Popular Science Monthly/Volume 3/October 1873/Finding the Way at Sea

by Richard Anthony Proctor

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FINDING THE WAY AT SEA.

By R. A. PROCTOR.

THE wreck of the Atlantic, followed closely by that of the City of Washington nearly on the same spot, has led many to inquire into the circumstances on which depends a captain's knowledge of the position of his ship. In each case, though not in the same way, the ship was supposed to be far from land, when in reality quite close to it. In each case, in fact, the ship had oversailed her reckoning. A slight exaggeration of what travellers so much desire—a rapid passage—proved the destruction of the ship, and in one case occasioned a fearful loss of life. And, although such events are fortunately infrequent in Atlantic voyages, yet the bare possibility that, besides ordinary sea-risks, a ship is exposed to danger from simply losing her way, suggests unpleasant apprehensions as to the general reliability of the methods in use for determining where a ship is, and her progress from day to day.

I propose to give a brief sketch of the methods in use for finding the way at sea, in order that the general principles on which safety depends may be recognized by the general reader.

It is known, of course, to every one, that a ship's course and rate of sailing are carefully noted throughout her voyage. Every change of her course is taken account of, as well as every change in her rate of advance, whether under sail or steam, or both combined. If all this could be quite accurately managed, the position of the ship at any hour could be known, because it would be easy to mark down on a chart the successive stages of her journey, from the moment when she left port. But a variety of circumstances renders this impossible.

To begin with: the exact course of a ship cannot be known, because there is only the ship's compass to determine her course by, and a ship's compass is not an instrument affording perfectly exact indications. Let any one on a sea-voyage observe the compass for a short time, being careful not to break the good old rule which forbids speech to the "man at the wheel," and he will presently become aware of the fact that the ship is not kept rigidly to one course, even for a short time. The steersman keeps her as near as he can to a particular course, but she is continually deviating, now a little on one side, now a little on the other, of the intended direction; and even the general accuracy with which that course is followed is a matter of estimation, and depends on the skill of the individual steersman. Looking at the compass-card, in steady weather, a course may seem very closely followed; perhaps the needle's end may not be a hundredth part of an inch (on the average) from the position it should have. But a hundredth part of an inch on the circumference of the compass-card would correspond to a considerable deviation in the course of a run of twenty or thirty knots; and there is nothing to prevent the errors so arising from accumulating in a long journey until a ship might be thirty or forty miles from her estimated place. To this may be added the circumstance that the direction of the needle is different in different parts of the earth. In some places it points to the east of the north, in others to the west. And, although the actual "variation of the compass," as this peculiarity is called, is known in a general way for all parts of the earth, yet such knowledge has no claim to actual exactness. There is also an important danger, as recent instances have shown, in the possible change of the position of the ship's compass, on account of iron in her cargo.

But a far more important cause of error, in determinations merely depending on the log-book, is that arising from uncertainty as to the ship's rate of progress. The log-line gives only a rough idea of the ship's rate at the time when the log is cast;^[1] and, of course, a ship's rate does not remain constant, even when she is under steam alone. Then, again, currents carry the ship along sometimes with considerable rapidity; and the log-line affords no indication of their action: while no reliance can be placed on the estimated rates, even of known currents. Thus the distance made on any course may differ considerably from the estimated distance; and, when several days' sailing are dealt with, an error of large amount may readily accumulate.

For these and other reasons, a ship's captain places little reliance on what is called "the day's work"—that is, the change in the ship's position from noon to noon as estimated from the compass-courses entered in the log-book, and the distances supposed to be run on these courses. It is absolutely essential that such estimates should be carefully made, because, under favorable conditions of weather, there may be no other means of guessing at the ship's position. But the only really reliable way of determining a ship's place is by astronomical observations. It is on this account that the almanac published by the Admiralty, in which the position and apparent motions of the celestial bodies are indicated, four or five years in advance, is called, par 'excellence, the Nautical Almanac. The astronomer, in his fixed observatory, finds this almanac essential to the prosecution of his observations; the student of theoretical astronomy has continual occasion to refer to it; but, to the sea-captain, the Nautical Almanac has a far more important use. The lives of sailors and passengers are dependent upon its accuracy. It is, again, chiefly for the sailor that our great nautical observatories have been erected, and that our astronomer-royal and his officers are engaged. What other work they may do is subsidiary, and, as it were, incidental. Their chief work is to time this great clock, our earth, and so to trace the motions of those celestial indices, which afford our fundamental time-measures, as to insure as far as possible the safety of our navy, royal and mercantile.^[2]

Let us see how this is brought about, not, indeed, by inquiring into the processes by which, at the Greenwich Observatory, the elements of safety are obtained, but by considering the method by which a seaman makes use of these elements.

