unit which is really a definite fraction of a degree. Before going into the subject of Indirect Laying, it is essential that the mil be thoroughly understood. A mil is an angle. It corresponds in form to a degree and not to lineal measures as feet, yards, etc. It is that angle which a tangent equal to 1/1,000 of a radius will intercept at the center of a circle. A tangent is a straight line perpendicular to the radius at its intersection with the circumference of the circle. (Figure 2.) Now it has been found that in any circle there are approximately 6,400 mils. Since there are 360° in a circle: All calculations, as has been said, must from now on be made in mils. It is readily seen how adaptable the unit is both to horizontal and vertical measurements, for if a mil is that angle which is intercepted at the center by a tangent equal to 1/1,000 of the radius, so the tangent which a mil will subtend at any range is equal to 1/1,000 of that range as illus trated in the figure. At any range the front of the target is taken as the tangent to a circle of which the range is the radius. In order to determine, then, what number of yards a mil subtends at a given range, it is only necessary to divide the range by 1,000. (Figure 3.) 20 mils subtend 40 yds. at R 2,000, Before proceeding further, it must be understood that the sum of the angles of any triangle But 180° 3,200 mils. = = 180°. = 3,200 mils. ...The sum of the angles of a triangle a and a, are vertical angles and so also b and b1. In Figure 5, x + 90° + a = x1 + 90° + a1 It should also be understood that the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle. The hypotenuse is the side opposite the right angle. (Figure 6.) This rule is called the Pons Asinorum; so named from the similarity of the geometrical figure to a bridge, and the difficulty many beginners experience in getting over it; hence pons asinorum-the asses' bridge. And here it may be said that it would be foolish indeed to attempt to cross to the next chapter without a thorough grasp of the meaning of the term mil. It is easy to remember if we recall its derivation from the Latin word mille, meaning thousand. CHAPTER II INDIRECT FIRE AND DEFLECTION Indirect fire involves many details which only constant practice and study will master. It is possible for a gunner to deliver an effective direct fire without much knowledge of gunnery, for he may be as skillful in estimating the range and in the mechanical adjustment of sights and fuse setter as the most learned artillerist. Before proficiency and effectiveness may be attained in indirect fire, however, it is absolutely necessary that a complete knowledge of the subject be had. In fact, it would be impossible to even practice indirect firing without understanding the underlying principles of the method. In indirect fire, it is contemplated that an obstacle intervenes between the guns and the target, the obstacle serving to mask the guns from the view of the enemy. If the guns are behind such an obstacle with respect to the target, it is obvious that the target is not discernible from the guns. It is, therefore, necessary for the battery commander to seek a position from which he can see both the target and the guns and rapidly communicate with the men at the latter. This point of observation should preferably be on a flank of the line of guns, or directly in rear of and above them. It is called the battery commander's station. Now it is plain that if the battery commander, from his observing station, B, Figure 1, sights his instrument at some point, P, visible through the telescopic sights of the guns, and then revolves his telescope until the target, T, is picked up, that the horizontal angle PBT fixes the direction of T with respect to B. This horizontal angle or a is called the azimuth of the target and the point P, visible from the guns, is called the aiming point. This angle may be measured by the battery commander's telescope (see page 109, Handbook of the 3-inch Field Artillery Material, 1908), by the battery commander's ruler, (ibid., 114) or by the hand. (The last two methods will be subsequently explained in this chapter.) Aiming Point. Before proceeding further, it is well to dwell upon the subject of "Aiming Point." (Drill Regulations, 1908, Paragraphs 444, 445.) When indirect laying is to be employed, the selection of a suitable aiming point calls for special attention. The aiming point should be: 1. Surely visible from the emplacement of each gun; 2. Distinctive and easily picked out; 3. At a considerable distance from the guns; and 4. Preferably near the normal to the line of guns. If any doubt whatever exists as to the visibility of the aiming point, it is always best, before the guns come up, to go to the point where each gun is to be placed and make sure that the aiming point will be visible through the sights from that point. Some object which quickly attracts the eye should be selected; and, if possible, it should be the only object of its kind in the vicinity, so that doubt, hesitation, and mistakes may not arise, either in the designation of the aiming point or in finding it quickly after looking away. A distant aiming point is preferable, for the more the aiming point is removed from the guns the more are errors in calculation of parallax minimized. But it is not desirable to take inconspicuous aiming points or those at distances so great as not to be readily determinable. Usually points not less |