THE simplest method of sighting a rifle is by ascertaining from experiment what height of back sight is necessary at any particular distance, and this can be measured by any convenient means. The only method by which a proper comparison can be made between the elevation required by different rifles is to measure the elevation on the back sight in degrees and minutes of a circle which has the fore sight for its centre. In this way the precise angle of inclination of the barrel above the mark is accurately measured and expressed in the same terms, whether the barrel be short or long, and whether the sights be near together or far apart. We have described elsewhere the means by which the zero or basis of the scale of elevation is found. It is evident, since the bullet in its flight falls with increasing rapidity, that the rise of elevation in the second hundred yards will be greater than in the first hundred, and that in the third hundred greater than in the second hundred, and so on, the curve described by the bullet growing gradually steeper. If the angles for three or more distances are correctly known, it is possible to construct tentatively a table of angles which shall give the elevation for the intermediate distances. In dealing with such matters it is necessary to check by experiment very carefully the series of angles arrived at. We give here a complete table, which appears also in the official Text Book for Small Arms, 1894, and for which Sir Henry Halford and Mr. Metford are responsible, giving the angles of elevation for the 303 rifle up to 2,500 yards. It is certainly correct, so far as it

TABLES OF ANGLES

ANGLES OF ELEVATION FOR 303 LEE-METFORD RIFLE '

Velocity, 2,037 f.s. Service Load

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goes, for it was checked by Mr. Metford up to fully that distance. Yet, such a table is never to be depended upon at distances beyond those at which it has been actually tested. It will be seen that the third difference is a constant quantity, and that the other differences and the angles are obtained merely by addition. A similar table can be constructed for any rifle with any load, but it will usually require to deal with many figures in the decimal columns. A word of warning here as to this is advisable. Although the steps of increase at each stage are in perfectly regular progression, yet if, to

This table depends upon a formula given to Mr. Metford by Mr. William Froude, C.E., which is fully explained in the Text Book for Small Arms, 1894. It is as follows:-Angle of elevation in minutes

where n the range in yards; A, the angular value of the fall for 1 yard in vacuo; B, C, D, values for air resistance, which have to be determined for each particular bullet and charge.

save space, they are only given to one or two places of decimals, and if then the differences be taken out from the figures as they stand, apparent discrepancies will arise, by dwelling on which the table can be made to appear inaccurate, although it is really so only in the omission of detail for the sake of convenience. The path of the projectile as given in the table of angles is one to which no individual shot can be expected absolutely to conform, for some deviation from the normal of every shot of a group fired is quite noticeable, but the trajectory table will give the central line round which the group of shots will form itself at each distance.

Such tables are not capable of perfectly rigid application. They are arranged to be correct for a normal temperature of 60° and a barometric pressure of 30 inches, and as is mentioned elsewhere, the variation of these conditions affects the flight of the bullet considerably. They represent, therefore, standard curves which any variation of temperature or pressure will affect proportionately in all of their parts. Wind pressure from the front or rear has a similar effect. The writer prefers building up tables of angles which accord with the experience of a good many hundred shots to any attempt to lay down what the path of the bullet should be from considerations of the effect of gravity, and of what in theory the loss of velocity from the resistance of the air should be at each stage. He has known calculations based upon Bashforth's admirable experiments to go entirely wrong from want of appreciation of the differences introduced by the use of leaden instead of iron shot, and by alteration in the shape of the head. In trajectory work, as in more abstruse matters, calculation may be misleading unless it goes hand in hand at every step with experiment.

Besides a complete table of the angles of elevation for the 303 rifle for a velocity of 2,037 f.s., and the normal Metford bullet of 215 grains, there has been added an elevation table for the Martini-Henry rifle up to 1,200 yards, for a velocity of 1,315 f.s., and a bullet of 480 grains; and one for the old Metford Match rifle of 461 bore up to the same distance for a velocity of 1,300 f.s., and a heavier bullet of 570 grains, which, owing to the shape of its head, as well as

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its weight, has a lower trajectory than that of the MartiniHenry. The table for the 402 experimental rifle is carried to 2,000 yards, its velocity being 1,570 f.s., with a bullet of 384 grains. These tables of angles correspond with the trajectory curves shown in the diagrams. Similarly with the 256 Mannlicher, for which a table of angles up to 1,100 yards is given.

Those who have tried shooting at unknown distances will most easily understand the advantages gained by high velocities combined with flat trajectories. The chief difficulty in the field, a difficulty which begins almost where the whole instruction in the art of aiming and firing correctly at the rifle range ends, is that of ascertaining the distance of the mark. As the firer is further from the mark, not only is it more difficult for him to estimate the distance accurately, but the flight of the bullet demands that it should be even more nearly known than at closer distances. For instance, while an exposed man standing would be hit at any distance up to 565 yards by the bullet from a 303 rifle sighted for that distance, and aimed at his feet, the flight of the bullet when fired with suitable sighting at a man 1,000 yards away will only jeopardise him if the distance be judged correctly to within less than 25 yards one way or the other, because the angle at which the bullet falls is so much steeper at further than at nearer distances. At 1,000 yards with the LeeMetford it is about 2° 25'. At 2,000 yards the bullet is falling at an angle of about 10°, and the danger zone for the man is only about 12 yards.

It is, of course, four times as hard to judge the distance at 2,000 yards to within 12 yards as it is to judge it at 1,000 yards within 25 yards, but much greater errors in estimation of distances than that of 25 yards at 1,000 are frequently made. With the Snider rifle, independently of the inaccuracy of its shooting, a far more exact estimation of distance was required, as the more rounded character of its trajectory at once shows. It is, perhaps, hardly necessary to enlarge upon this subject, since it is one the comprehension of which goes with the most rudimentary knowledge of the flight of a bullet. Whereas in early times the path of a projectile was imagined