In the measures heretofore considered, the captain of a ship in reality relies on terrestrial measurements. He reasons that, being on such and such a day in a given place, and having in the interval sailed so many miles in such and such directions, he must at the time being be in such and such a place. This is called "navigation." In the processes next to be considered, which constitute a part of the science of nautical astronomy, the seaman trusts to celestial observations independently of all terrestrial measurements.

The points to be determined by the voyager are his latitude and longitude. The latitude is the distance north or south of the equator, and is measured always from the equator in degrees, the distance from equator to pole being divided into ninety equal parts, each of which is a degree.^[3] The longitude is the distance east or west of Greenwich (in English usage, but other nations employ a different starting-point for measuring longitudes from). Longitude is not measured in miles, but in degrees. The way of measuring is not very readily explained without a globe or diagrams, but may be thus indicated: Suppose a circle to run completely round the earth, through Greenwich and both the poles; now, if this circle be supposed free to turn upon the polar axis, or on the poles as pivots, and the half which crosses Greenwich be carried (the nearest way round) till it crosses some other station, then the arc through which it is carried is called the longitude of the station, and the longitude is easterly or westerly according as this half-circle has to be shifted toward the east or west. A complete half-turn is 180°, and, by taking such a half-turn either eastwardly or westwardly, the whole surface of the earth is included. Points which are 180° east of Greenwich are thus also 180° west of Greenwich.

So much is premised in the way of explanation to make the present paper complete; but ten minutes' inspection of an ordinary terrestrial globe will show the true meaning of latitude and longitude more clearly (to those who happen to have forgotten what they learned at school on these points) than any verbal description.

Now, it is sufficiently easy for a sea-captain in fine weather to determine his latitude. For places in different latitudes have different celestial scenery, if one may so describe the aspect of the stellar heavens by night and the course traversed by the sun by day. The height of the pole-star above the horizon, for instance, at once indicates the latitude very closely, and would indicate the latitude exactly if the pole-star were exactly at the pole instead of being merely close to it. But the height of any known star when due south also gives the latitude. For, at every place in a given latitude, a star rises to a given greatest height when due south; if we travel farther south, the star will be higher when due south; if we travel farther north, it will be lower; and thus its observed height shows just how far north of the equator any northerly station is, while, if the traveller is in the Southern Hemisphere, corresponding observations show how far to the south of the equator he is.

But commonly the seaman trusts to observation of the sun to give him his latitude. The observation is made at noon, when the sun is highest above the horizon. The actual height is determined by means of the instrument called the sextant. This instrument need not be here described; but thus much may be mentioned to explain that process of taking the sun's meridian altitude which, no doubt, every one has witnessed who has taken a long sea-journey. The sextant is so devised that the observer can see two objects at once, one directly and the other after reflection of its light; and the amount by which he has to move a certain bar carrying the reflecting arrangement, in order to bring the two objects into view in the same direction, shows him the real divergence of lines drawn from his eye to the two objects. To take the sun's altitude, then, with this instrument, the observer takes the sun as one object and the horizon directly below the sun as the other: he brings them into view together, and then, looking at the sextant to see how much he has had to move the swinging arm which carries the reflecting glasses, he learns how high the sun is. This being done at noon, with proper arrangements to insure that the greatest height then reached by the sun is observed, at once indicates the latitude of the observer. Suppose, for example, he finds the sun to be 40° above the horizon, and the Nautical Almanac tells him that, at the time the sun is 10° north of the celestial equator, then he knows that the celestial equator is 30° above the southern horizon. The pole of the heavens is, therefore, 60° above the northern horizon, and the voyager is in 60° north latitude. Of course, in all ordinary cases, the number of degrees is not exact, as I have here for simplicity supposed, and there are some niceties of observation which would have to be taken into account in real work. But the principle of the method is sufficiently indicated by what has been said, and no useful purpose could be served by considering minutiae.

Unfortunately, the longitude is not determined so readily. The very circumstance which makes the determination of the latitude so simple introduces the great difficulty which exists in finding the longitude. I have said that all places in the same latitude have the same celestial scenery; and precisely for this reason it is difficult to distinguish one such place from another, that is, to find on what part of its particular latitude-circle any place may lie.

