222 



SCIENCE 



[N. S. Vol. LI. No. 1314 



where and at length. You have been told 

 the story of aviation, of the physical labora- 

 tory on wing; the story of wireless between 

 stations on the surface of the earth, -under 

 water and high in the air; the story of signal- 

 ing through the darkness of night or the 

 brightness of day; the story of sound- ranging, 

 of spotting enemy guns and the explosions of 

 our own projectiles seeking out those guns 

 and of the re-directing of our guns until those 

 of the enemy had been destroyed; the story 

 of submarine detection and of the extremely 

 valuable applications which the study of that 

 problem brought to us — the ability literally 

 to soimd the ocean — ^the ability to guide a 

 ship through fog or past shoals. These and 

 other stories you know. Indeed, many of you 

 contributed to their unfolding. It is my 

 desire here to present briefly some develop- 

 ments in a branch concerning which little has 

 been written, viz., warfare with guns, project- 

 iles, bombs. Later I want to turn from the 

 contemplation of problems of war to view our 

 subject in its relation to peace. 



The English playwright, John Drinkwater, 

 represents Abraham Lincoln as saying "the 

 appeal to force is the misdeed of an imperfect 

 world." Unfortunately the world is still im- 

 perfect. In the horrible business of killing 

 people in war, guns of all sizes and kinds are 

 the effective weapons. Have you reflected on 

 the enormous extent to which artillery was 

 used in the Great War? According to Sir 

 Charles Parsons, on the British Front alone, 

 in one day, nearly one million rounds of 

 nearly 20,000 tons of projectiles were fired. 

 Extend this along both sides of the Eastern 

 and Western fronts and you may gain some 

 idea of the daily amount of metal fired by 

 gtms. 



The actual American contribution of artil- 

 lery to the war was very small but at the time 

 of the Armistice we were making progress. 

 In America we often measure things by 

 money. The total amount of money author- 

 ized for artillery, including motor equipment, 

 was $3,188,000,000, and for machine guns 

 was $1,102,600,000. Judged by the money ex- 

 pended for them, guns are of importance. 



It is essential that we get as effective gvms as 

 possible and that we know how to use them. 

 Aircraft, and anti-aircraft warfare, barrage 

 firing, long range gims — all of these call for a 

 very complete and accurate knowledge con- 

 cerning the motion of a projectile and the 

 energy required to carry it to a certain place 

 and to cause it there to explode at a chosen 

 time. Exterior and interior ballistics are 

 thus matters of great importance. 



For two hundred years or more the subject 

 of exterior ballistics has been regarded as 

 belonging to' pure mathematics. But into 

 this realm physicists at times intruded. To 

 Newton we ascribe the law that the resistance 

 which a body experiences in passing through 

 the air varies as the square of the velocity. 

 But that great scientist made it clear that 

 that might not be the only law. Euler, one 

 hundred and fifty years ago, proved various 

 mathematical results. Assmning the air re- 

 sistance to vary as the square of the velocity 

 and that the density of the air did not change 

 with altitude, he showed that the coordinates 

 X, y, and the time can be computed by quad- 

 ratures. His method of taking the angle of 

 slope of the trajectory as the independent 

 variable has been followed by most of his 

 successors in ballistics. 



Even in Euler's method the variation of the 

 density of the air with altitude can be allowed 

 for by using small arcs and by changing the 

 constant of proportionality in the law of air 

 resistance to accord with the new density. 

 His method can in general be followed where 

 the law of air resistance is that given by 

 Mayevski, viz., 



where 



71 = 2 for F between and 790 f.s. 



= 3 790 970 



■=5 970 1,230 



= 3 1,230 1,370 



c=2 1,370 1,800 



== 1.7 1,800 2,600 



= 1.55 2,600 3,600 



Siacci, with his elusive pseudo-velocity, has 

 been the chief contributor along this line. Hia 



