1887.] C. Piazzi Smyth on the Edinburgh Equatorial. 21 
Observatory, Edinburgh; ignored arrangements supposed to have 
been made for all perpetuity, and rendered impossible, even to the 
Central Office of Works in London, the completion of this hitherto 
unfortunate Equatorial tele-spectroscope. A grand beginning, how- 
ever, of a first class instrument, it must be allowed ; and still safely 
preserved under a sound wind-and- water-tight Dome for any eventu- 
alities which the future may be charged to bring along with it. 
5. On Cauchy’s and Green’s Doctrine of Extraneous 
Force to explain dynamically Fresnel’s Kinematics 
of Double Refraction. By Sir William Thomson. 
1. Green’s dynamics of polarisation by reflection, and Stokes’s 
dynamics of the diffraction of polarised light, and Stokes’s and 
Rayleigh’s dynamics of the blue sky, all agree in, as seems to me, 
irrefragably demonstrating Fresnel’s original conclusion, that in 
plane polarised light the line of vibration is perpendicular to the 
plane of polarisation; the “plane of polarisation” being defined as 
the plane through the ray and perpendicular to the reflecting surface, 
when light is polarised by reflection. 
2. E’ow when polarised light is transmitted, through a crystal, and 
when rays in any one of the principal planes are examined, it is 
found that — 
(1) A ray with its plane of polarisation in the principal plane 
travels with the same speed, whatever be its direction (whence it 
is called the “ ordinary ray ” for that principal plane) ; and (2) 
a ray whose plane of polarisation is'[perpendicular to the principal 
plane, and which is called “the extraordinary ray ” of that plane, is 
transmitted with velocity differing for different directions, and 
having its maximum and minimum values in two mutually perpen- 
dicular directions of the ray. 
3. Hence, and by § 1, the velocities of all rays having their 
vibrations perpendicular to one principal plane are the same ; and 
the velocities of rays in a principal plane which have their direc- 
tions of vibration in the same principal plane, differ according to the 
direction of the ray, and have maximum and minimum values for 
directions of the ray at right angles to one another. But in the 