If we consider, however, how longitude is measured, and what it really means, we shall readily see where a solution of the difficulty is to be sought. The latitude of a station means how far toward either pole the station is; its longitude means how far round the station is from some fixed longitude. But it is by turning round on her axis that the earth causes the changes which we call day and night; and therefore these must happen at different times in places at different distances round. For example, it is clear that, if it is noon at one station, it must be midnight at a station half-way round from the former. And if any one at one station could telegraph to a person at another, "It is exactly noon here," while this latter person knew from his clock or watch that it was exactly midnight where he was, then he would know that he was half-way round exactly. He would, in fact, know his longitude from the other station. And so with smaller differences. The earth turns, we know, from west to east—that is, a place lying due west of another is so carried as presently to occupy the place which its easterly neighbor had before occupied, while this last place has gone farther east yet. Let us suppose an hour is the time required to carry a westerly station to the position which had been occupied by a station to the east of it. Then manifestly every celestial phenomenon depending on the earth's turning will occur an hour later at the westerly station. Sunrise and sunset are phenomena of this kind. If I telegraph to a friend at some station far to the west, but in the same latitude, "The sun is rising here," and he finds that he has to wait exactly an hour before the sun rises there, then he knows that he is one hour west of me in longitude, a most inexact yet very convenient and unmistakable way of speaking. As there are twenty-four hours in the day, while a complete circle running through my station and his (and everywhere in the same latitude) is supposed to be divided into 360°, he is 15° (a 24th part of 360) west of me; and, if my station is Greenwich, he is in what we, in England, call 15° west longitude.^[4]

But what is true of sunrise and sunset in the same latitudes and different longitudes, is true of noon whatever the latitude may be. And of course it is true of the southing of any known star. Only unfortunately one cannot tell the exact instant when either the sun or a star is due south or at its highest above the horizon. Still, speaking generally, and for the moment limiting our attention to noon, every station toward the west has noon later, while every station toward the east has noon earlier, than Greenwich (or whatever reference station is employed).

I shall presently return to the question how the longitude is to be determined with sufficient exactness for safety in sea-voyages. But I may digress here to note what happens in sea-voyages where the longitude changes. If a voyage is made toward the west, as from England to America, it is manifest that a watch set to Greenwich time will be in advance of the local time as the ship proceeds westward, and will be more and more in advance the farther the ship travels in that direction. For instance, suppose a watch shows Greenwich time; then when it is noon at Greenwich the watch will point to twelve, but it will be an hour before noon at a place 15° west of Greenwich, two hours before noon at a place 30° west, and so on: that is, the watch will point to twelve when it is only eleven o'clock, ten o'clock, and so on, of local time. On arrival at New York, the traveller would find that his watch was nearly five hours fast. Of course the reverse happens in a voyage toward the east. For instance, a watch set to New-York time would be found to be nearly five hours slow, for Greenwich time, when the traveller arrived in England.

In the following passage these effects are humorously illustrated by Mark Twain:

"Young Mr. Blucher, who is from the Far "West, and on his first voyage" (from New York to Europe) "was a good deal worried by the constantly-changing 'ship-time.' He was proud of his new watch at first, and used to drag it out promptly when eight bells struck at noon, but he came to look after a while as if he were losing confidence in it. Seven days out from New York he came on deck, and said with great decision, 'This thing's a swindle!' 'What's a swindle?' 'Why, this watch. I bought her out in Illinois—gave $150 for her, and I thought she was good. And, by George, she is good on shore, but somehow she don't keep up her lick here on the water—gets sea-sick, may be. She skips; she runs along regular enough, till half-past eleven, and then all of a sudden she lets down. I've set that old regulator up faster and faster, till I've shoved it clear round, but it don't do any good; she just distances every watch in the ship,^[5] and clatters along in a way that's astonishing till it's noon, but them "eight bells" always gets in about ten minutes ahead of her any way. I don't know what to do with her now. She's doing all she can; she's going her best gait, but it won't save her. Now, don't you know there ain't a watch in the ship that's making better time than she is; but what does it signify? When you hear them "eight bells," you'll find her just ten minutes short of her score—sure.' The ship was gaining a full hour every three days, and this fellow was trying to make his watch go fast enough to keep up to her. But, as he had said, he had pushed the regulator up as far as it would go, and the watch was 'on its best gait,' and so nothing was left him but to fold his hands and see the ship beat in the race. We sent him to the captain, and he explained to him the mystery of 'ship-time,' and set his troubled mind at rest. This young man," proceeds Mr. Clemens, à propos des bottes, "had asked a great many questions about sea-sickness before we left, and wanted to know what its characteristics were, and how he was to tell when he had it. He found out."

