350 CARNEGIE INSTITUTION OF WASHINGTON. 



MATHEMATICAL PHYSICS. 



Moulton, F. R., University of Chicago, Chicago, Ilhnois. Investigations in 

 mathematics, cosmogony, and celestial mechanics. (For previous reports 

 see Year Books Nos. 5, 6, 8-17.) 



The greater part of the year was spent in the Government service 

 as major in ordnance, U. S. Army, in charge of the ballistics branch 

 of the Ordnance Department. The duties were (1) the planning and 

 direction of range firing of all the artillery of the U. S. Army, (2) the 

 preparation of range tables for all artillery of the U. S. Army, (3) 

 mathematical investigations in ballistics, (4) the formulation and 

 direction of experiments on artillery problems. 



The subject of ballistics was found in a very unsatisfactory state 

 both mathematically and practically. So far as it pertains to the 

 translation of projectiles and the influences of abnormal conditions, it 

 was placed on an entirely new basis. The results of these investiga- 

 tions were issued in confidential blueprint pamphlet form by the 

 Ordnance Department. The titles of the papers written by the 

 author of this report are : 



1. On Methods of Computing Trajectories (a collection of nine different investigations). 



2. Effects of the Earth's Rotation on the Flight of Projectiles. 



3. On the Determination of the Law of Retardation of a Projectile by the Atmosphere 



from Firings through Velocity Screens. 



4. The Second and Higher Order Terms in Differential Variations. 



5. Fundamental Theorems on the Solution of Differential Equations and the Logical 



Basis for the Numerical Solution of Differential Equations. 



6. Effects of Variations in the Velocity of Sound on Trajectories. 



7. Formulas for Interpolation. 



8. General Theory of the Computation of Differential Variations. 



9. Curves of Constant Fx' and Fy'. 



10. On the Determination of the Law of Retardation of a Projectile by the Atmosphere 



from Firings through Velocity Screens (second paper). 



A summary of all the work was embodied in a history of the Ballistics 

 Branch and was issued in a final report of 91 pages. 



In the last few months work has been resumed on periodic orbits, 

 and the manuscript for the final chapter on this work is receiving 

 its final touches. 



