168 
MESSRS. A. E. H. LOVE AND F. B. PIDDUCK 
Article. Page. 
The First Reflected Waves. 
18. Conditions determining the First Reflected Wave from the Left.186 
19. Determination of the First Reflected Wave from the Left.187 
20. Determination of the First Reflected Wave from the Right.188 
21. Relation between Velocity and Pressure at a Piston.190 
22. Integration of the Equation for X.191 
23. Determination of the Coefficients B.. . 192 
24. Second Method of determining the Coefficients A .... .193 
25. Third Method of determining the Coefficients A.196 
The Second Middle Wave. 
26. Method of determining the Second Middle Wave. ... 198 
27. Determination of the Second Middle Wave.200 
28. Indication of a General Method. 202 
29. Pistons of Equal Mass.203 
30. Incidence of the Second Middle Wave upon the Pistons .203 
31. Transformation of the Formula for the Second Middle Wave.204 
The Second Reflected Waves. 
32. Relation between Pressure and Velocity at a Piston. 206 
33. Relation between Velocity and Time at a Piston.208 
34. Displacement of a Piston.208 
35. General Method for the Second Reflected Waves.209 
36. Method of determining t .209 
37. Formula for the Time. 211 
38. Formula for Z. 212 
39. Formula for x 0 . 214 
40. State of the Gas at any Time. 214 
PART II. 
41. Numerical Constants .. 216 
42. Details of the Calculation.217 
43. Results. 220 
44. Calculation of Recoil ..222 
45. A Special Solution of the Hydrodynamical Equations.222 
46. Application to Ballistics.225 
PART I. 
1 . Introduction .—The first part of this paper, written by Love, contains a theoretical 
solution of the problem of rational hydrodynamics which has been named by writers 
on ballistics, Lagrange’s problem ” ; the second part, written by Pidduck, gives 
the application to ballistics. 
