Incluye índice: páginas 585-596

1. Introduction: Two existence-theorems -- 2. Cauchy's theorem -- 3. Linear equations and complete linear systems -- 4. Non-linear equations: Jacobi's second method, with mayer's developments -- 5. Classes of integrals possessed by equations of the first order: generalisation of integrals -- 6. The method of characteristics for equations in two independent variables: geometrical relations of the various integrals -- 7. Singular integrals and their geometrical properties: singularities of the characteristics -- 8. The method of characteristics in any number of independent variables -- 9. Lie's methods applied to equations of the first order -- 10. The equations of theoretical dynamics