516 
NATURE 
| April 27, 1871 

of reflection, the successive polarisation is right-handed when the 
analyser moves from left to right, and if it is to the right of the 
plane of refraction, other circumstances remaining the same, the 
successive polarisation is left-handed. 
It must be taken into consideration that the principal section 
of the film is inverted in the reflected image, so that if the plane 
of polarisation of the quickest ray in the film is to the left of the 
plane of reflection, it is to the right of that plane in the reflected 
image. 
It may not be uninteresting to state a few obvious conse- 
quences of this successive polarisation in doubly refracting lami- 
nz, right-handed and left-handed according to the position of the 
plane of polarisation of the quickest ray. They are very striking 
as experimental results, and will serve to impress the facts more 
vividly on the memory. 
1. A film of uniform thickness being placed on the diaphragm 
with its principal section 45° on either side the plane of reflec- 
tion, when the analyser is at 0° or 90°, the colour of the film re- 
mains unchanged, whether the film be turned in its own plane 
go”, or be turned over so that the back shall become the front 
surface ; but if the analyser be fixed at 45°, 135°, 225°, or 315°, 
complementary colours will appear when the film is inverted 
from back to front, or rotated in its own plane either way 90°. 
2. If a uniform film be cut across and the divided portions be 
again placed together, after inverting one of them, a compound 
film (fig 4) will be formed, which, when placed on the diaphragm, 
will exhibit simultaneously both right-handed and left-handed 
successive polarisation, When the analyser is at 0° or 90° the 
colour of the entire film uniform ; as it is turned round the tints 
of one fportion ascend, while those of the other descend ; and 
when the analyser is at 45° or 7290°+45°, they exhibit comple- 
mentary colours. 
3. A film increasing in thickness from one edge to the other is 
well suited to exhibit at one glance the phenomena due to films 
of various thicknesses. It is well known that such a film placed 
between a polariser and an analyser will show, when the two 
planes are parallel or perpendicular to each other, and the princi- 
pal section of the film is intermediate to these two planes, a 
series of parallel coloured bands, the order of the colours in 
each band from the thick towards the thin edge being that of 
their refrangibilities, or R, O, Y, G, B, P, V. The bands seen 
when the planes are perpendicular, are intermediate in position 
to those seen when the planes are parallel ; on turning round the 
analyser these two systems of bands alternately appear at each 
quacrant, while in the intermediate positions they entirely dis- 
appear. 
Now let us atcend to the appearances of these bands when the 
wedge-form film is placed on the diaphragm of the instrument, 
Fig. 1. As the analyser is moved round the bands advance towards 
or recede from the thin edge of the wedge without any changes 
occurring in the colours or intensity of the light, the same tint 
occupying the same place at every half revolution of the analyser. 
If the bands advar.ce towards the thin edge of the wedge, the 
successive polarisation of each point is left-handed ; and if they 
recede from it the succession of colours is right-handed ; every 
circumstance, therefore, that with respect to a uniform film 
changes right-handed into left-handed successive polarisation, in 
a wedge of the same substance transforms receding into advancing 
bands, and zice versd. These phenomena are also beautifully 
shown by concave or convex films of selenite or rock-crystal, 
which exhibit concentric rings contracting or expanding in ac- 
cordance with the conditions previously explained. 
4. Few experiments in physical optics are so beautiful and 
striking as the elegant pictures formed by cementing lamine of 
selenite of different thicknesses (varying from g;yy to z/5 of an 
inch) between two plates of glass. Invisible under ordinary 
circumstances, they exhibit, when examined in the usual polarising 
apparatus, the most brilliant colours, which are complementary 
to each other in the two rectangular positions of the analyser. 
Regarded in the instrument, Fig. 1, the appearances are still 
more beautiful ; for, instead of a single transition, each colour 
in the picture is successively replaced by every other colour. In 
preparing such pictures it is necessary to pay attention to the 
direction of the principal section of each laminze, when different 
pieces of the same thickness are to be combined together to 
form a surface having the same uniform tint ; otherwise in the 
intermediate transitions the colours will be irregularly disposed. 
