collaboration with the administrators at the source of power from whom, alone, they can derive the practical assistance necessary to the maturing of their plans. The plans they prepare become, in brief, the statement of military principles affecting all naval activities.

9. A word about the technical side. How frequently it is remarked that a battleship is the apotheosis of mechanical complexity! The inferences might be drawn that genius must be called to its production and genius also to its successful operation. But there is this difference: the greater the genius involved in production, the less mechanical genius will be required for operating. Consider the remark of the skilled advertiser: "A child can run it!" Consider as well the stress and excitement of battle, which seriously reduces the ability of the average man to engage in activities requiring mental effort. Only the simplest acquired habits of action, rendered practically mechanical by drill, can be relied on. What better principle, then, could be found for the design of naval ships and their equipment than to obtain operational simplicity? Nor what requiring greater skill of the designer? We must come to a realization that there is a limit to human capacity. We must recognize that superlative engineering talent is produced of superlative qualities made expert by intensive training and extensive experience. No seagoing officer can at once be an expert in his profession and an engineer of equal ability. But it is not beyond his powers to become an expert in his profession and at the same time to gain sufficient knowledge of engineering that he can direct and assist the activities of real engineering experts in attacking naval problems. In fact, we must have officers who spend their time alternately at sea and in this work ashore-and we also must have real engineers to devote their entire time to purely technical matters.

10. There is no logical objection to developing ordnance engineers, propulsive engineers-in fact, all types of engineering experts from our own ranks, if we feel that our available material in Naval Academy graduates will yield the requisite supply and still provide us with line officers of ability. But these engineers must be recognized as such. They must be educated as such, must receive early training and post graduate training as such, must go through all the long process recognized as necessary in civil life, and more. They will have no time for regular sea

service, nor will their need for constant touch with the technical details of their work permit it, except for those sent forth from time to time to note performances with a technical eye. There would be an advantage in recruiting these men from the Naval Academy because they would have the spirit of loyalty which permeates the service, and they would receive their early training in contact with the sea. But it does not appear to me that the service can afford this method to secure all of its engineering talent. The fascination of technical work appeals to youth, and we would be very apt to lose many of our budding leaders to the ranks of the technicists. This we must not do. The success of the navy in war is the primary consideration, and to ensure it we require a wide field from which to select military leaders. Civil life abounds with engineers from among whom may be drawn the preponderance of talent required. Naval Academy graduates of pronounced technical ability and inclination should be specially trained as engineers after a brief service at sea. They would form a strong link between the line and purely civilian technicists, and would provide a logical field for producing necessary leaders in naval engineering. But we must recognize the fact that civilian technicists of adequate ability must be paid according to the scale prevailing in civil life-we cannot retain such men at the salaries now paid.

II. We may venture now to state the rôle of the line of the navy. It is to study and apply the art of naval warfare; to guide and co-ordinate the production of equipment, to institute appropriate training, to conduct the operations of the navy in the event of war. Three types of men are required: First, the leaders who combine the attributes of the others; second, the planners; third, the executives. And of each type we must know accurately the relative excellence of its membership so that the greatest ability may be applied at the top and the dead wood may be eliminated from the bottom. The fields of activity for these men are both ashore and afloat, but their primary field is the sea, for there alone can they gain first hand the experience which must fit them as experts in their profession, comparable in efficiency with the experts in technical endeavors.

[COPYRIGHTED]

U. S. NAVAL INSTITUTE, ANNAPOLIS, MD.

NEW METHODS OF EXTERIOR BALLISTIC
COMPUTATION1

By LIEUT. COMMANDER A. G. KIRK, U. S. Navy

During the war just ended it soon became evident that modern. high-powered guns would be fired at elevations considerably in excess of those formerly used. "Direct fire" was more or less out of date in land warfare. These new angles of elevation coupled with high initial velocities gave long trajectories. And in the endeavor to fire from protected positions far in the rear of the line of combat, or to injure the enemy in vital spots well behind its own front line, it was found absolutely necessary to be able to compute with accuracy these long trajectories. Similarly, it was essential that suitable means be provided for correcting the trajectory for any variation from standard conditions.

In general, it may be said that up to the outbreak of the war the calculation of the path of a projectile was performed by the method developed by Siacci. In America his method was modified in certain particulars by Prof. P. R. Alger, U. S. N., and by Major J. M. Ingalls, U. S. A. Essentially, it consisted of simple analytical equations, requiring a single operation for the solution of the entire trajectory. To accomplish this result it was necessary to replace certain of the variables with constants which represented their best mean values. The two factors of the ballistic coefficient which most affect the accuracy of that expression are: First, the constant of integration, B, and second, the altitude factor, fa. In

This article was originally prepared for the midshipmen at the Naval Academy; permission to print it has been kindly granted by Commander A. P. Fairfield, U. S. N., head of department. For certain information herein I am indebted to a note on "Numerical Integration" by Captain Dunham Jackson, U. S. A., and to the prefatory remarks of Bennett's Ballistic Tables," by Captain A. A. Bennett, U. S. A.

some quarters it was customary to include still another factor for the range-wind, fw, using data obtained from surface conditions. only.

The constant of integration, ß, has been given the value of unity by Prof. Alger in his work, so long as the angle of departure remained less than 15°. He states that in direct fire such an assumption may be considered correct with less than 1 per cent of error. Above that elevation, an approximation of B-Vsec has been proposed; and in certain army tables this value is used throughout (Artillery Circular M, 1917). Since ẞ is the mean value of COS"-2a where n is Mayevski's exponent, in long trajectories where a has a value in excess of 15°, considerable error arises from this source. The actual value of ẞ changes throughout the trajectory, being greatest at the terminals and least at the vertex. So that with large angles of departure a mean value is not satisfactory for accurate computation of the trajectory.

The altitude factor, fa, was intended to allow for the variation in the density of the air with altitude. As the projectile travels in its path, it passes through an air-medium of varying densities. These variations were taken care of in the Siacci method by assigning to fa a value corresponding to the mean height of the trajectory. Alger has assumed the trajectory on low angles of departure to be a parabola of vertical axis with the mean height equal to two-thirds the maximum ordinate. As the path of the projectile is not parabolic, and differs materially from this form on large angles of departure, a considerable error is introduced from this source.

It might also be mentioned that certain range-table assumptions with reference to standard conditions under which the data are computed, are not adaptable to any except the given set of rangetable conditions. Thus there are several refinements from this cause; which include rotation of the earth, air temperature effect on velocity functions, variations in ballistic wind and density in the upper air, and variations in the amount and direction of the force of gravitation. All of these produce appreciable errors in long trajectories, and for which an adequate method of correction does not exist in the old Siacci method.

The mean-value methods may then be summed up as inadequate for these reasons: