nearest to the earth in March being above the surface of the paper, that nearest to our place in September being below it. If the planet passed in line with us and the sun between December and June, then it would appear to go above it; if between June and the following December, below it. There are two days in each year when we are crossing the line in which the planes of the two orbits cut each other. At these times the path of Venus, if it were a visible ring, would be seen like a slanting line on the sun; but, as the planet may be anywhere else on her path (as, for instance, at V2), it is evidently only under a rare conjunction of favoring circumstances that we see her passage across the sun's face (at V1), as a black circle on a brilliant background. This phenomenon, which can only, as appears from what has been said, occur in June and December, is known as the Transit of Venus.

PSM V06 D230 Orbits of venus and the earth.jpg
Fig. 2.—Orbits of Venus and the Earth.

Owing to the fact that Venus makes about thirteen revolutions in eight years, her transits frequently come in pairs eight years apart, though with an interval of over a century from one pair to the next; and thus transits have occurred in December, 1631 and 1639, in June, 1761 and 1769, and will occur in December, 1874 and 1882. That of 1631, though predicted by Kepler, passed unobserved; that of 1639 was the first known to have been seen by any one, and the circumstances of this epoch in the history of our subject deserve mention.

Jeremiah Horrocks, a young man, devoted to astronomical studies, though without counsel or support, had found from his own computations that a transit was likely to occur, though none had been looked for by others. He had time only to warn a friend of the expected event, then close at hand, and prepared himself to observe it, by forming, through a small aperture in a darkened room, an image of the sun upon a sheet of paper. This he watched continuously on the important day, a Sunday, till the time came for church. Though knowing that the opportunity, which would not occur again to any one then living, might pass in his absence, he left it for what he deemed a religious duty, and did not resume his observation till late in the afternoon. "At this time," said he, "an opening in the clouds, which rendered the sun distinctly visible, seemed as if Divine Providence encouraged my aspirations, when, oh, most gratifying spectacle! the object of so many earnest wishes! I perceived a new spot of unusual magnitude and perfectly round, which had just entered on the left limb of the sun." His friend had been equally fortunate, "and thus," says Mr. Grant, in his "History of Physical Astronomy," whence this account is taken, "did two young men, cultivating astronomy together in a state of complete seclusion in one of the northern counties of England, enjoy the privilege of witnessing a phenomenon which human eyes had never before beheld, and which no one was destined again to see till more than a hundred years had passed away." Horrocks attempted to obtain the sun's parallax, but without much success; good results from such observations requiring, as will be inferred from what has been said, to be made by a pair of observers removed from each other, nearly as far as the limits of the earth will allow.

In 1761 and 1769 astronomers were fully aware of the importance of the occasion. Special preparations were made by different European governments, especially for the latter year, when parties were sent, as now, to various portions of the illuminated hemisphere of the globe. Among the names of those employed are the familiar ones of Captain Cook, who made his first voyage to Tahiti for this purpose, and of Mason and Dixon, the surveyors of the "line" which bore their name, and which was once so frequently heard of in our own affairs.

One, who is less known, but whose singularly bad luck deserves sympathy, was Le Gentil. Sailing for Pondicherry, where he expected to observe the transit of 1761, he was unable to land, and got no other observations than such as could be made at sea. A voyage from Europe to the Indies in those days was something so formidable, that Le Gentil, who was resolved to see the transit of 1769, decided on waiting for it abroad through eight years of voluntary exile, but, by a cruelly hard fortune, when the long-expected day came, the sun was shut out from his view by clouds which had left the sky clear till the eventful occasion.

It is perhaps worth while to recall such a disappointment, to remind us that all the skill, means, and labor, which have gone to fit out the expeditions now absent, are equally liable to frustration by causes beyond human control; a contingency very remote, however, as affecting the entirety of the observers, and from which it is to be heartily hoped all will be exempted.

The results of the transit of 1769 were rendered uncertain, to some extent, by a curious attendant phenomenon called "the black drop," consisting in an apparent clinging of the planet to the limb, to which it is seemingly attached by a black ligament. The exact cause of this illusion is not quite agreed on, but there can be little doubt that it is in part a product of bad definition and inferior telescopes, and, as such, need be expected to give less trouble in our present observations of the times when the planet is really in contact with the edge. It may, however, cause an error of some seconds in noting the time, and in this particular seconds are all-important. Encke, who discussed these results, found from them that the parallax was 8."56, a value always known to be questionable; but whence the sun's distance of "95,000,000 miles," which found a place in our schoolbooks, was derived.

