It has often been pointed out, in text-books of navigation and elsewhere, that altitudes observed at sea are subject to error when peculiar—atmospheric conditions operate to produce an extraordinary deflection of the ray of light from the horizon, and thus to make the actual angle of dip vary from its tabulated value. It is believed that attention can not be too frequently directed to this important subject, for the reason that there are undoubtedly many navigators who do not realize the magnitude of the error that may be involved; some have the impression that this error is such as to throw the results out by no more than a mile or so, and hence may be neglected for all practical purposes; others, while knowing that in the Red Sea and other special localities the error is to be guarded against, do not consider that it need ordinarily be feared by the navigator. It can be demonstrated that this error may attain a value so great as to jeopardize a vessel, even if a very large margin be allowed for inaccuracy of the sights; and that the conditions under which it is produced are such that it may occur in any region of the ocean.
It is possible that the lack of knowledge regarding the error is due to the fact that the reason for its occurrence has not been made sufficiently clear; it is frequently spoken of merely as "excessive refraction due to temperature," and as a glance at the table given in Bowditch and kindred works shows that the correction for temperature to be applied to the refraction is of small amount, this description does not ordinarily impress the student of navigation. Many explanations have gone further, it is true, and pointed out that a difference in the temperatures of the sea water and the air causes an arrangement of the air in strata of varying temperature and density, to which the error is due; but even this is not a complete description, and remains to be amplified before the full consequences of such an arrangement become apparent. It is proposed to give a full explanation of the extraordinary deflections that occur, in the hope that their frequency and possible magnitude may be better understood.
It may be, remarked, by way of preface, that the conditions that produce these deflections are analogous to those under which occurs the phenomenon of mirage, so familiar to seamen; and when one considers what great distortion of the rays of light must take place to produce the inverted, duplicate and other extraordinary images of objects seen in a mirage, it may be realized how little dependence can be placed upon the position of the sea horizon under similar circumstances.
If, in Fig. 1, MM' and NN' are two media of different density, the former being the more dense, a ray of light, AO, in passing from MM' into NN', will suffer refraction, taking up in the latter medium a new direction, OA', which will make a greater angle with the line PP' (perpendicular to the line of junction between the media) than it made while in MM'. The angle P'OA' will therefore be greater than the angle POA by an amount dependent upon the relative density of the two media. Conversely, a ray, A'O, which passes through the less dense medium, NN', will, in entering MM', take up a new direction, OA, which will make a smaller angle, POA, with the perpendicular than P'OA', which it made before. Consider, now, a ray BO passing through MM' at such an angle that BOP plus the increase due to refraction equals P'OB'; it may be seen that the effect is such as to prevent this ray from entering the medium NN', and it will take up a direction OB' along the line of junction of the media. It is therefore clear that it would be impossible for any ray, CO, making a greater angle than BOP with PP', to penetrate NN', and the fate of such rays is to undergo a total reflection from the line of junction as if that line were a mirror, and to re-enter the denser medium, taking a direction OC, such that the angle COP equals the angle C'OP.
In Fig. 2, let QR represent a small part of the earth's surface; E, the eye of an observer at a height EF above the surface, and A the most distant visible point of the earth's surface; then the path of the ray of light from A to E under ordinary atmospheric conditions is shown by the curved line AE, which will be concave toward the earth. This is because, under normal conditions, the density of the atmosphere is found to diminish from the surface of the earth upward, as each successive stratum carries less and less weight of air from above; thus the ray of light, in passing from the more to the less dense strata, makes a constantly increasing angle with the perpendiculars to the lines of junction of the layers. The direction in which the horizon then appears to the observer is along the tangent EH to the curve EA, and it is for such apparent directions under normal conditions that tables of dip are computed.
