In the course of supplying the numerous wants of navigation, it will often be found necessary to cut off, on a given bearing, the beam proceeding from a Lighthouse, as a guide to the seaman to avoid some shoal, or as a hint to put about and seek the opposite side of a channel. This is attended with some little practical difficulty, especially in lights from reflectors arranged externally on a circle, because a certain portion of light, chiefly due to the divergence caused by the size of the flames, and partly from the effects of the diffraction or inflexion of the light, spreads faintly over a narrow sector between the light arc and the dark one. Masking Lights. It becomes necessary, of course, to make allowance for this penumbral arc by increasing the masked portion of the lantern; and, where a very sharp line of demarcation is required, a board is sometimes placed on the outside of the Lightroom, in such a position, and of such length, that while it does not enter the boundaries of the luminous sector, it prevents the more powerful part of the penumbral beam from reaching the observer’s eye. This effect is, of course, more conveniently produced, where the circumstances admit of its adoption, by distributing the reflectors round the concave side of the lantern, towards the land; but such an arrangement is inapplicable when the illuminated sector exceeds the dark one. I have found, by observation, that the sector intercepted between the azimuth on which the lantern is masked and that on which total darkness is produced to an observer, at moderate distances, may be estimated at not less than 3° for dioptric, and 7° for catoptric lights of the highest class.[79]
[79] The method which I adopted for determining those quantities, was to mask a certain portion of the lantern of a lighthouse subtending an horizontal sector of about 30° or 40°, and at night to fix, by actual observation, at the distance of 5 or 6 miles, two points on the coast between which the light so masked was obscured. The angle included between the lines joining those points and the centre of the lantern was then determined by triangulation next day, and half the difference between the observed angle (which is always the lesser of the two) and the computed subtense of the masked sector of the lantern, is, in each case, the amount of the allowance stated in the text.
Those quantities may therefore serve to guide the Lighthouse engineer to approximate more rapidly to his object, as he will generally be safe in increasing the dark sector, by one or other of the above constants, according to the kind of apparatus employed. I need not add, that in a matter of this kind, a final appeal to actual observation is, in all cases, indispensable.
A few words on the subject of double lights, naturally spring out of what has been said about the masking of lights. Double Lights. The term double lights is properly and distinctly confined to lights on different levels, but not necessarily (as leading-lights are) in separate towers. The sole object of using double lights is for distinction from neighbouring lights; and they are unquestionably most effective in this respect, when they are placed in the same tower. In this point of view, therefore, I shall speak of them; and it is obvious that all that peculiarly belongs to them is, that the difference of level between them shall be sufficiently great to present the lights as separate objects to the eye of the seaman, when placed at the greatest distance at which it may be desirable that he should be able to recognise their characteristic appearance. In many cases it is not necessary (but it is certainly always desirable) that the lights should, from the first moment of their being seen, be known as double lights; but in others, it may well consist with safety, that two lights, which appear as a single light when first seen at the distance of 20 miles, shall at 15 or 10 miles distance be discovered to be double. Now we should at first be apt hastily to imagine, that all that is required to produce that effect, is to raise the one light above the other to such an extent, that the distance between them shall be somewhat more than a minimum visibile at the most distant point of observation, or, in other words, that the difference of the height of the lights should be such as to subtend to the eye at the point of observation, an angle greater than 13″·02, which is the subtense of a minimum visibile during the day.[80] But the effect of irradiation, to which I have already alluded, tends to blend together the images of the lights long before their distance apart has become so low a fraction of the observer’s distance from the Lighthouse, as to subtend so small an angle; and I have accordingly found by experiments, conducted under various circumstances, and at various distances, that repeated observations gave me 3′ 18″ as the mean of the subtenses calculated in reference to the distances at which the lights began to be blended into one.
[80] This quantity is deduced from observations made by my friend Mr James Gardner, while engaged on the Ordnance Survey, and may be regarded as the extreme limit of visibility, under the most favourable circumstances as to the state of the atmosphere and also the contrast of colours. The observed object, also, was a pole, not a round disc; and it is familiar to every one accustomed to view distant objects, that vertical length is an important constituent in their visibility.
Adopting this as the smallest angle which the two lights should subtend at the observer’s eye, we may find the least vertical distance between them which will cause them to appear as separate objects by the following formula:
H = 2 Δ . tan θ
in which Δ is the observer’s distance in feet; θ, half the subtense, = 1′ 39″; and H the required height of the tower between the two lights in feet. The following Table gives the height in feet corresponding to the distance in nautic miles, from 1 to 20 inclusive: the heights, which are the bases of similar isosceles triangles, increase, of course, in an arithmetical series:
| Distance of the observer in Nautic Miles. | Vertical distance in feet between the Lights. | Distance of the observer in Nautic Miles. | Vertical distance in feet between the Lights. |
|---|---|---|---|
| 1 | 6·02 | 11 | 66·22 |
| 2 | 12·04 | 12 | 72·24 |
| 3 | 18·06 | 13 | 78·26 |
| 4 | 24·08 | 14 | 84·28 |
| 5 | 30·10 | 15 | 90·30 |
| 6 | 36·12 | 16 | 96·32 |
| 7 | 42·14 | 17 | 102·34 |
| 8 | 48·16 | 18 | 108·36 |
| 9 | 54·18 | 19 | 114·38 |
| 10 | 60·20 | 20 | 120·40 |
Akin to the subject of Double Lights, is that of Leading Lights. Leading Lights, the object of which is to indicate to the mariner a given line of direction by their being seen in one line. In most instances, this line of direction is used to point out the central part of a narrow channel; and the alternate opening of the lights, on either side of their conjunction, serves to indicate to the mariner (who ought to conjoin with his watching of the lights the observation of the elapsed time and also frequent soundings) the proper moment for changing his tack. In some places, the line of conjunction of the lights is placed nearer to one side of a channel than the other, according as the set of the tides, or the position of shoals, may seem to require. In other situations, this line only serves as a cross-bearing to shew the mariner his approach to some danger, or to indicate his having passed it, and thus to assure him of his entry on wider sea-room. Similar considerations to those which determine the difference of elevation for double lights regulate the choice of the distance between two leading lights; but the question is less narrow, and may be generally solved graphically by simply drawing the lines on an accurate chart of the locality. In some few situations, the configuration of the coast does not admit of a separation between the lights, sufficient to cause what is called a sharp intersection; but, in most cases, there is room enough to place them so far apart, that but a few yards of deviation in the vessel’s course, from the exact line of the conjunction of the lights in one, produces a distinct opening between them on the opposite side of that line. In order to insure the requisite sharpness of intersection, the distance between the lights, wherever attainable, should be not less than one-sixth of the distance between the more seaward of the two Towers and that point at which the seaman begins to use the line of conjunction as his guide. I have only to add, that in situations where the land prevents a considerable separation between leading lights, they should be placed as nearly on one level as is consistent with their being seen as vertically separated, so as in some measure to compensate for their horizontal nearness, by rendering their intersection more sharp and striking than it can be where the observer must draw from the upper light an imaginary perpendicular in his mind, and then estimate the separation of the lights by the sine of an angle, which decreases as the difference of their apparent elevations increases.