198 REPORT—1885. 
ce and w being defined by the equations of page 195, so that the expres- 
sion for the refracted wave is 
2rr 
Lege ean = | Rea cos (w+a)+ysiné+ vel, 
where, it must be remembered, w is measured in the negative direction. 
Thus the coefficient of absorption is 
a Re sin (w+ a). 
According to the experiments of Jamin and Quincke, the refractive index 
Ros a for metal varies between } and }. 
§ 3. Wernicke,'! however, deduced, from some experiments of his own, 
values lying between 3 and 4. Wernicke’s experiments, however, were 
made by measuring the light transmitted at various angles of incidence 
by thin films of metal, and assuming that the light absorbed by a thick- 
ness d may be expressed by bk“*°®, while the refractive index p is given 
by sin @/sin 6’, Hisenlohr, in the paper already quoted, shows that the 
quantity calculated by Wernicke is really {R?+sin?4}', and that his 
experiments confirm Jamin’s and Quincke’s. 
In the second paper quoted Wernicke suggests, as the complete equa- 
tions of motion, the form 
ae ame dé ar di f 
de Dh _ — Sk 2¢ d » 
pte (AB) HBP BG Y's): Yai 
and other equations might be suggested which would give for the dis- 
turbance in the metal due to a point source expressions of the form 
Ae-® sin = (or — ot) : 
Chapter VI.—Dirrraction anp THE Scarrertne or Licut sy SMALL 
PARTICLES. 
§ 1. The principle first enunciated by Huygens, and applied so trium- 
phantly by Fresnel to the phenomena of diffraction, which consists in 
breaking up a wave front into elementary portions, calculating the effect 
of each in disturbing a distant point, and then finding the total dis- 
turbance at that point by simply summing the effects due to each ele- 
ment of the wave front, is a direct consequence of the fact that the 
disturbances and velocities are so small that their squares and higher 
powers may be neglected. The differential equations found for the 
motion are linear, and the complete solution is the simple sum of all the 
individual solutions. Again, it is fairly clear that the disturbance pro- 
duced at any point by an element of a wave front will vary as the area of 
the element and the reciprocal of the distance between it and the point 
answered; but it is not so clear how the effect is related to the angles 
which the line joining the element and the point make with the wave 
normal and the direction of vibration respectively. 
In Fresnel’s theory of diffraction the consideration of effects produced 
1 Wernicke, ‘On the Reflexion of Light from Metals,’ Pogg. Ann. t. clix. and clx. 
