With the appearance of the "New Navigation" about fifteen years ago there began a period of increased interest in the technique of that art. The Institute has printed numerous articles devoted to such subjects as arc and tangent methods, azimuth finding, haversine formulæ, Aquino's Tables, and even the humble latitude and longitude factors. Pages with a wealth of long unfamiliar mathematical signs have been written in minute analysis of the relative advantages and disadvantages of different methods of working out sights. All of this work is, without question, excellent. As representing the trend of present-day investigation, however, might it not give rise to the impression that the last refinement of the art of navigation is now being sought in some instantaneous and unlaborious method of working out sights? Such may, indeed, be the case. There is certainly an air about those navigators that have just learned to work Marcq St. Hilaire instead of the time sight. The Naval Examining Board, too, has introduced an examination question of late years requiring the solution of the intersection of two lines of position by computation, which looks as if "practical" navigation were getting hackneyed.
For the benefit of a possibly limited following I urge that some attention be given to those practical problems and those tricks of the trade, as it were, that are still known to mark a difference between navigators, even if the only research needed be to collect the information from its scattered resting-places and put it in handy form. A broad field of utility is offered in the matter of apparatus alone. The attachment of a reading lamp to the sextant was worth more than a new formula for working out the sight. A telescopic alidade is as important in its way as a telescopic sight. A table of vertical angles that did not always have a hiatus in the neighborhood of the exact mountain height required would be a comfort. We have transparent parallel rulers now but the merchant service had them fifteen years ago. While it would be ridiculous to assert that anybody could become lost on the Southern Drill Grounds, a simple machine for grinding out complicated dead reckoning would be soothing to many a navigator. Its construction almost suggests itself. Even a device for keeping the navigator's pencils secure during his temporary absences from the chart-board would have its elements of uplift.
As a modest beginning in this suggested development, or rehabilitation, of the art the following notes are offered.
Let us consider why celestial observations at sea are necessary. There is record of a trans-Atlantic liner having made the passage and having entered her English port in a fog without having obtained a sight, either celestial or terrestrial, during the voyage. Every navigator of experience can recall certain passages when his dead reckoning checked practically perfectly with his fixes. In our speed runs we depend upon engine revolutions to give us the speed to the hundredth part of a knot. Assuming good weather, in these days of large ships, good speed, standardized screws, and gyro compasses it is certain that, except for one cause, our dead-reckoning is accurate within the limits ordinarily accepted as applying to positions by observation. The disturbing element, of course, is current. When we find current where no current is supposed to exist we call it bad steering and compass error. These errors probably have less influence than they are generally credited with, but if they have a constant and measurable tendency their effect is the same as current and they may be regarded as such. It is current, then, that makes us dependent upon observations. It would appear that some quick method of determining the current is one of the most important problems of navigation. Every navigator undoubtedly considers this question in some way and has an individual method of making correct or incorrect allowances for it. He is helpless otherwise, for he gets no practical assistance from the authorities. This is what we find in the Naval Academy textbook on the subject. Starting from the noon fix, and barring star-sights, which seem to be regarded as non-union labor in this connection, the "current in longitude" is discovered next morning and its other component is determined at the succeeding noon. That is, once a day we determine the average current for the preceding twenty-four hours. If we happen to be following the axis of the Gulf Stream we may apply this average current to our dead-reckoning during the following day with some degree of confidence, but, aside from such a special case, the information has lost its usefulness by the time it is required.
An experience of about six years as navigator, and many weary hours as watch-officer spent in plumbing a ship over a deep-sea sounding wire, have convinced me that deep-sea currents have small respect for the current arrows shown on the charts. Vagrant currents are to be met anywhere—well defined flows persisting for only a single hour or for a whole day and rising sometimes to three knots in strength. The variations of even the best-defined currents are such as to cause practically the same phenomenon. These things matter very little to a ship in the open sea, but in coming on the coast at night, in such a poorly-lighted region as the Caribbean, for example, an error of a few miles is of some importance. Any method of measuring, or even of detecting the presence of these currents at the time of their existence is obviously worth striving for, and it seems that if the apparent available talent were applied to the problem there should be some hope of a solution. If solved by means of observations, then our sights would show us where we are and whither we are going instead of where we might have been.