I cannot leave Mark Twain's narrative, however, without gently criticising a passage in which he has allowed his imagination to invent effects of longitude which assuredly were never perceived in any voyage since the ship Argo set out after the Golden Fleece. "We had the phenomenon of a full moon," he says, "located just in the same spot in the heavens, at the same hour every night. The reason of this singular conduct on the part of the moon did not occur to us at first, but it did afterward, when we reflected that we were gaining about twenty minutes every day; because we were going east so fast, we gained just about enough every day to keep along with the moon. It was becoming an old moon to the friends we had left behind us, but to us Joshuas it stood still in the same place, and remained always the same." O Mr. Clemens, Mr. Clemens! In a work of imagination (as the "Innocents Abroad" must, I suppose, be to a great extent considered), a mistake such as that here made is perhaps not a very serious matter; but, suppose some unfortunate compiler of astronomical works should happen to remember this passage, and to state (as a compiler would be tolerably sure to do, unless he had a mathematical friend at his elbow) that, by voyaging eastward at such and such a rate, a traveller can always have the moon "full" at night, in what an unpleasant predicament would the mistake have placed him! Such things happen, unfortunately; nay, I have even seen works, in which precisely such mistakes have been made, in use positively as text-books for examinations. On this account, our fiction writers must be careful in introducing science details, lest peradventure science-teachers (save the mark!) be led astray.

It need scarcely be said that no amount of eastwardly voyaging would cause the moon to remain always "full" as seen by the voyager. The moon's phase is the same from whatever part of the earth she may be seen, and she will become "new," that is, pass between the earth and the sun, no matter what voyages may be undertaken by the inhabitants of earth. Mr. Clemens has confounded the monthly motion of the moon with her daily motion. A traveller who could only go fast enough eastward might keep the moon always due south. To do this he would have to travel completely round the earth in a day and (roughly) about 50½ minutes. If he continued this for a whole month, the moon would never leave the southern heavens; but she would not continue "full." In fact, we see that the hour of the day (local time) would be continually changing—since the traveller would not go round once in twenty-four hours (which would be following the sun, and would cause the hour of the day to remain always the same), but in twenty-four hours and the best part of another hour; so that the day would seem to pass on, though very slowly, lasting a lunar month instead of a common day.

Every one who makes a long sea-voyage must have noted the importance attached to moon observations; and many are misled into the supposition that these observations are directly intended for the determination of the longitude (or, which is the same thing in effect, for determining true ship-time). This, however, is a mistake. The latitude can be determined at noon, as we have seen. A rough approximation to the local time can be obtained also, and is commonly obtained, by noting when the sun begins to dip after reaching the highest part of his course above the horizon. But this is necessarily only a rough approximation, and quite unsuited for determining the ship's longitude. For the sun's elevation changes very slowly at noon, and no dip can be certainly recognized, even from terra firma, far less from a ship, within a few minutes of true noon. A determination of time effected in this way serves very well for the ship's "watches," and accordingly when the sun, so observed, begins to dip, they strike "eight bells" and "make it noon." But it would be a serious matter for the crew if that was made the noon for working the ship's place; for an error of many miles would be inevitable.

The following passage from "Foul Play" illustrates the way in which mistakes have arisen on this point: The hero, who, being a clergyman and a university man, is, of course, a master of every branch of science, is about to distinguish himself before the heroine by working out the position of the ship Proserpine, whose captain is senselessly drunk. After ten days' murky weather, "the sky suddenly cleared, and a rare opportunity occurred to take an observation. Hazel suggested to Wylie, the mate, the propriety of taking advantage of the moment, as the fog-bank out of which they had just emerged would soon envelop them again, and they had not more than an hour or so of such observation available. The man gave a shuffling answer. So he sought the captain in his cabin. He found him in bed. He was dead drunk. On a shelf lay the instruments. These Hazel took, and then looked round for the chronometers. They were safely locked in their cases. He carried the instruments on deck, together with a book of tables, and quietly began to make preparations, at which Wylie, arresting his walk, gazed with utter astonishment" (as well he might).

"'Now, Mr. Wylie, I want the key of the chronometer-cases.'

"'Here is a chronometer, Mr. Hazel,' said Helen, very innocently, 'if that is all you want.'

"Hazel smiled, and explained that a ship's clock is made to keep the most exact time; that he did not require the time of the spot where they were, but Greenwich time. He took the watch, however. It was a large one for a lady to carry; but it was one of Frodsham's masterpieces.

"'Why, Miss Rolleston,' said he, 'this watch must be two hours slow. It marks ten o'clock; it is now nearly mid-day. Ah, I see,' he added, with a smile, 'you have wound it regularly every day, but you have forgotten to set it daily. Indeed, you may be right; it would be a useless trouble, since we change our longitude hourly. Well, let us suppose that this watch shows the exact time at Sydney, as I presume it does, I can work the ship's reckoning from that meridian, instead of that of Greenwich.' And he set about doing it." Wylie, after some angry words with Hazel, brings the chronometers and the charts. Hazel "verified Miss Rolleston's chronometer, and, allowing for difference of time, found it to be accurate. He returned it to her, and proceeded to work on the chart. The men looked on; so did Wylie. After a few moments, Hazel read as follows: 'West longitude 146° 53' 18". South latitude 35° 24'. The island of Oparo^[6] and the Four Crowns distant 420 miles on the N. N. E.,'" and so on. And, of course, "Miss Rolleston fixed her large, soft eyes on the young clergyman with the undisguised admiration a woman is apt to feel for what she does not understand."

