Veblen and Lieutenant Alger. In France, similar work was done by Captain R. H. Kent. It is seen that these experiments added greatly to the effectiveness and therefore to the value of the guns in question. The work belongs to physics, notwithstanding the fact that one of these civilian officers was and is a professor of mathematics of the purest quality. That he was able to bring himself temporarily to neglect the fundamental concepts of geometry, in which realm he is one of our foremost thinkers, to enter into the problems of the war with an eagerness for close observation of actualities and a readiness to try out new methods, is very greatly to his credit. He is evidently a physicist by intuition and a mathematician by profession. It is to be noted (Fig. 4) that between the summers of 1918 and 1919 the range of the 6inch seacoast gun had been increased from about 14,000 yards to 28,000 yards for a 2 The range of 14,000 yards for the 6-inch gun is computed for a muzzle velocity of 3,000 feet per second at 45° elevation, basing the computation on the range obtained with a muzzle velocity of 2600 f.s. It ought to be pointed out that the Army had muzzle velocity of 3,000 feet per second, by variations in the form of the projectile suggested by crude experiments. In the case of the last projectile (Mark VIII.) there was rather large dispersion. Had the cardboard test been made it could have been foreseen that there would be this dispersion, for the projectile is evidently not sufficiently stable. In Fig. 5 it is seen that one projectile (6-inch Mark VIII.) has acquired a large yaw not far from the gun. This accounts for the fact that the dispersion for this projectile was large, of the order of 3,000 yards in 28,000. It may be contended that some of the experiments and tests here recorded are too crude to be classed as belonging to the domain of physics. But let me remind you that Galileo, who may be regarded as the father of our science, climbed the tower of Pisa and let fall two weights, one large and one small, to show that they fell in the same way. We a 6-inch shell which for a muzzle velocity of 2,600 feet per second had a range of 15,000 yards at 15° elevation, but this was a heavy projectile-108 lbs. -while that of the projectile experimented upon was 90 lbs. have made some progress since Galileo's time. We know that bodies are retarded by the air but we have assumed, on some experimental evidence, in the case of projectiles at any rate except for a constant of proportionality, that they are retarded in the same way. It is evident that in the matter of the laws of air resistance we are not far from the condition that the scientists of Galileo's time were in regard to gravitation. It is evident from the results of these experiments at Aberdeen that a very slight change in the form of the projectile may make a considerable change in the range obtained. And it is equally clear that those experiments merely touched the matter. The entire subject is still open. A number of years ago the Ordnance Department made inquiries concerning the possibility of using air streams of high velocity in tests on projectiles. During the war the project was submitted to the National Research Council. It was found that air streams one foot in diameter, with speed of 1,500 feet per second, requiring for their production 5,000 kw., could be furnished by the General Electric Company at their plant at Lynn, Massachusetts. There, with the most loyal support of the Bureau of Standards, and with the effective collaboration of Dr. L. J. Briggs of the bureau the Ordnance Department has conducted experiments which have for their object the determination of the forces of such air streams on projectiles of various forms. Velocities of the air have, so far, varied from 600 up to 1,200 feet per second and temperatures from 0° to 130° C. In these air streams, which are vertical, projectiles of various shapes can be held nose down, and the forces on them and pressures at various points on their surfaces, can be measured. A number of important results have been secured. First, for head-on resistance there is no one curve similar to the French B curve which gives the law of air 3 Without a knowledge on his part of other inquiries, negotiations for these experiments were carried on and pushed to a conclusion by Major Moulton. resistance for all projectiles. For example, in that law it will be seen by inspection (Fig. 1) that F/v2 is multiplied by the factor 3 when the velocity changes from 200 to 380 meters per second. In our curves the corresponding factor varies from 1.3 to 4 for the various forms of projectiles. In other words the force exerted on one projectile may be less at one velocity and more at another than the force for the corresponding velocity in the case of another projectile. It follows that there is no "best form" of projectile unless we specify the approximate velocity with which we are dealing. Second, the results obtained indicate the resistance introduced by the rotating band and show where this band should be placed to produce the least increase of resistance. Third, it appears that the rapid rise of the B curve in the neighborhood of V = 340 meters per second is not entirely determined by the velocity of the compressional wave, i. e., by the velocity of sound in the air. In some cases the force of air streams at 130° C. are identical with those at 30° C. (It is understood that the density of the air is standardized, i. e., that the forces plotted are those which an air stream of equal speed and of density 0.001206 gms./cm. would have exerted.) In other cases, however, the results indicate that the velocity of the compressional wave is one of the factors determining the resistance. The temperature relation seems to be a complicated one and our results are not at all complete on this point. Fourth, though we have not made quantitative measurements of the variation of force with the angle of attack of air and projectile, we have had some experimental evidence of the large forces which are called into play when this angle changes from “ nose on" to oblique. In one case, the force of the air on a fifty pound 4-inch projectile was of the order of 44 pounds, so that there was still about six pounds of down force. When the projectile was being removed from the air stream it was accidently tipped slightly. The air stream forced it farther from the vertical, bent off the steel rod holding it to the balance arm and blew the projectile up several feet over a railing into the yard. In another case, when the up force due to the air on a twoinch projectile was only about one third of the weight, i. e., about 1.5 pounds, an oblique action at a slight angle drove the projectile farther from the vertical, finally turned its nose up, bending the steel spindle in the process. It is evident that the oblique forces of air streams on projectiles may be many times the "nose-on" force for corresponding velocities. It is clear then that unless a projectile turns "nose-on" to a wind the method now in use for finding wind corrections are greatly in error. Enough has been said to show that the fundamental problem of the projectile is not one of mathematics. There are various mathematical methods of handling the problem. The English have a method highly analytical and complete. The French have a method rather tedious