X. The Aerodynamics of a Spinning Shell. 
By K. H. Fowler, E. G. Gallop, C. N. H. \ jock and H. W. Richmond, F.R.S. 
Received January 14,—Read May 6, 1920. 
Contents. 
Page 
Introduction.296 
Part I.—A General Description op the Motion of a Spinning Shell and the 
Principal Experimental Results. 
§ 1.0. The classical theory of the plane trajectory.299 
§1.1. The detailed specification of the complete force system.301 
§1.2. The numerical results of the experiments.307 
§1.3. A description in general terms of the angular motion of the axis of a shell.311 
Part II.—Details of the Experimental Arrangements and Material. 
§ 2.0. General arrangements.315 
§2.1. Measurement of the holes in the cards.319 
§ 2.2. Determination of the dynamical constants.323 
§ 2.3. Possible disturbing factors.324 
Part III.—Methods of Obtaining and Solving the Equations of Motion of 
a Spinning Shell. 
§ 3.0. Introductory.325 
§3.1. The general vector equations of motion.326 
§ 3.2. Equations of motion of type a. 329 
§ 3.3. Equations of motion of type (3 .331 
§ 3.4. Equations of motion of type y .333 
§ 3.5. The additional force components H, J and Iv.334 
§ 3.6. The approximate solution of equations of type ct .336 
§ 3.7. The solution of equations of type y.343 
Part IV.—Analysis of the Experimental Results. 
§ 4.0. Equations of motion in polar co-ordinates.344 
§4.1. Analysis of the experimental results.347 
§ 4.2. Determination of the motion of the shell in space.357 
§ 4.3. Estimate of the errors in the various solutions. 362 
Part V.—Summary and Conclusion. 
§ 5.0. Summary of preceding results.367 
§5.1. Problems for further discussion. .... 368 
§ 5.2. Effect of size and shape of shell.369 
VOL. CCXXI.-—A 591. 2 T [Published December 3, 1920. 