Fig. 3, shows the case of deflection of the ray when the air is very much warmer than the sea, as frequently occurs, for example, in the Red Sea, where the hot air from the desert blows across the cooler water. The stratum of air in immediate contact with the sea falls in temperature from the effect of the cooler mass, and the strata next above are similarly lowered in temperature, but by a less and less amount as the height increases. This condition increases the difference in density that normally exists, the curve having the same general shape as in the usual state of the atmosphere, but the deflection being more marked; a ray now reaches the observer from the point A', more distant than A; its first direction is comparatively oblique to the surface but it is gradually bent away from the perpendicular until the angle becomes too acute to enter one of the less dense media above and it suffers total reflection, and then curves downward, or toward the perpendicular, as it returns toward the earth through strata of increasing density. The direction in which the observer appears to see the point A' is along the tangent EH', which is above the usual direction EH; if, therefore, .an observed altitude be corrected by the amount of the normal dip, the "true" altitude thus obtained will be too small by an amount HEH', and the sight will result in a line of position too far from the body; that is, for example, too far to the southwest if the body bears northeast, or too far to the north if the body bears south. This condition of atmosphere will also affect the visibility of objects, making it possible to see points that would be below the horizon in a normal state and increasing the altitude of objects above the horizon.
In Fig. 4, it is assumed that the sea is warmer than the air, a case that presents itself, for example, to a vessel in the Gulf Stream. In this condition the lower strata of air become more heated and consequently less dense than those above, and the ray of light from the most distant visible point A", to the observer E, suffers refraction in a direction that is convex toward the earth, since it passes through media of increasing density and is therefore bent more and more toward the perpendicular. Under these circumstances the apparent direction of the horizon is along the tangent EH", which is below the normal direction EH; hence, in correcting for dip on the assumption that the horizon lies, as usual, toward EH, the resulting altitude will be too large by an amount HEH", and the resulting line of position will erroneously lie too near to the observed body—too far to the northeast if the body bears northeast, or too far to the south if the body bears south. Another effect of this state of atmosphere will be to reduce the visibility of objects, a point which is usually seen from the distance FA, with height of eye EF, now remaining invisible until approached within the distance FA". The apparent height of an object above the horizon will also be reduced under these circumstances, the direction of the ray that reaches the eye being at first obliquely downward, then suffering total reflection and finally curving upward.
It has been seen that the conditions necessary to produce extraordinary deflections of the rays require that the atmosphere shall arrange itself in a series of horizontal strata of uniformly varying density. It follows, therefore, that the mere difference in temperature between air and water is not sufficient in itself to produce the error, and that any cause that interferes with the formation of strata will prevent the occurrence of the deflection. As wind, by keeping the air in motion, renders the conditions unfavorable for the existence of layers of unequal density, it follows that a light breeze will, in general, greatly reduce the error, and that a strong one will effectually prevent it hence it is that the maximum bending of rays is to be expected M calm weather. It seems probable that the stratification is more likely to be disturbed when the air is colder than the sea than in the opposite condition, since the heavier particles are then above the lighter and the atmosphere is in a state of unstable equilibrium that may be easily deranged.
Both theory and experience show that the higher the eye of the observer is placed above sea level the smaller are the deflections from the causes under consideration. It is therefore well, especially when there is reason to suspect the conditions that produce abnormal deflections, to observe altitudes from the highest available position.
One of the most dangerous features of this error is that there is no satisfactory method of arriving at a correct estimate of its amount. If the conditions with which it is necessary to deal were fixed in their nature, such for example, as the mean atmospheric conditions for which the ordinary dip table is computed, it would be a simple matter to arrive, either by theory or experiment, at the amount of the deflection. But the elements of the problem can not, in their nature, be known. For instance, the conditions of temperature and wind at a distance of several miles from the observer, which can not be determined at the ship, have an important bearing on the solution; so also with the amount of moisture in the air, which is doubtless a material factor. The navigator may, however, recognize the existence of the disturbing conditions and the probable direction in which the disturbance will affect the results of his observations; and with this knowledge he must make ample allowance for possible errors.
