

Sir George Gabriel Stokes. 203 



the highest possible wave (capable of propagation without change of 

 type) enclose an angle of 120. 



The other is the great treatise on the Effect of Internal Friction of 

 Fluids on the Motion of Pendulums. Here are given the solutions of 

 difficult mathematical problems relating to the motion of fluid about 

 vibrating solid masses of spherical or cylindrical form ; also, as a 

 limiting case, the motion of a viscous fluid in the neighbourhood of 

 a uniformly advancing solid sphere, and a calculation of the resistance 

 experienced by the latter. In the application of the results to actual 

 pendulum observations, Stokes very naturally assumed that the 

 viscosity of air was proportional to density. After Maxwell's great 

 discovery that viscosity is independent of density within wide limits, 

 the question assumed a different aspect; and in the reprint of the 

 memoir Stokes explains how it happened that the comparison with 

 theory was not more prejudiced by the use of an erroneous law. 



In 1849 appeared another great memoir on the Dynamical Theory 

 of Diffraction, in which the luminiferous aether is treated as an elastic 

 solid so constituted as to behave as if it were nearly or quite in- 

 compressible. Many fundamental propositions respecting the vibration 

 of an elastic solid medium are given here for the first time. For example, 

 there is an investigation of the disturbance due to the operation at 

 one point of the medium of a periodic force. The waves emitted are 

 of course symmetrical with respect to the direction of the force as axis. 

 At a distance, the displacement is transverse to the ray and in the 

 plane which includes the axis, \vhile along the axis itself there is no 

 disturbance. Incidentally a general theorem is formulated connecting 

 the disturbances due to initial displacements and velocities. " If any 

 material sj^stem in which the forces acting depend only on the positions 

 of the particles be slightly disturbed from a position of equilibrium, 

 and then left to itself, the part of the subsequent motion which 

 depends on the initial displacements may be obtained from the part 

 which depends upon the initial velocities by replacing the arbitrary 

 functions, or arbitrary constants, which express the initial velocities by 

 those which express the corresponding initial displacements, and 

 differentiating with respect to the time." 



One of the principal objects of* the memoir was to determine the 

 law of vibration of the secondary waves into which in accordance with 

 Huygens' principle a primary wave may be resolved, and thence by a 

 comparison with phenomena observed with gratings to answer a 

 question then much agitated but now (unless restated) almost 

 destitute of meaning, viz., whether the vibrations of light are parallel 

 or perpendicular to the plane of polarisation. As to the law of the 

 secondary wave Stokes' conclusion is expressed in the following 

 theorem : " Let = 0, >/ = 0, = f(bt - x) be the displacements 



