If c is the velocity of radiation in free space and ,u the refractive index of a transparent body, V= c/ï¿½; thus it is the expression c2 fï¿½ 2 (u'dx-}-v'dy+w'dz) that is to be integrable explicitly, where now (u',v',w') is what is added to V owing to the velocity (u,v,w) of the medium.
Now the expression above given cannot be integrable exactly, under all circumstances and whatever be the axes of co-ordinates, unless (ï¿½2u',ï¿½2vi,ï¿½2w') is the gradient of a continuous function.
If we eliminate P, Q, R from (22), the resulting equations are integrable with respect to t; thus Moa - M0a.
If we adopt this hypothesis, and substitute s= 2C T, where c is a constant, in the fundamental equation (9), we obtain at once d 2 E/d T 2 = - 2 (c' -c"), which is immediately integrable, and gives dE/dt=p = 2 (t Â° -t) (c'-c") .1 (m) E1_,'=(t-t') (c'-c") 12to-(t-}-t')1 (11) where t o is the temperature of the neutral point at which dE/dt = o.
They soon realized that the three body problem is not integrable, which means that no exact solution can ever be found.
How would you define integrable? Add your definition here.