196 REPORT—1885. 
and therefore csecO=m, u=y’ 
Fe tiler, \. et eBay 
For light polarised at right angles to the plane of incidence, Hisenlohr 
proceeds by transforming Fresnel’s tangent formula in a similar manner, 
and finds 
7/2 = tan (g —im) . ; ; : (57) 
where 
cot g = cos (a — uw) sin Man "( pw : : (58) 
and the change of phase is given by 
1 
(59) 
tan d! = sin (a — u) tan 2tan™ aaa 
Hence in the general case the ratio of the amplitudes of the two 
reflected components is tan 8 where 
cos 23 = cos (a + w) sin 2tan'( ; ; (60) 
and the difference of phase is given by 
te ee eae 4 «) tan. Stent SP (61) 
(ae cos @ ) ir 
These last equations depend on Fresnel’s tangent formula, and this 
we know is not strictly true for transparent bodies. It is hardly 
probable, therefore, that the final equations for the difference of phase 
and the ratio of the amplitudes can be accepted as representing accurately 
the phenomena, and, in fact, Cauchy’s theory as here developed is no great 
advance on MacCullagh’s original expressions, with which it agrees 
throughout. 
In this theory the expression for the disturbance in the metal 
et (p—7) R(cos a+esin a), 
is € or, as we may write it, 
2 oR ot A Wd 
Ae ee e (rR cos a — ct). 
Hence the velocity of wave propagation is c/R cos a, as against c in 
air, and R cosa may be called the refractive index of the metal, while 
R sin a measures the co-efficient of absorption. Now Jamin, Quincke, 
and others have measured the quantities d — d' and # of the formule 
above, and from these Hisenlohr, in the paper already quoted, has calculated 
the values of Rand a. He finds that for silvera = 83°. This result Lord 
Rayleigh has made the basis of a serious criticism on the whole theory. 
Lord Rayleigh ! endeavours to attach a physical meaning to the con- 
stants in these formule, and in so doing starts from equations taken to 
represent the motion in the medium. 
Thus, for light polarised in the plane of incidence he assumes 
ag Wiel woof e aere 
7p +h en ae unre E 
1 Hon. J. W. Strutt, ‘On the Reflexion and Refraction of Light by intensely 
Opaque Matter,’ Phil, Mag. May, 1872. 
D, (62) 
