remains to see what light the recent volley firing throws on this point. The only data where the observed dispersion of the projectiles is referred to the individual mortar from which each was fired, and the plane of the trajectory passing through it, are the following, which are derived from the two volley tables given above. It must not be forgotten that every mortar mounted for service has its own "personal equation," and that this will depend not only on its own perfection of manufacture but also very largely on the accuracy of graduation of the azimuth circle, the correct placing of the zero in the meridian, the care given to accurately level the platform and especially the axis of the trunnions, etc., etc. It is therefore apparent that the numerical coefficient of a formula derived from practice with single pieces must be too small when the firing of different mortars is combined in a volley. All that should be expected is that the law of the squares should be confirmed, and that this is confirmed by these data is shown by the following figures: For the shorter range, 29962 × 2244 20 142 200 00Q. Accepting then the dictum that in single mortar practice, or in volley practice when the deviations of each projectile are referred to its own piece and to the plane of its own trajectory, the 25 per cent. probable rectangle is a function of the square of the range, the coefficient of the formula applicable to the Sandy Hook battery can be easily computed from the above table. Thus Adopting 7 or 8 as a sufficiently close approximation to the numerical value of this coefficient the Sandy Hook battery formula becomes A = 0.00007 R2 or A= 0.00008 R2. Comparing this with the expression for single mortar practice, viz: A = 0.00001 R2, it appears that the area of the 25 per cent. probable rectangle for a single mount is only increased seven or eight times when the firing is done from sixteen different mortars, carriages and platforms, a fact which certainly speaks well for the care exercised by both the Ordnance and Engineer Departments in equipping this battery. The next matter for consideration, and this is the important practical question, is the total distribution to be expected when the firing is done from the entire battery, and is estimated from the middle point of the group and from the vertical plane passing through this point and parallel to the several planes of the trajectories. A similar discussion might be undertaken for each pit referred to its middle point, but it would possess comparatively little interest and will not be attempted. It is to be noted that the deviations caused by separating the mortars when the points of impact are referred to a common system of coordinate axes, is relatively less as the range increases. Moreover every deviation from the plane of fire increases the dispersion when referred to that plane, while deviations toward an intermediate plane of reference may increase the apparent accuracy. For these and other reasons it may be inferred that when referred to the central plane the 25 per cent. probable rectangles will vary with a lower power of the range than the square. The data available for this investigation are the following, derived from the two volley tables given above. Since the engineer requirements for magazine cover, etc., compel the facing of the four pits at the corners of a rectangle, not a square, the relative positions of the mortars will depend upon the angle which the plane of fire makes with the axis of the long gallery. When firing parallel to this axis the dispersion in range will have its maximum value; and the dispersion laterally, its minimum value. With the plane of fire at right angles to this axis, the reverse will hold in both cases. For the 3000 yard volley the actual angle between these lines was 37 degrees, and for the 6000 yard volley 23 degrees. The figures therefore correspond to fair average conditions. As at the 6000 yard volley only nine of the shell were identified with the mortars from which they were fired, although all were accurately located, the results are discussed separately in the table. The elevations in every case were 60 degrees. It is evident from an inspection of these figures that the 25 per cent. probable rectangle is proportional to the first power of the range rather than to its square, as in the case of single mortar firing referred to the actual plane of fire; and it remains to decide from the several values of the coefficient whether the accordance is sufficient to,justify an assumption that this is the true function. For the shorter range 2101 = 0.701, For the longer range For the longer range 0.735, These values vary so little from each other that the assumption made seems proper; and also that, until further data are obtained, we may adopt 0.7 provisionally as the value of the coefficient; giving the following formula, used in the sixth column of the last table: A = 0.7 R. It may be urged that the existing data are insufficient to warrant definite mathematical conclusions on these several points, and I incline myself to this opinion; but it should be remembered that some estimate must be formed as to practical results to be expected in actual firing, and that conclusions based on a careful and rigid analysis of such materials as we have, are more to be trusted than the only alternative, bald guessing. To sum up then, it appears from this important firing that the conclusion reached from earlier practice with single mortars and referred directly to the plane of fire, that the precision will vary inversely with the square of the range, is confirmed; but that when mortars are grouped as in the battery at Sandy Hook, the area included in the probable rectangle will be seven or eight times as large as when the practice is from a single piece. Also that when the service is by volley from the entire battery and is referred to a central plane of fire with ranges estimated from the middle point of the entire group, the precision will vary inversely with the first power of the range, and that the area of the 25 per cent. probable rectangle in square yards may be provisionally |