The scene here described corresponds pretty closely, I have little doubt, with one actually witnessed by the novelist, except only that the captain or chief officer made the observations, and that either there had not been ten days' murky weather, or else that in the forenoon, several hours at least before noon, an observation of the sun had been made. The noon observation would give the latitude, and, combined with a forenoon observation, would give the longitude, but alone would be practically useless for that purpose. It is curious that the novelist sets the longitude as assigned much more closely than the latitude, and the value given would imply that the ship's time was known within less than a second. This would in any case be impracticable; but, from noon observations, the time could not be learned within a minute at the least. The real fact is, that, to determine true time, the seaman selects, not noon, as is commonly supposed, but a time when the sun is nearly due east or due west. For then the sun's elevation changes most rapidly, and so gives the surest means of determining the time. The reader can easily see the rationale of this by considering the case of an ordinary clock-hand. Suppose our only means of telling the time was by noting how high the end of the minute-hand was: then, clearly, we should be apt to make a greater mistake in estimating the time, when the hand was near XII., than at any other time, because then its end changes very slowly in height, and a minute more or less makes very little difference. On the contrary, when the hand was near III. and IX., we could in a very few seconds note any change of the height of its extremity. In one case we could not tell the time within a minute or two; in the other, we could tell it within a few seconds.

But the noon observation would be wanted to complete the determination of the longitude; for, until the latitude was known, the captain would not be aware what apparent path the sun was describing in the heavens, and therefore would not know the time corresponding to any particular solar observation. So that a passenger, curious in watching the captain's work, would be apt to infer that the noon observations gave the longitude, since he would perceive that from them the captain worked out both the longitude and the latitude.

It is curious that another and critical portion of the same entertaining novel is affected by the mistake of the novelist on this subject. After the scuttling of the Proserpine, and other events, Hazel and Miss Rolleston are alone on an island in the Pacific. Hazel seeks to determine their position, as one step toward escape. Now, "you must know that Hazel, as he lay on his back in the boat, had often, in a half-drowsy way, watched the effect of the sun upon the boat's mast: it now stood, a bare pole, and at certain hours acted like the needle of a dial by casting a shadow on the sands. Above all, he could see pretty well, by means of this pole and its shadow, when the sun attained its greatest elevation. He now asked Miss Rolleston to assist him in making this observation exactly. She obeyed his instructions, and, the moment the shadow reached its highest angle and showed the minutest symptom of declension, she said 'Now,' and Hazel called out in a loud voice" (why did he do that?) "'Noon!' 'And forty nine minutes past eight at Sydney,' said Helen, holding out her chronometer; for she had been sharp enough to get it ready of her own accord. Hazel looked at her and at the watch with amazement and incredulity. 'What?' said he. 'Impossible! You can't have kept Sydney time all this while.' 'And pray why not?' said Helen. 'Have you forgotten that some one praised me for keeping Sydney time? it helped you somehow or other to know where we were.'" After some discussion, in which she shows how natural it was that she should have wound up her watch every night, even when "neither of them expected to see the morning," she asks to be praised. "'Praised!' cried Hazel, excitedly, 'worshipped, you mean. Why, we have got the longitude by means of your chronometer. It is wonderful! It is providential. It is the finger of Heaven. Pen and ink, and let me work it out.'" He was "soon busy calculating the longitude of Godsend Island." What follows is even more curiously erroneous. "'There,' said he. 'Now, the latitude I must guess at by certain combinations. In the first place the slight variation in the length of the days. Then I must try and make a rough calculation of the sun's parallax.'" (It would have been equally to the purpose to have calculated how many cows' tails would reach to the moon.) "'And then my botany will help me a little; spices furnish a clew; there are one or two that will not grow outside the tropic,'" and so on. He finally sets the latitude between the 26th and 33d parallels, a range of nearly 500 miles. The longitude, however, which is much more closely assigned, is wrong altogether, being set at 103½° west, as the rest of the story requires. For Godsend Island is within not many days' sail of Valparaiso. The mistake has probably arisen from setting Sydney in west longitude instead of east longitude, 151° 14'; for the difference of time, 3h. 11m., corresponds within a minute to the difference of longitude between 151° 14' west and 103½° west.