The perspicacious reader will immediately perceive that this is but a roundabout way of stating the old problem of getting a fix with one observation. But not exactly. With a little greater precision in our dead-reckoning and not a hopeless improvement in the precision of observations—but including the highly objectionable feature of taking a great many more of them—a partial solution may be found by altering our method of getting intersections of lines of position.
The method suggested hereafter rests upon the assumption of an accuracy in the taking of observations that will be little credited wherever it is not vigorously disputed. By the term accuracy is meant the uniformity of error in observations taken by a practiced observer with the same instrument on the same day under good conditions. Mathematically it can be proved, probably, that there is an infinitesimal chance of the occurrence of such accuracy. Since it does exist it is waste of time to speculate on the probability of it. It is not doubt on this point that causes the great diffidence I feel in presenting the following "wrinkle," but rather because it is so elementary and simple that hardly any one will be able to read it without a conviction that he has always known and practiced it. There is a natural disinclination to be classed among those "strong on the obvious." If it has already been published it is contained in such obscure publications that the present effort to call attention to it is justified.
In Figure 1, let us assume a vessel steaming East at eight knots. O is the noon fix, A is the D. R. position at 2 p. m., and G a line of position taken at that time. It crosses the course only a mile from the D. R. position. Close enough. Maybe we have a little current with us. At 4 o'clock we take another observation. We get the line K, crossing the course at C. If we have carried our D. R. from the 2 p. m. D. R. position, our 4 p. m. D. R. position is at B. Our line crosses the course still a mile ahead. That, of course, is the same mile we found at 2 o'clock. If there was any current between noon and two o'clock (which, generally it is thought ridiculous to assume just because our 2 o'clock line was one mile out), it has disappeared between 2 and 4 o'clock. So we run our 2 o'clock line up to 4 o'clock (dotted line H), and get an intersection at C, exactly on the course.
Let us now admit the possibility that some among us are given to error, and assume that these frailer brethren have transferred their D. R. from 2 o'clock on to the point F. At 4 o'clock their D. R. position is at C. Line K passes directly through it and there appears to be no reason for running up our 2 o'clock line.
Now let us start all over again and do some assuming of a different order. In fact we shall assume nothing less than that our D. R. and our observations are both correct.
At 2 o'clock we find we have had a knot of current with us, that is, the current has one component of which both force and direction are known. But the current has another component, probably, and we shall assume its direction as along the line G, up or down; its force is unknown. At 4 o'clock our D. R., carried along from noon, brings us to B. If the current has been steady that component that carried us from A to F in two hours will have carried us twice as far in four hours, or from B to D. We know the direction of the other component. We know we are on the line K. Therefore, instead of being at C—there or or thereabouts—we are at E, and instead of speculating as to the possibility of a quarter-knot or half-knot current along the course we find good reason to believe that we have about nine-tenths of a knot in the direction BE,—almost at right angles to the course.
Figure 2 illustrates a few additional features. A, B, and C are hourly D. R. positions from the fix O. G, H, and I are position lines observed at these hourly intervals. The one component of the current that we are able to define at A amounts to the small distance AD—against us. Laying twice this distance off at B, and three times at C, we get the points E and F. From E we parallel our line G and the intersection K gives our fix. From F again we must parallel our original line G, not our later line H (unless, of course, we desire to start over again from our later fix K), and we get a second fix at L. If the current has been steady the points O, K, and L will lie in a straight line. Notice the deceptive aspect of the first two lines in their close agreement with the D. R. positions. There is apparently nothing in the situation at either A or B, as judged by ordinary standards, to indicate the advisability of taking another sight within the hour. It is true that if we get an ordinary intersection of line G with line I we obtain a fix pretty close to the true fix L; but if we have neglected taking the first two lines what should we judge from the data presented at C? Obviously there is a discrepancy that calls for an accounting, but the indications are as likely to lead to a decision that we have been set ahead as to the truth, viz., that the current is about two knots athwart and a little against us.
