1 6 Stokes, on the Nature of the Rbntgen Rays. 



(which I will call O) from which it came, P a point in 

 front of the wave, where the disturbance which will 

 arrive there is sought. From P let fall a normal P Q 

 on the front of the wave, and let A B, taken around Q, 

 be a small portion of the spherical shell which at the 

 present moment is the seat of the pulse, and suppose 

 the breadth of A B to be small compared with P Q and 

 with the radius of the shell, but large compared with 

 the shell's thickness. Let CD be an element of the 

 shell of similar size to A B, but situated in a direction 

 from P distinctly inclined to P Q ; and supposing all the 

 disturbance in the shell stopped except what occupies 

 one or other of the elements A B, CD, let us inquire 

 what will be the disturbance subsequently produced at 

 P in the two cases respectively. 



I have shown elsewhere* that in our present problem 

 the disturbance at P is expressed by a double integral 

 taken over such portion of the surface of a sphere with 

 P for centre and b t for radius (b being the velocity of 

 propagation) as lies within the disturbed region, which 

 in this case is the spherical shell or a part of it. It 

 will be convenient to think of a series of spheres drawn 

 round P with radii b t for increasing values of t. When 

 t is such that the sphere just touches the shell at Q, 

 and then goes on increasing, the disturbance is nearly 

 the same all over that portion of the surface of the 

 sphere which lies within the small region A B, and 

 that, whether we take the portion of the expression 

 for the disturbance at P which depends on the dis- 

 turbance (displacement or velocity) at the surface of 

 the sphere whose radius is b t, or the portion which 

 depends on the differential coefficient of the displace- 



* " On the Dynamical Theory of Diffraction." Cambridge Philo- 

 sophical Transactions, Vol. IX., p. i, or Collected Papers, Vol. II., p. 243, 

 Arts. 19-22. 