Mere mistakes of calculation, however, matter little in such cases. They do not affect the interest of a story even in such extreme cases as in "Ivanhoe," where a full century is dropped in such sort that one of Richard I.'s knights holds converse with a contemporary of the Conqueror, who, if my memory deceives me not, was Cœur de Lion's great-great-grandfather. It is a pity, however, that a novelist or indeed any writer should attempt to sketch scientific methods with which he is not familiar. No discredit can attach to any person, not an astronomer, who does not understand the astronomical processes for determining latitude and longitude, any more than to one who, not being a lawyer, is unfamiliar with the rules of conveyancing. But, when an attempt is made by a writer of fiction to give an exact description of any technical matter, it is as well to secure correctness by submitting the description to some friend acquainted with the principles of the subject. For, singularly enough, people pay much more attention to these descriptions when met with in novels, than when given in text-books of science, and they thus come to remember thoroughly well precisely what they ought to forget. I think, for instance, that it may not improbably have been some recollection of "Foul Play" which led Mr. Lockyer to make the surprising statement that longitude is determined at sea by comparing chronometer time with local time, which is found "at noon by observing, with the aid of a sextant, when the sun is at the highest point of its path." Our novelists really must not lead the students of astronomy astray in this manner.

It will be clear to the reader, by this time, that the great point in determining the longitude is, to have the true time of Greenwich or some other reference station, in order that, by comparing this time with ship-time, the longitude east or west of the reference station may be ascertained. Ship-time can always be determined by a morning or afternoon observation of the sun, or by observing a known star when toward the east or west, at which time the diurnal motion raises or depresses it most rapidly. The latitude being known, the time of day (any given day) at which the sun or a star should have any particular altitude is known also, and, therefore, conversely, when the altitude of the sun or a star has been noted, the seaman has learned the time of day. But to find Greenwich time is another matter; and, without Greenwich time, ship-time teaches nothing as to the longitude. How is the voyager at sea or in desert places to know the exact time at Greenwich or some other fixed station? We have seen that chronometers are used for this purpose; and chronometers are now made so marvellously perfect in construction that they can be trusted to show true time within a few seconds, under ordinary conditions. But it must not be overlooked that in long voyages a chronometer, however perfect its construction, is more liable to get wrong than at a fixed station. That it is continually tossed and shaken is something, but is not the chief trial to which it is exposed. The great changes of temperature endured, when a ship passes from the temperate latitudes across the torrid zone to the temperate zone again, try a chronometer far more severely than any ordinary form of motion. And then it is to be noted that a very insignificant time-error corresponds to a difference of longitude quite sufficient to occasion a serious error in the ship's estimated position. For this reason and for others, it is desirable to have some means of determining Greenwich time independently of chronometers.

This, in fact, is the famous problem for the solution of which such high rewards were offered and have been given.^[7] It was to solve this problem that Whiston, the same who fondly imagined Newton was afraid of him,^[8] suggested the use of bombs and mortars; for which Hogarth pilloried him in the celebrated mad-house scene of the Rake's Progress. Of course Whiston had perceived the essential feature of all methods intended for determining the longitude. Any signal which is recognizable, no matter by eye or ear, or in whatsoever way, at both stations, the reference station and the station whose longitude is required, must necessarily suffice to convey the time of one station to the other. The absurdity of Winston's scheme lay in the implied supposition that any form of ordnance could propel rocket-signals far enough to be seen or heard in mid-ocean. Manifestly the only signals available, when telegraphic communication is impossible, are signals in the celestial spaces, for these alone can be discerned simultaneously from widely-distant parts of the earth. It has been to such signals, then, that men of science have turned for the required means of determining longitude.

Galileo was the first to point out that the satellites of Jupiter supply a series of signals which might serve to determine the longitude. When one of these bodies is eclipsed in Jupiter's shadow, or passes out of sight behind Jupiter's disk, or reappears from eclipse or occultation, the phenomenon is one which can be seen from a whole hemisphere of the earth's surface. It is as truly a signal as the appearance or disappearance of a light in ordinary night-signalling. If it can be calculated beforehand that one of these events will take place at any given hour of Greenwich time, then, from whatever spot the phenomenon is observed, it is known there that the Greenwich hour is that indicated. Theoretically, this is a solution of the famous problem; and Galileo, the discoverer of Jupiter's four satellites, thought he had found the means of determining the longitude with great accuracy. Unfortunately, these hopes have not been realized. At sea, indeed, except in the calmest weather, it is impossible to observe the phenomena of Jupiter's satellites, simply because the telescope cannot be directed steadily upon the planet. But even on land Jupiter's satellites afford but imperfect means of guessing at the longitude. For, at present, their motions have not been thoroughly mastered by astronomers, and though the Nautical Almanac gives the estimated epochs for the various phenomena of the four satellites, yet, owing to the imperfection of the tables, these epochs are often found to be appreciably in error. There is yet another difficulty. The satellites are not mere points, but, being in reality also as large as or larger than our moon, they have disks of appreciable though small dimensions. Accordingly, they do not vanish or reappear instantaneously, but gradually, the process lasting in reality several seconds (a longer or shorter time, according to the particular satellites considered), and the estimated moment of the phenomenon thus comes to depend on the power of the telescope employed, or the skill or the visual powers of the observer, or the condition of the atmosphere, and so on. Accordingly, very little reliance could be placed on such observations as a mean for determining the longitude with any considerable degree of exactness.