Within a few years past, it has become certain, by evidence from various quarters, that this is too much. Till toward the close of the last century, astronomers had no other means of finding the sun's distance than by observations on Venus and Mars; though, from those of the latter planet, indeed, a much closer approximation to the solar parallax than Kepler's value had long been obtained. Chiefly during the present century, other methods have been added, of which the most remarkable is that due to the French academician, Foucault.

Though the speed of the earth in its orbit, and that of light, were both unknown, yet the ratio of these two velocities had long been ascertained. From the assumed distance of the sun above given (95,000,000 miles), it was evidently possible to tell the circumference of the earth's orbit, and thence to say how many miles it went in a year, or a second, and, by a simple multiplication, a value for the velocity of light was obtained; since, as has just been said, the latter velocity bore a known proportion to the former. In this way, the value of 192,000 miles per second for the speed of light was found—a quantity which, being derived from an assumed distance of the sun, could not, of course, be used in turn to determine it. When, however, Foucault actually measured the velocity of light by a direct physical experiment, it became possible, by a reversal of the above process, to say how far the earth moved in a second; whence we learn how far it moves in a year, or, in other words, the length of its annual path; whence, again, the distance across it and the sun's distance obviously follow, the latter being thus found to be 92,260,000 miles, instead of 95,000,000.

From a discussion of all the different methods, Prof. Newcomb has concluded that the solar parallax cannot be far from 8".85; while Mr. Stone, from a rediscussion of the results of the transit of 1769, believes that it is nearer 8".91. The first value corresponds to a distance of 92,380,000 miles, the second to one of 91,730,000. It follows that we have heretofore made an error of about three per cent, in estimating the distances, and about ten per cent, in estimating the masses of the solar system. Neither authority regards his result as more than approximative, Prof. Newcomb, for instance, considering that his own may, as likely as not, be over a hundred thousand miles from the truth.

We get no idea from these large-sounding numbers of the all but inconceivable minuteness of the error of observation which would cause them; and such a measure of uncertainty, far from casting any discredit on the exactness of modern astronomy, is an evidence of its surprising advance toward absolute truth. Modern astronomy began with the age of Kepler; but, while the angle which represents the error in the parallax Kepler found, would correspond to that filled by the width of one of the pages of this magazine at a distance of 2,000 feet from the eye, the error now admitted as probable by Prof. Newcomb is represented by a less angle than that filled at the same distance by the same leaf turned edgewise.

 

Now that we have considered the delicacy of the measurements which have already been made, we are prepared to appreciate the task of those who, on the 8th of this month, are about to try to better them, and to examine the principles underlying the methods which will be actually used in the trial. To do this, we may, perhaps, here recur to a former illustration. If we suppose a person looking at a remote object—let us say a lighted window—from a distance which is quite half a mile, the distance between his eyes bears nearly the same relation to that of the light, that the distance between any two stations practically usable on the earth does to that of the sun. Accordingly, the difficulty of obtaining the sun's parallax, without moving: from off the earth, is the same in degree that the observer would experience in measuring the distance of the light without moving from his place, and by means of the small virtual change of his point of view, obtained by looking at it with either eye; and it is under such all but insuperably hard conditions that astronomers will actually be working this month.

To see how Venus comes to their aid, we may represent her motion by a car moving at a uniform rate on a circular track, between the light and the observer. If the car pass across the light from left to right (as Venus crosses the sun), it will of course cut off the observer's view of the left side of the window from the left eye first, and, if the motion be slow enough, we may suppose him to note the exact time before the sight of the same point by the right eye is intercepted.

If he know from previous watching how long it takes the car to make its whole circuit of 360°, he knows from his watch, by an obviously simple computation, just what part of a degree it went over in passing, or in its shadow's passing, from one eye to the other; the angle in other words, that the distance between his eyes would appear under as seen from the light. But this is the parallax of the light, and it gives him its distance at once (that between the eyes—the base-line—being known).

This suggests the principle of a method of obtaining the sun's parallax, on which the English astronomers will largely rely.

For, neglecting matters of detail, and supposing Venus to pass centrally across the sun, since she completes her revolution of 360° in 225 days, nearly, we find, on dividing 360° by the number of minutes in that period, that in one minute she moves through an arc of 4.", and dividing 360° by the number of minutes in our year, that the earth moves through 2”.46 in the same time. Hence, as Venus is gaining 1”.54 every minute, the case is the same as though the earth stood still, and the shadow of Venus (could she throw one so far) passed over the earth at that rate as seen from the sun.

Suppose an observer on the left or eastern side of the on be had his view of part of the left side of the sun intercepted by the interior planet at nine o'clock, and one placed opposite the centre of the globe (at half the earth's diameter west of the first), five and three-quarter minutes later, then, since 5¾ times 1”.54 is 8”.85, this angle 8”.85 represents the difference of directions in which the sun would be seen by the two observers, or, what is the same thing, the angle the earth's semi-diameter would fill to an eye at the sun. This is the solar parallax, and on reference to our tables we should find that such a difference of direction could only be caused by an object nearly 92,000,000 miles off. In practice, observers are not stationed at the extreme edge of the earth (as seen from the sun), because from such a station the sun itself would be seen in the horizon, where vision of it is obscured and rendered unsteady by the vapors of our atmosphere. Neither is it needful to place observers just half a diameter of the earth apart, since it is easy to allow for the effect of greater or less

PSM V06 D234 Showing the displacement of venus.jpg
Fig. 3.—Showing the Displacement of Venus.

distance, and, in reality, the time would be longer than that supposed, because Venus's path lies aslant to the sun's edge, and it takes her longer to cross it. But it will, of course, be understood that such matters as these, and such complications as arise from the elliptical form of the orbits, the real inequality of the motion, the fact of the earth's being constantly turning and changing the observers' positions whether they will or no—that such things as these, and many more, need not occupy us here, except as they suggest how excessively intricate the actual details are with which the astronomer deals.

Quite another method might be used by our imaginary observer, if we suppose him to incline his head so that one eye is higher than the other, and to be able to see over the passing car. In this case, if the lower eye had the view of the lower part of the window hidden, the other, seeing more over the car, would see somewhat farther down—how much farther down would be easily calculated if the proportionate distances of the car from the eyes and the window were known. This suggests a very important method for actual use in the transit; for, if we now have two stations, one in the north or upper side of the earth (upper to us, that is), the other in the south or lower side, it is clear that the upper observer, seeing more over Venus, so to speak, will see it as it crosses the sun at V2, nearer the centre than the observer who is in the south, and who sees it at V1. (Fig. 3).

If the northern station is 6,000 miles higher than the other, since Venus is two and a half times as far from the sun as from us, it will appear to cross nearer the centre by two and a half times 6,000, or 15,000 miles. Knowing how large an angle this 15,000 miles on the sun's face fills, we have, as it will readily be seen, the knowledge of how large an angle a line any given part of its length (such as the earth's radius) would fill as seen from this distance.

PSM V06 D235 Path of venus across the sun by different observers.jpg
Fig 4.—Path of Venus across the Sun as seen by different Observers.

But it is immaterial whether we see such a length as the earth's radius from here, when it is supposed to be laid down on the sun, or from the sun when it is here. In either case we have got the same parallax and hence the same distance.

This apparent displacement of Venus will give us two chords of a circle (Fig. 3), the shorter one being her track to the southern observer, the longer to the northern. In Fig. 4, a b is her apparent path in the first case, c d in the second. This figure shows the direction of the planet's motion, and, with approximate truth, its apparent size as compared with the sun and the decree of actual displacement. Its first appearance, touching the outside of the sun as at a, is what is called "first external contact." This is shortly followed by "first internal contact," when the planet has moved wholly on to the sun's face, and is just quitting the edge. After some four hours it touches the edge again ("second internal contact"), crosses it and disappears ("second external contact"). The external contacts have not hitherto been much relied on, but, now that with the spectroscope we can see the planet a little way off the sun, they can be better observed. The internal contacts are the important ones, and these have heretofore been rendered more or less uncertain, by the phenomenon called the "black drop," already referred to, as consisting in an optical illusion, by which the planet seems to cling to the limb and pull out of shape, like a drop of ink just about falling from the pen. (Fig. 5.)

PSM V06 D236 Portion of the sun at first internal contact of venus.jpg
Fig. 5.—A Portion of the Sun at First Internal Contact of Venus, showing the "Black-Drop."

