...auxiliary equations dt+\ds=0, dt + \ds = 0 ........... (13). If the integrals of these are 8 = 0lt T=c,, respectively, then we have Now v being determinable...The particular forms of the arbitrary functions <f, and ty will depend solely upon the nature of the problem under consideration. One other point remains...

...being determinable by an equation of the same form as u, it follows that of the above two values of M one must be assigned to v, so that the solution of...system The particular forms of the arbitrary functions <£ and ifr will depend solely upon the nature of the problem under consideration. One other point...

...correspond the respective auxiliary equations If the integrals of these are respectively, then we have w Now, v being determinable by an equation of the same...problem will be contained in the system or in the system v=V(8) The particular forms of the arbitrary functions * and '/" will depend solely upon the nature...

...respectively, then we have v=V(T) Now, v being determinable by an equation of the same form as «, it follows that of the above two values of u one must...problem will be contained in the system or in the system «=«P(T) The particular forms of the arbitrary functions * and V will depend solely upon the nature...

...are S=c> respectively, then we have Now, v being <leterminable by an equation of the same form as M, it follows that of the above two values of u one must...solution of the problem will be contained in the system M or in the system « The particular forms of the arbitrary functions * and V will depend solely upon...