No other celestial phenomena present themselves except those depending on the moon's motions.^[9] All the planets, as well as the sun and moon, traverse at various rates and in different paths the sphere of the fixed stars. But the moon alone moves with sufficient rapidity to act as a time indicator for terrestrial voyagers. It is hardly necessary to explain why rapidity of motion is important; but the following illustration may be given for the purpose. The hour-hand of a clock does in reality indicate the minute as well as the hour; yet, owing to the slowness of its motion, we regard the hour-hand as an unsatisfactory time-indicator, and only consider it as showing what hour is in progress. So with the more slowly-moving celestial bodies. They would serve well enough, at least some among them would, to show the day of the year, if we could only imagine that such information were ever required from celestial bodies. But it would be hopeless to attempt to ascertain the true time with any degree of accuracy from their motions. Now, the moon really moves with considerable rapidity among the stars.^[10] She completes the circuit of the celestial sphere in 27⅓ days (a period less than the common lunation), so that in one day she traverses about 13°, or her own diameter (which is rather more than half a degree), in about an hour. This, astronomically speaking, is very rapid motion; and, as it can be detected in a few seconds by telescopic comparison of the moon's place with that of some fixed star, it serves to show the time within a few seconds, which is precisely what is required by the seaman. Theoretically, all he has to do is, to take the moon's apparent distance from a known star, and also her height and the star's height above the horizon. Thence he can calculate what would be the moon's distance from the star at the moment of observation, if the observer were at the earth's centre. But the Nautical Almanac informs him of the precise instant of Greenwich time corresponding to this calculated distance. So he has, what he requires, the true Greenwich time.

It will be manifest that all methods of finding the way at sea, except the rough processes depending on the log and compass, require that the celestial bodies, or some of them, should be seen. Hence it is that cloudy weather, for any considerable length of time, occasions danger, and sometimes leads to shipwreck and loss of life. Of course the captain of a ship proceeds with extreme caution when the weather has long been cloudy, especially if, according to his reckoning, he is drawing near shore. Then the lead comes into play, that by soundings, if possible, the approach to shore may be indicated. Then, also, by day and night, a careful watch is kept for the signs of land. But it sometimes happens that, despite all such precautions, a ship is lost; for there are conditions of weather which, occurring when a ship is nearing shore, render the most careful lookout futile. These conditions may be regarded as included among ordinary sea-risks, by which term are understood all such dangers as would leave a captain blameless if shipwreck occurred. It would be well if no ships were ever lost save from ordinary sea-risks; but, unfortunately, ships are sometimes cast ashore for want of care; either in maintaining due watch as the shore is approached, or taking advantage of opportunities, which may be few and far between, for observing sun, or moon, or stars, as the voyage proceeds. It may safely be said that the greater number of avoidable shipwrecks have been occasioned by the neglect of due care in finding the way at sea.

 