Since there is no actual track left to reckon the distance between the chords from, the northern and southern observers time the planet across, very accurately, and, from the times, the lengths of these chords, and hence the distance between them, may plainly be found, since we know just how long the planet would take to go over the sun's diameter. There is another way, by measuring the distance, from the sun's centre, of Venus at different stages of her progress, as seen by a pair or any number of pairs of observers; but probably best of all is photography, which is to be used by nearly every station, and which will give us almost any number of pictures (as many as 150 or 200 to a station), showing exactly how the planet looked from minute to minute to the photographer's lens—an observer which does not get flurried, is perfectly impartial, and whose observations take the form of an instantaneous but permanent record.

Preparations of the most elaborate kind have been made by the leading nations of the world for this event for years beforehand; and the side of our globe, turned sunward on the important day, will be occupied by over seventy astronomical stations. As an amicable interchange of results is to be counted on, the means for trying every method here alluded to, as well as others, will be of the amplest kind; and there is every reason to hope that they will give us a value of the sun's distance, accurate in proportion to the knowledge, energy, and skill, which have gone to furnish them.

From what has been already said, it must be abundantly plain that, unlike an eclipse of the sun, which is total over a very small area, the transit of Venus will be visible over a whole hemisphere of the earth—over more, in fact, since the rotation of our globe brings new countries into the sunlight during the hours the passage lasts, and some will see it begin who will not see it close; others see it close

PSM V06 D237 Earth as seen from the sun in two consecutive days.jpg
Fig. 6.—Earth, as seen from the Sun, December 8th, at 9h.10m., p.m. New York Time. (First Internal Contact.) Fig. 7.—Earth, as seen from the Sun, December 9th. at 1h.13m., a m. New York Time. (Second Internal Contact.)

Names of American stations, as seen located in the above diagrams:

No. 1. Wladiwostock. No. 5. Bluff Harbor.
2. Pekin. 6. Chatham Island.
3. Nagasaki. 7. Kerguelen"
4. Hobarttown. 8. Possession"

who do not see it begin. While the transit continues, wherever the sun can be seen, there Venus will be seen on it, with the exception of the few minutes of entry, when those on the extreme left of the earth will see her before the rest, and the corresponding time of exit.

We do not see the phenomena at all in the United States, because all America is on the night side of the earth at the time, a fact made plainer by the accompanying diagrams, showing the earth as it is poised in space, viewed from the sun; first at the beginning of the transit (to the whole earth), and again at its close, with the effects of the earth's rotation in the interval. These diagrams are made from those prepared by Mr. Proctor (to whose admirably lucid illustrations the writer is otherwise indebted), and by Mr. Hill, under the charge of Prof. Coffin, of our own "Nautical Almanac" office; and on them have been marked the eight stations occupied by American parties. The next transit, in December, 1882, will be visible, it may be observed, from beginning to end, in the United States.

On the whole, it will appear, from what has been stated, that a transit of Venus, though not the only means of determining the sun's distance, and not possessing the relative importance it once did, remains probably the best, as it is the best known, and, if it may be so called, the most classic method.

Judging from what appears to be the probable error of our best independent determinations of the solar parallax (those from Mars), and the presumption that the majority of astronomers regard those obtainable by modern methods from Venus as still better, it is no unreasonable anticipation that the probable error of the coming result will not exceed one-hundredth of a second. In other words, it may be. expected to be at least an even wager that the error of angular measurement in the final result—made up, let us remember, from the independent results of observers working in distant parts of the globe—will not exceed that which would be represented by the breadth of a hair, seen at the distance of one mile. So slight is that error, which will seem so large when carried out in the enormous numbers which represent the distance of the sun, and those numbers still more inconceivable which represent his own distance from his brother stars.

In one of the most remarkable writings which have descended to us from ancient philosophy, the "Arenaria" of Archimedes, that geometer undertakes to show his contemporaries that it is in the power of number to reckon not only every grain of sand upon the sea-shore or even in the whole earth, but more than would fill a solid sphere extending beyond the sun; and, in the course of his demonstration, he describes to us how he attempted to find its diameter by measurements carried on with a staff and a rod, when the morning and evening mists rendered its light bearable to the eye. If the striking picture of this "Newton of the ancient world" gazing at the setting sun, to attempt, with such rude means, a portion of the task which remains unsolved after two thousand years, be recalled here, it is because it seems fittingly to remind us of the early steps of that ascent on which man's long effort has raised him to the power of questioning Nature with means of the wonderful exactness just described, and to remind us also how long human thought has rested on the great problem to which we hope this present month may bring an answer.