There seem to be two opinions as to the best basis from which to find the correct sight-bar range in battle; one opinion being that the best basis is the use of a range-finder, and the other opinion being that the best basis is spotting.
In an article in the last number of the INSTITUTE, the present writer endeavored to prove that, even if spotting from aloft be the best basis for target practice in absolutely smooth water, it could not be used long in battle; and that the use of protected rangefinders, supplemented during the opening stages of the battle by an observer aloft, is the only practical way of securing accurate sight-bar ranges in battle.
The intention of the present paper is to point out briefly that even under peaceful conditions, and no matter what method, or what instrument, we use, the accuracy of the sight-bar range resulting must be strictly proportional to the accuracy of the method or the instrument used. Its intention is further to point out that no spotting "method" can be nearly as accurate as a range-finder, with an error less than one-tenth per cent per 1000 yards.
Probably no one will gainsay in words the statement that "no matter what method or what instrument we use, the accuracy of the sight-bar range resulting must be strictly proportional to the accuracy of the method or the instrument used." But does every one appreciate clearly what this means? It means that if we are to secure an accuracy of sight-bar range, which, for instance, with a target 6000 yards distant, will tell us within 36 yards how far a given shot fell short, the instrument or the method by which we do it must be capable of attaining that accuracy. If spotting be used, and the spotter be, say 75 feet above the water, then the method, or the instrument, which he uses must be such that he can ascertain accurately the difference between 5964 and 6000 yards; that is the difference between the angle subtended by 75 feet at 5964 yards and the angle subtended by 75 feet at 6000 yards that is 6 seconds of arc. If he makes an error of 6 seconds of arc in ascertaining the size of this angle of 6 seconds of arc, he makes an error of 36 yards, no matter what instrument, oz what method, he uses.
It hardly seems worth while to argue that no living man can ascertain any angle, big or small, with an error no greater than 6 seconds of arc, except with a mathematical instrument designed for that purpose. And therefore how futile must be any attempt to ascertain the correct sight-bar range at long distances by spotting, even in smooth water, except by continual trial and error; "up" and "down."
In the NAVAL INSTITUTE for September, 1906, in an article on the "Horizometer" by the present writer, is the paragraph: "It may be pointed out that the theory of spotting pre-supposes that the sea is absolutely flat, the water-line of a target a straight line, and the freeboard of the enemy's ship a constant quantity. But an extended series of observations at sea on a recent trip to Madeira, using the Denver, Des Moines, and Cleveland as targets, and using the horizometer as the observing instrument, showed that the mere height of the waves near the observed ship exercises a very disturbing influence on any attempt to estimate, or measure, the distance short of a distant ship that any point may be. The crest of a wave short of a distant ship is seen to be above her water-line and not below it; so that a point on that wave, such as splash made by a shot striking it, would seem to fall short, and yet the shot might be a perfect one; one that would have hit the ship, if it had not hit the wave. Furthermore, the bow or stern, when a long ship is pitching only a little, may rise and fall five feet each side of the horizontal; so that an absolutely perfect shot might go over it, or a poor shot might hit it. Any attempt to spot successive shots, and change the range by them under these conditions, which are normal and not abnormal, would produce confusion, and be impracticable."
This paragraph made the writer the recipient of some rather harsh language in which was intimated, without unnecessary delicacy, that he did not know what he was talking about, and was a "back number" generally; that ''practical experiments," carried on by a great many officers, had proved vertical spotting to be extremely accurate, etc.
In the last number of the NAVAL INSTITUTE, on page 292, the present writer showed the scientific inaccuracy of the usual "vertical spotting diagram," and pointed out that, although it purports to be a scientific diagram, it is distorted, the vertical line being drawn to a scale about 30 times as great as that on which the horizontal line is drawn. On page 294 of the same article he showed the diagram, or a portion of it, as it would appear if correctly drawn, supposing waves to be 100 feet apart and 10 feet from crest to hollow.
The period of faith in vertical spotting seems now, however, to have passed away; but it has been succeeded by another faith which to the writer seems equally unpractical. The new faith seems to be based upon the Theory of Probability, which teaches that, if a number of shots be fired under the same conditions at a target at any certain distance, we can compute from the number of shots that go over, or short, or hit, the probable distance by which the range used was in error.
This is very plausible and appears at first sight to be very simple. But in the whole domain of mathematics there is probably no more complicated theory than the Theory of Probability. And the practical application of the theory to spotting is just as difficult as the theory itself. For instance, if we fire 8 shots at the water-line of the target, it seems very simple to say that, if four go above the water-line and four short, the sight-bar range is correct. But it is not necessarily true. For instance, the four shots that went above, might all have gone only a little bit above, while the four shots that fell short, might have fallen very far short; in which case it is plain that the sight-bar range was too short.
But how much was the sight-bar range too short? What shall we do about it? Evidently the problem is indeterminate. We have not sufficient data to start from. If the four shots that went over, went over by exactly the same amount, and if each of the four shots that went short, went short by exactly that amount, we should feel warranted in concluding that the sight-bar range was correct. That is we would feel warranted, if we knew that all the shots that went over, went over by the same amount, and if we knew also that each of the shots that went short, went short by that amount. But we have no means of knowing those things.