Referring again to the statement as to the unsuspected accuracy of sights, I may mention that many times I have obtained a straight line of as many as five intersections in sights taken at about half-hourly intervals. This indicates an absolute constancy of error in that many observations. The absolute error does not affect the exact determination of current. Of course it does affect the absolute accuracy of the fix.
An apparent limitation of the method lies in the necessity of working from a good fix. If we have only three lines of position with course and speed, the problem is indeterminate, because a solution can be obtained for any point assumed in the first line. The opportunity exists, however, for anybody interested to devise an easy graphic method of reconciling the indications given by three or more lines taken in quick succession with a fix obtained many hours before, as, for example, by star-sights. If the current has been steady the solution already given is sufficient, but on account of the sudden variations of current mentioned the device needed is some graphic solution of the probabilities in the case. It is apparent, of course, that once having obtained a fix we can maintain it by taking enough observations; but it is very discouraging to have this feature of increased labor always pushing itself into the foreground when all modern tendency is directed towards its elimination.
Another limitation lies in the necessity of good weather both for D. R. and observations. This is hardly a fair criticism in view of the modest improvement claimed for the method since, in bad weather, all signs fail anyhow. Again, a fix obtained from landmarks should not be associated with astronomical observations, on account of the difference in error. Similarly, because of the well-known discrepancy between a. m. and p. m. sights, some judgment should be used in combining lines of the two periods.
But these are minutiæ that will occur to any one that seriously considers the method. The principle involved is the valuable part of it and this may be briefly stated thus: Work to the utmost accuracy both sights and dead-reckoning and do not assume that discrepancies are due to errors and indeterminate causes. If the work in each case has been accurate, the discrepancies are the information we seek and are subject to easy analysis.
It may not be out of place at this point to mention the almost obvious bearing of this principle upon the question of omitting seconds in working navigational sights. In Lieutenant Schuyler's interesting paper on this subject in the December issue of the PROCEEDINGS he gives the following values for the mean errors in ships' positions as determined by an examination of their signaled positions during eleven days.
Noon latitudes ± 1.63 miles
Noon longitude ± 2.77 miles
8 p.m. latitude ± 2.06 miles
8. p.m. longitude ± 2.07 miles
These are errors in signaled positions, not in sights, except in the case of the noon latitude. Moreover they are errors by different navigators. The errors due to different allowances for current, different times of taking the observations on which they are based, and even different practice in regard to omitting or carrying along the seconds in working out the sights all enter into them. If such errors were to be expected in the sights worked by the same navigator, it is evident that there would be little hope of obtaining the current by the method suggested. I do not know where any data can be found on which to base an estimate of the uniformity of error. The illustrations cited hereafter are fairly conclusive as regards those individual cases, and it is an easy matter for anybody to prove it in individual cases for himself. What I suspect is that if every navigator used exactly the same methods of obtaining his current and combining his lines of position the errors quoted by Lieutenant Schuyler would be much reduced. The data on its face rather supports this assumption. Why should the longitude errors exceed the noon latitude error if so small an error is introduced by working to seconds of time? Why should the 8 p. m. latitude error exceed the noon latitude error except for errors in combining lines of position, or different methods of treating discrepancies between sights and dead-reckoning?
Without some illustration of what practical purpose this method might serve in ordinary sea-going, it would be easy to conclude that we have mistaken a molehill for a mountain. From an experience that includes scores of successful employments of this solution I will therefore offer two that I recall most clearly. The figures are taken from memory after a lapse of several years and are meant to be illustrative only.