for computation but they excel in the graphic representation of results. The Italians still cling to the Siacci method. There are at least three methods in use in America, each one claiming points of merit. The problem is one of experimental science. We must first determine the complete law of air resistance for every probable form of projectile, then we must determine the variation of force as the axis of the projectile changes in direction; the torque about the center of gravity; the precessional and nutational motions under these forces, and the consequent effective lift and drag, as these terms are used in aerodynamics. Mathematicians may then find it necessary, using these known facts, to formulate the differential equations of a twisted trajectory and to evolve methods of integration. But it is quite probable that simple physical methods of integration may be devised. It is evident even from a superficial study of the matter that a gun is an inefficient engine. An appreciable part of the energy of the powder takes the form of heat and kinetic energy of the gas developed. Of the initial energy of the projectile a large part is used in overcoming the resistance of the air. Per haps in the warfare of the future we shall not need guns, on land at any rate. Rather we may hoist a carload of projectiles on dirigible, carry them over the enemy's cities or lines and drop them on carefully selected spots. But if we are to drop projectiles or bombs accurately we must know the laws governing the motion of such bodies. During the war, Drs. A. W. Duff and L. P. Seig carried on a series of experiments at Langley Field, in which the object was to find by photography the path of a bomb dropped from an airplane. By placing an intense light in a bomb they were able to photograph its path, to measure its velocity at any point, to obtain the speed of the airplane, and the wind velocity. These important results were contributed to the Americal Physical Society at the April meeting. At Aberdeen, Dr. F. C. Brown, then captain later major in the Ordnance Department, while flying over a shallow body of still water observed the image of the airplane in the water. To a casual observer this would have excited no special interest. But, being a physicist, knowing the meaning of a level surface and a line of force, Dr. Brown saw that he had with him a visible vertical line. However the airplane tossed and pitched the vertical direction could be identified. He made use of this fact in a very skillful way. Attaching to the airplane a motion picture camera he was able to photograph a bomb released from the plane at a height of about 3,000 feet during the whole course of the projectile to the earth. Time can be obtained either from the rate of motion of the camera or from the photograph of a watch placed so that its image also falls on the film. The distance that the bomb has fallen and its orientation in space can be determined from the dimensions of its image. Its angle of lag or its distance behind the vertical line from the plane can be found by measuring the distance between the image of the bomb and that of the airplane. Hence not only the complete trajectory can be found but also the relation of the trajectory at any point with the variation in direction of the axis of the bomb. It is assumed here that the motion of the airplane has been kept constant. The motion picture film which I shall show, which was kindly loaned to us by the Aircraft Armament Section of the Ordnance Department, will bring out clearly the tossing, pitching motion of the bomb in its course to the earth. INTERIOR BALLISTICS In interior ballistics, there are a number of unsolved problems. The first is concerned with the pressure produced in a gun by the exploding charge and its time rate of change. The ordinary method which has been in use has been to measure the so-called maximum pressure by the shortening produced in a copper cylinder. But experiments have shown that the amount which a cylinder of copper is compressed by an applied pressure depends on the amount of the pressure, the time of application, the previous history as regards tempering, annealing, compression, etc. It is known for example that an application of a pressure of say 36,000 pounds per square inch will give an extra shortening to a cylinder previously compressed to 40,000 pounds per square inch. But the ordinary procedure has been to place in the gun a copper cylinder which had been precompressed to an amount nearly that to be expected. Obviously such a cylinder may indicate a pressure in the gun in excess of 40,000 pounds when in reality it was less. Moreover, the copper cylinder need not indicate the maximum. Rather it indicates a summation of the total effect of the gases upon it. A smaller pressure applied for some time may produce a shortening equal to that due to a larger pressure for a shorter time. Notwithstanding this uncertainty in the behavior of a copper cylinder, that is the kind of gage which has been used to standardize all the powder used in guns. It is clear that we may doubt whether these powders have been standardized at all. What is wanted evidently is a gage which will register the pressure accurately at a certain instant and therefore which will give the complete variation of the pressure with time. Several gages have been devised which have points of excellence as well as defects. In the Petavel gage the compression of a steel spring was registered on a revolving drum by a light pointer. But the mechanical processes were not well worked out. Colonel Somers improved on Petavel's design in the mechanical details but neglected the optical. For small arms, both mechanical and optical details have been worked out by Professor A. G. Webster. In the gage the spring is a single bar of steel about 5 mm. square and 20 mm. long, which is bent by a plunger fitting into a cylindrical opening through the wall of the gun. Its moving parts have small mass and high elasticity, and it seems capable of giving an accurate record of the changes in pressure even when the whole time is of the order of a few thousandths of a second. But its use appears to be limited to the cases of guns which can be rigidly clamped during the explosion. a steel In the Bureau of Standards, Drs. Curtis and Duncan have been perfecting a gage which has been used in the large naval guns. Here a steel cylinder compresses spring. During the compression a metal point makes electrical contact with conductors equally spaced. Consequently electrical signals can be indicated by an oscillograph for these equal steps. The time pressure curve is then given if the spring can be properly calibrated. There is however some doubt on this point and there is also uncertainty in electrical contacts and in the friction of the system. What is needed is a method of calibrating accurately any gage by means of a known rapidly changing high pressure. Such a method has been worked out by the technical staff of the Ordnance Department, but the mechanical and experimental work still has to be done. I have given you here some applications of the older physics to old and new problems of war. The list even in this limited field might be easily increased. By means of the photography of sound waves from a projectile we may determine many facts concerning its motion, the frequency of its precessional and |