5. A plate of rock-crystal cut perpendicular to the axis loses 
its successive polarisation, and behaves exactly as an ordinary 
crystallised film through which rectilinear polarised light is 
transmitted. 


6. A thick plate of unannealed glass undergoes a series of 
regular transformation, 
The phenomena of successive or rotatory polarisation I 
have experimentally demonstrated admit of a very simple expla- 
nation. 
The polarised light incident on the crystallised plate is resolved 
into two portions of equal intensity polarised at right angles to 
each other, one in the principal section, the other perpendicular 
thereto. These resolved portions, when they fall on the silver 
plate, have their planes of polarisation each at an azimuth of 
45°, one to the right, the other to the left of the plane of 
reflection. These are a-ain resolved in the plane of reflection 
and the plane perpendicular thereto, and are in consequence of 
the unequal retardation, which in silver at an angle of 72° 
amounts toa quarterof an undulation, converted into circularly 
polarised beams, one right-handed, the other le!t-handed. 
The various homogeneous rays being accelerated differently in 
their transmission through the two sections of the crystallised 
plate this difference is preserved after reflection from the silver 
plate, and the oppositely circularly polarised beams are reflected 
with the same difference of phase as the two plane-polarised rays 
are when emerging from the crystailised lamina. The composi- 
tion of two circular waves, one right-handed the other left- 
handed, gives for resultant a plane wave, the azimuth of which 
varies with the difference of phase of the two components. 
When the plane of polarisation does not lie equally between 
the two rectangular sections of the laminze, these still remaining 
45° from the plane of reflection of the silver plate, the beam is 
resolved into two unequal portions, the amplitudes of which are 
as sin a, to cos a, 
Each therefore gives rise to a circular undulation of different 
amplitude. The resultant of two opposite circular undulations 
of different amplitudes is an ellipse of constant form, the axes of 
which vary in position according to the difference of phase. The 
same phenomena of successive polarisation are therefore ex- 
hibited in whatever azimuth the laminze is turned in its own plane, 
but the tints become fainter and fainter until ultimately, when 
the principal or perpendicular section is parallel to the plane of 
reflection of the polarising plate, all colour disappears. 
By means of the phenomena of successive polarisation it is 
easy to determine which is the thicker of two films of the same 
crystalline substance. Place one o! the films on the diaphragm 
(2) of the instrument (Fig. 1 a) in the position to show, say, 
right-handed polarisation, then cross it with the other film ; if the 
former be the thicker, the successive polarisation will be still 
right-handed ; if both be equal there will be no polarisation ; and 
if the crossed film be the thicker, the successive polarisation wi! 
be left-handed. In this manner a series of films may be readily 
arranged in their proper order in the scale of tints. 
In the experiments I have previously described the planes 
of reflection of the polarising-mirror and of the silver plate were 
coincident ; some of the results obtained when the azimuth of 
the plane of reflection of the silver plate is changed are in- 
teresting. 
I will confine my attention here to what takes place when the 
plane of reflection of the silver plate is 45° from that of the 
polarising-reflector. 
When the principal sections of the film are parallel and per- 
pendicular to the plane of reflection of the polarising mirror, as 
the whole of the polarised light passes through one of the sectio ns 
no interference can take place, and no colour will be seen, what- 
ever be the position of the analyser. 
When the principal sections of the film are parallel and per- 
pendicular to the plane of reflection of the silver plate, they are 
45° from the plane of reflection of the polarising mirror. 
The polarised ray is then resolved into two components polar- 
ised at right angles to each other, one component is polarised 
in the plane of reflection of the silver plate, the other perpen- 
dicular thereto ; and one is retarded upon the other by a quarter 
of an undulation. 
When the analyser is 0° or 90° no colours are seen, because 
there is no interference ; but when it is placed at 45° or 135°, 
interference takes place, and the same colour is seen as if light 
circularly polarised had been passed through the film. The 
bisected and inverted film shows simultaneously the two comple- 
mentary colours. 
But when the film is placed with one of its principal sections 
223° from the plane of reflection of the polarising-mirror, on 
turning round the analyser the appearances of successive polari- 
sation are reproduced exactly as when the planes of reflection of 
the silver plate and of the polarising-mirror coincide, In this 