In the fall of 1907 or spring of 1908, making passage from Guantanamo to New York in the Dubuque, the course was laid for Diamond Shoals Light Vessel, crossing the Gulf Stream. The weather was clear and the sea smooth, almost ideal for observations. Before reaching the point where, according to the chart, we might have expected to feel the first decided effects of the Stream, I began to take observation at intervals of, perhaps, 75 minutes. The surface temperature made its characteristic rise at practically the exact point indicated by the chart. Everything indicated normal conditions. For several hours thereafter, certainly for a distance of about thirty miles during which we should have been in a current of more than a knot, the observations showed none whatever. When it did come it came with a rush. I increased my observations to about two an hour and made half-hourly determinations of the gradually increasing current to tenths of a knot. The captain was of those that show a helpful interest in the navigator's hobbies, and, after watching with some amusement this unprecedented activity with the sextant, he entered with a spirit of raillery into a guessing contest as to the time and bearing of the first sight of the lightship. The ship was due to enter the circle of visibility just at sunset, and, according to my calculations there was a possibility of several minutes of uncertainty depending upon whether the vessel's masts or the light itself was first sighted. This led me to make a tabulation of predicted times and corresponding bearings, because the current was sweeping athwart the course at a rate that changed our bearing by one degree in about three minutes. That it was no guessing contest is proved by the fact that this prediction was exact—to the minute and to the degree.
The circumstances attending the other occasion I have in mind were such as to illustrate particularly the practical value of the method in addition to its accuracy. As navigator of a division flagship I had laid a course from the Chesapeake Capes for Nantucket Shoals Light Ship. It was good weather with smooth sea, but a trifle hazy by the time we were nearing the vicinity of the Shoals. The latitude and longitude reports from all four vessels of the division plotted very closely together up to and including the noon position just preceding the passage of the light ship, where we were due at about 10 p. m. A few sights taken during the afternoon showed me a current beginning about 4 p. m. and setting to the northward at about a knot and a half. The conditions were much like those in Figure 2, where the lines are deceptive from their apparent close agreement with the D. R. It clouded up in the evening and there was a chance for only one star-sight, the azimuth of which was not greatly different from that of the last sun-sight. At 8 p. m. the course laid from the flagship's position passed just north of the light ship. The other three vessels' positions plotted in a neat little group some five or six miles to the southward, actually indicating a small southerly set since noon. Notwithstanding this three-to-one majority against us the flagship changed course about one-and-a-half points to starboard at 8 o'clock and passed the light ship some two hours later, distant about a mile and a half on the port hand. As I have said the figures are from memory and not to be taken too seriously. My recollection is distinct, however, that from the 8 o'clock position plotted by the other three ships the change of course would have passed the light ship outside the range of visibility in the hazy weather prevailing at the time.
Piloting.—There is a rather widespread impression among officers, younger officers particularly, that the elegant solution of this problem lies in making a thorough preliminary study of the chart and then standing in "by eye." An analysis of the causes for this impression might disclose that it is based upon conceptions of the pilots of literature, or upon very superficial observation of professional pilots. Certainly it is antagonistic to that scientific habit of mind toward whose development the government has spent charitably—as we are given to understand nowadays—some twenty thousand dollars per midshipman. There is a brilliancy and finish and ease about the method (when it is successful), that is very appealing, and those who practice it have a tendency to be amused by the man who lays his course off beforehand and then sticks to it as if it were a railroad track. The weight of reason, however, lies with this less brilliant method. No person's eye is so good in estimating an actual channel as it is in sizing up a chart. If the exact line to be followed be laid down beforehand with all its various turns and courses chosen with reference to all the chart affords in the way of leading marks, ranges, stern bearings, turning points, etc., and if the ship be once put upon this line and kept there a whole host of complications falls away at once. A simple glance ahead or astern tells athwartship set. Knowing the athwartship position the eye may be trusted for a bearing to give a quick determination of the position along the course, and at every instant the exact position of the ship is known with all necessary accuracy. More important still, changes of course are determined ahead of time and are based upon absolute factors instead of being influenced by the look of things at the moment. If a deviation from the predetermined line becomes necessary because of some temporary obstruction, get back on the line as soon as possible even if it is only fifty yards away, and do not be influenced by the fact that the chart shows nothing to choose as between where you are and where you had intended to be. After several such uncorrected variations the advantages of preconsideration may be wiped out and you may be placed in the position of only crossing bridges as you come to them; good philosophy sometimes, but always poor navigation. The practice of changing course just because of the "look of things," with a casual reference to the chart for assurance that "we are all right here," often culminates in a sudden shock to the nervous system and a wild activity with compass, parallel rulers, casts of the lead and other paraphernalia at hand. Nobody ever saw cross-bearings taken and plotted quickly enough to be of real use in an emergency in narrow waters. Their proper function is checking up.
There is not a harbor in the country where five minutes steaming can be saved by making these slight changes of course suggested from time to time by the "look of things" instead of following the best course indicated by the chart. Therefore determine the complete approach to the anchorage on the chart beforehand, and make the ship go where you have determined she shall go. This is what professional pilots actually do, however, much they may appear to be influenced by nothing except an intimate familiarity with the bottom. Each of them has a cut-and-dried course of his own which he never departs from without reason, and probably no two of them use exactly the same set of leading and turning marks throughout. Those small changes of course that a pilot makes now and then, apparently with little reason, are to put him exactly on his line.
By following this plan the eye is trained as it never can be when there is no definite criterion by which to measure its inaccuracies. Development of skill requires a definite objective. If the objective be made so broad that it takes account only of getting through pilot waters without accident, the eye will never develop a fine skill in this work. It is as if the bull's eye covered the whole of the target.
Every course in pilot waters should be laid down, first, with reference to the channel, and then prolonged to the edge of the chart, if need be, in minute search for distinctive objects. If there is none on the line others will be discovered that suggest a better course. It is excellent practice also in studying a chart to close the eyes and try to visualize the actual sea and landscape. There will always be occasions enough when a trained eye will be perhaps the only factor of safety.
One-fifth Rule.—One of the handiest bits of information for the navigator to remember is that the sine of one point is equal to one-fifth (exactly 0.19509), and that, for practical purposes, the sine increases as the angle up to two points. With this little tool a great many trips to the chart board can be saved. Its applicability to different cases will widen its use. A single example will suffice.
In coasting it is our distance off shore that is generally in doubt. Our position along the course is known within a mile by a glance at the watch. Suppose we round a point and sight a light fifteen miles distant which we wish to give a berth of one mile. The sine of one point being one-fifth, if we bring the light one point on the bow we shall pass at three miles distance. Ergo, bring it one-third of a point on the bow, or say four degrees. Set the alidade at four degrees on the bow and steady when the light is on. This is more rational and easy than trying to lay off a compass course from an assumed position with a ± I° compass error. As we run up on the light, until it gets beyond two points on the bow, we may stand by the alidade and with a sight, a glance at the watch, and an easy mental calculation, determine the thwart-ship set almost instantly. Bear in mind, however, that the Captain is also interested in the navigation and may not be an admirer of thumb-rules; so it is perfectly sound policy to do the visible chart work too.
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A higher artisanship in the practice of navigation seems just now the most promising line of endeavor. The naval officer's preliminary training in this science is greatly superior to that of the average officer of the merchant marine, but the latter, because he practices it all his life, has developed a wealth of practical resources, apparatus, thumb-rules, axioms for fog navigation and what not that are not to be found in our textbooks. These minutiæ are the more valuable to naval navigators since, ordinarily, not one officer in a dozen gets enough navigating experience to evolve them for himself.