§1. 
§2. 
§3. 
84. 
§5. 
§6. 
§7. 
§8. 
§9. 
§10. 
aie 
g12. 
§13. 
§14. 
§15. 
§16. 
§17. 
gis. 
g19. 
§20. 
§2l. 
§22. 
Analytical Table of Contents 
The equations of hydrodynamics, allowing for compressibility, 
but neglecting viscosity and heat conduction. The Lagrange- 
ian form. One-dimensional case -----=-------=----=----=---=-— 
The conservation of energy and the principle of isentropy ----- 
The formation of shocks ------------<---<9---<=—--=- == === == ===== 
The shock equations of Rankine and Hugoniot. Shocks and entropy 
Mathematical complications caused by the presence of shocks --- 
The idea of a simplified numerical approximative procedure. 
Discussion of a special case. The degradation of energy ---- 
Expressions for the degradation of energy --------------------- 
Physical interpretation of the proposed numerical approximative 
NERO CCU a a 
Continuation -----------<--9 99-999 === 
The behavior of energy =---=--—~<<--— <9 388 $= = = 
Discussion of an example ----------------~-------~--------~----- 
The oscillations caused by shocks ------~--------------------=-- 
Mathematical interpretation. Weak convergence ---------------- 
Statement of the program. Choice of AGand At ---------- 
Procedure. Criteria by which the computations can be con- 
trolled. The importance of "experimental" problems --------- 
The three problems which were solved at the Ballistic Research 
Laboratory at Aberdeen, Maryland. Description ---------~---- 
Continuation -------------------------------------------------- 
Continuation -----------<----------------- - -—-- ---- - -- -- --------- 
Analysis and interpretation of the results -------------------- 
Conclusions. Proposed extensions of the program -------------- 
The spherically symmetric case -------------------------------- 
Two- and three-dimensional problems --------------------------- 
Figures 1 and 2 
311 
