March 5, 1920] 



SCIENCE 



231 



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 two- 

 inch 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 pro- 

 jectile 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 prob- 

 lem. 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 com- 

 plete law of air resistance for every probable 

 form of projectile, then we must determine 

 the variation of force as the axis of the pro- 

 jectile changes in direction; the torque about 

 the center of gravity; the precessional and 

 nutational motions luider these forces, and 

 the consequent effective lift and drag, as these 

 terms are used in aerodynamics. Mathe- 

 maticians may then find it necessary, using 

 these known facts, to formulate the differ- 

 ential 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 a 

 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 pho- 

 tograph its path, to measure its velocity at 

 any point, to obtain the speed of the airplane, 

 and the wind velocity. These important re- 

 sults were contributed to the Americal Phys- 

 ical 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 dis- 

 tance 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 varia- 

 tion in direction of the axis of the bomb. 