1. The log is a flat piece of wood of quadrantal shape, so loaded at the rim as to float with the point (that is, the centre of the quadrant) uppermost. To this a line about 300 yards long is fastened. The log is thrown overboard, and comes almost immediately to rest on the surface of the sea, the line being suffered to run freely out. By marks on the log-line divided into equal spaces, called knots, of known length, and by observing how many of these run out, while the sand in a half-minute hour-glass is running, the ship's rate of motion is roughly inferred. The whole process is necessarily rough, since the line cannot even be straightened.
2. This consideration has been altogether lost sight of in certain recent propositions for extending government aid to astronomical inquiries of another sort. It may be a most desirable thing that government should find means for inquiring into the physical condition of sun and moon, planets and comets, stars and all the warious orders of star-clusters.But, if such matters are to be studied at government expense, it should be understood that the inquiry is undertaken with the sole purpose of advancing our knowledge of these interesting subjects, and should not be brought into comparison with the utilitarian labors for which our Royal Observatory was founded.
3. Throughout this explanation all minuter details are neglected. In reality, in consequence of the flattening of the earth's globe, the degrees of latitude are not equal, being larger the farther we go from the equator. Moreover, strictly speaking, it is incorrect to speak of distances being divided into degrees, or to say that a degree of latitude or longitude contains so many miles; yet it is so exceedingly inconvenient to employ any other way of speaking in popular description, that I trust any astronomers or mathematicians who may read this article will forgive the solecism.
4. In this case, he is "at sea" (which, I trust, will not be the case with the reader), and, we may suppose, connected with Greenwich by submarine telegraph in course of being laid. In fact, the position of the Great Eastern throughout her cable-laying journeys, was determined by a method analogous to that sketched above.
5. Because set to go "fast." Of course, the other watches on board would be left to go at their usual rate, and simply put forward at noon each day by so many minutes as corresponded to the run eastward since the preceding noon.
6. The island fixes the longitude at about 147°, otherwise I should have thought the 4 was a misprint for 7. In longitude 177° west, Sydney time would be about 2 hours slow, but about 4 hours slow in longitude 147° west.
7. For invention of the chronometer, Harrison (a Yorkshire carpenter, and the son of a carpenter) received £20,000. This sum had been offered for a marine chronometer which would stand the test of two voyages of assigned length. Harrison labored fifty years before he succeeded in meeting the required condition.
8. Newton, for excellent reasons, had opposed Whiston's election to the Royal Society. Like most small men, Whiston was eager to secure a distinction which, unless spontaneously offered to him, could have conferred no real honor. Accordingly he was amusingly indignant with Newton for opposing him. "Newton perceived," he wrote, "that I could not do as his other darling friends did, that is, Team of him without contradicting him when I differed in opinion from him: he could not in his old age bear such contradiction, and so he was afraid of me the last thirteen years of his life."
9. If but one star or a few would periodically (and quite regularly) "go out" for a few moments, the intervals between such vanishings being long enough to insure that one would not be mistaken in point of time for the next or following one, then it would be possible to determine Greenwich or other reference time with great exactness. And here one cannot but recognize an argument against the singular theory that the stars were intended simply as lights to adorn our heavens and to be of use to mankind. The teleologists who have adopted this strange view can hardly show how the theory is consistent with the fact that quite readily the stars (or a few of them) might have been so contrived as to give man the means of travelling with much more security over the length and breadth of his domain than is at present possible. In this connection I venture to quote a passage in which Sir John Herschel has touched on the usefulness of the stars, in terms which, were they not corrected by other and better-known passages in his writings, might suggest that he had adopted the theory I have just mentioned: "The stars," he said, in an address to the Astronomical Society, in 1827, "are landmarks of the universe; and, amid the endless and complicated fluctuations of our system, seem placed by its Creator as guides and records, not merely to elevate our minds by the contemplation of what is vast, but to teach us to direct our actions by reference to what is immutable in his works. It is indeed hardly possible to over-appreciate their value in this point of view. Every well-determined star, from the moment its place is registered, becomes to the astronomer, the geographer, the navigator, the surveyor, a point of departure which can never deceive or fail him—the same forever and in all places, of a delicacy so extreme as to be a test for every instrument yet invented by man, yet equally adapted for the most ordinary purposes; as available for regulating a town-clock as for conducting a navy to the Indies; as effective for mapping down the intricacies of a petty barony as for adjusting the boundaries of transatlantic empires. When once its place has been thoroughly ascertained, and carefully recorded, the brazen circle with which the useful work was done may moulder, the marble pillar may totter on its base, and the astronomer himself survive only in the gratitude of posterity; but the record remains, and transfuses all its own exactness into every determination which takes it for a groundwork, giving to inferior instruments, nay, even to temporary contrivances, and to the observations of a few weeks or days, all the precision attained originally at the cost of so much time, labor, and expense." It is only necessary, as a corrective to the erroneous ideas which might otherwise be suggested by this somewhat high-flown passage, to quote the following remarks from the work which represented Sir John Herschel's more matured views, his well-known "Outlines of Astronomy:" "For what purpose are we to suppose such magnificent bodies scattered through the abyss of space? Surely not to illuminate our nights, which an additional moon of the thousandth part of the size of our own world would do much better; nor to sparkle as a pageant void of meaning and reality, and bewilder us among vain conjectures. Useful, it is true, they are to man as points of exact and permanent reference, but he must have studied astronomy to little purpose, who can suppose man to be the only object of his Creator's care; or who does not see, in the vast and wonderful apparatus around us, provision for other races of animated beings."
10. It was this doubtless which led to the distinction recognized in the book of Job, where the moon is described as "walking in brightness."