In other words, even if a method be employed, instead of an instrument, the method cannot lead us to accurate results, unless some instrument be employed besides by which we can measure the amount by which shots go over or short. If we could fire an infinite number of shots, it is true, no such instrument would be needed; because, supposing the shots to be fired under the same conditions, the probability would be a certainty that the average distance by which the shots went over would be exactly equal to the average distance by which the shots fell short. Even if we fired only a thousand shots, the method would probably be sufficiently accurate for the purpose of gunnery at sea; but where only a small number can be fired, it seems hardly worth insisting that the method must be supplemented by some instrument which will measure the amount by which the shots fall short or over: that is, if we wish to lose as few shots as possible.
In other words, the method proposed is not a scientific one, under the conditions; and even if the weather be fine and the sea smooth, it cannot be made even to approximate accuracy, because the number of "events" that can be utilized must of necessity be too few; too few even to permit the method to be classed logically as coming under the Theory of Probability, because it does not permit the degree of probability to be known. The reason why it appears so good at first sight is simply because it is so crude that only large errors show out clearly. Imagine any one trying to tell by this method the difference between 5964 and 6000 yards!
It has been said that the use of range-finders has two disadvantages as compared with spotting.
These two alleged disadvantages are:
1. That a range-finder is not strong enough to resist the shock of discharge of guns, especially if it is placed on a turret. To this objection it may be answered:
(a) On April 15, 1907, in Chesapeake Bay, five 12-inch shells were fired from the turret of the Arkansas and the range-finder mounted upon the turret was not harmed or disadjusted in the least. It gave the same indications of distance of a lighthouse after the shots were fired as it did before. The lighthouse was about 6300 yards distant.
(b) The objection that any proposed appliance is "not strong enough" is the silliest objection that can be made against it, unless it is proved that the appliance cannot be made strong enough. It was this same miserable objection that held back the use of what we then called "mechanical gun carriages," telescope sights, prismatic telescopes, and all electrical appliances for so many years. Everybody knows that almost every new appliance ever introduced into the navy has had to be made stronger than it was originally; and that there is probably not a single officer in the navy who, if given the job of making any given range-finder strong enough to withstand the shock of guns, would fail to do it.
2. The second objection is a very sensible one. It is, that the vibration going on in a ship during a battle would be so great that no range-finder could be used. It is perfectly true that for two or three seconds after the discharge of any gun, a range-finder, even if at a different part of the ship, will show such dancing images that no reliable range can be read. The writer found this out on board the Maine in 1903; but the reason why these images dance is not because the instrument which shows them is a rangefinder, but because the instrument is an optically-magnifying instrument. Any telescope of equal magnification shows images that dance as much. This is optically a necessity. The reason why we notice the dancing more in a range-finder than in a telescope is simply because the images are so aligned as to make us detect it.
But in reality the same difficulty exists if we attempt accurate spotting. In order to make a spotting method accurate, we must use aloft instruments (not telescopes) of considerable magnifying power, so as to detect small differences in range; that is small vertical angles. If the observer be 75 feet high, then the magnifying power of the instrument used, whatever it is, must be as much as one-fifth of the magnifying power of a range-finder of 15-feet base, because its base line is five times as great. If the water were absolutely smooth, and the water-line of the target ship as precisely defined as the top of a mast of a ship which a range-finder ordinarily uses to sight on, then, supposing the instrument used for spotting to be constructed on an equally scientific principle, its indications would be equally accurate.
Now, as such an instrument would be only one-fifth of the magnifying power of the range-finder, it would be affected only one-fifth as much by equal amounts of vibration. But the vibration on a mast 75 feet above the water-line is at least five times as great as the vibration on the top of a turret, which is perhaps the solidest structure in the world.
So it seems that if an instrument, or a method, were invented as accurate as a range-finder, for use say 75 feet above the water, it would be no better than a range-finder, even if the sea were absolutely smooth and the water-line of the target ship were as sharply defined as the upper part of a mast against the sky. But the sea is never smooth, and no water-line can possibly be as accurately defined as the mast of a ship. Besides, in wartime every captain will make the water-line as deceptive in appearance as he can; or ought to do so.
Inasmuch as any instrument, or any method, for finding a sight bar range must be unfavorably influenced by vibration and other causes, it is plain that, to insure accuracy, there must be occasional, perhaps frequent, "cease firings," in order that the sight-bar range used may be verified. The frequency of these "cease firings" will, of course, depend on the conditions at the time, and principally on the rate of change of range.
It may be objected that instruments which show correctly the rate of change of range will enable us to use the correct sight-bar range indefinitely, after it has once been ascertained.
No; because, while such instruments are very accurate, per se, they depend on spotting, and on a more or less accurate estimate of the course and speed of the enemy, both for their original setting and their later corrections. If the spotting should indicate, rightly or wrongly, that the shots were falling short, we would correct our sight-bar range, no matter how much confidence we might feel in the rate of change of range instruments, or in our estimate of the course and speed of the enemy.
The essay of Lieutenant-Commander Stirling in this number of the INSTITUTE shows with perfect clearness how easy it will be to fool the range projector, by changes of course too small to be detected.