In considering the effects of this error, it must be remembered that the dip directly affects the altitude, and the altitude, in turn, the line of position; when an error in altitude occurs, the line of position is correspondingly moved at right angles to its. length, either directly toward or away from the observed body. It may be seen at once that the error of the Sumner line due to this cause may be considerably increased, and even magnified a number of times, in the position resulting from the oblique intersection of two lines, or in the longitude corresponding to an assumed latitude, or the latitude corresponding to an assumed longitude.
It may be mentioned that an analogous error can occur in observed horizontal angles where masses of land or other causes create a difference in temperature to right and to left of the observer. This fact is worthy of note in surveying.
From a very large number of recorded instances of abnormal deflections of the rays of light from the horizon, due to inequality of temperature between sea and air, a few will be chosen to illustrate the possible magnitude of this error.
It is related that on one of Captain Cook's voyages the meridian altitude of the sun was being taken when a light snow squall came on. The horizon and sun remaining visible, the altitude shown by the sextant had almost instantly to be altered 32' to maintain contact, the horizon having appeared to fall by that amount when the air surrounding the observers was cooled by the snow squall. At the same time a distant mountain peak, which before had stood well above the horizon, almost disappeared from view. Both of these effects vanished with the passing of the squall, the measured altitude resuming its former value and the peak rising again above the horizon. Even if we are inclined to doubt the instruments of those times, and therefore the exactness of the observed difference, this account is of interest in showing at how early a day the existence of this error was recognized in navigation.
According to Raper, Mr. Fisher observed in the Arctic regions a variation of 18' in the place of the horizon.
The late Captain Lecky, in his "Wrinkles," states that on a clear day in midwinter, off the coast of Long Island, five observers at noon closely agreed upon an altitude which gave a certain latitude; in less than two hours afterwards the land was Sighted, and the latitude brought forward from the meridian altitude was found to be 14' in error.
Lieutenant Koss and Ensign Thun-Hohenstein, of the Austrian navy, while conducting observations near Pola for finding the variation in the dip of the horizon, observed on a quiet day a rise of the apparent horizon above its computed position of 8' 47" at a height of so feet, and of 9' 23" at a height of 33 feet above water.
Of the numerous instances that might be cited of extraordinary errors in the results given by astronomical sights in the Red Sea, (so extraordinary as to have given rise to an erroneous belief as to the currents existing in that body of water), it may be mentioned briefly that Lieutenant Marshall, U. S. Navy, of the U. S. S. Detroit, found errors of position from 12' to 18' arising from sights of the sun; Captain Nedden, of the S. S. Madeline, found the latitude by observation to differ 10 miles from the correct one and images of islands to be greatly distorted; and Captain Lecky discovered the positions of certain islands to be apparently 7 to 8 miles in error in one direction from morning sights and a similar amount in error in the opposite direction from afternoon sights.
A similar instance of error in the region of the Gulf Stream was reported by Lieutenant Commander W. L. Rodgers, U. S. Navy, of the U. S. S. Lancaster, two lines of position from the sun intersecting at about 7 miles to the southeast of the ship's true position and two from stars intersecting at a like distance in the opposite direction, the direction of the error in each case according with that which was to be expected from the observed differences in temperature of air and water.
As a result of what has been set forth, the following brief summary may be given for the guidance of navigators:
(a) The inaccuracy of tables showing the dip and the visibility of objects should always be suspected when there is a marked difference between the temperature of the air and that of the sea water.
(b) The errors will be largest in calm weather and when the eye is not far elevated above the sea, and will decrease as the wind increases and the eye is raised.
(c) When the air is warmer than the water, the visible horizon is raised above its normal position; the altitude corrected by the ordinary dip table will be too small, and the resulting Sumner line will be farther from the observed body than the true line. An object will be sighted from a greater distance than usual.
(d) When the water is warmer than the air, the visible horizon is lowered below its normal position; the altitude corrected by the ordinary dip table will be too large, and the resulting Sumner line will be nearer the observed body than the true line. An object will be sighted from a less distance than usual.