154 
POPULAR SCIENCE REYIEW. 
again, the light is said to be polarized. It is plane polarized if 
each particle moves backwards and forwards in a straight line. 
After a has performed a whole number of paths, the form into 
which ah c will be thrown is afh' c' . . . 
Before describing the methods of producing the beautiful 
colours so well known to be produced by the polariscope, it will 
be necessary to say something of the laws of refraction of light 
in crystals, and of the interference of waves. 
And first as to plane polarized light. 
Suppose ahc (fig. 8) to be a line of particles in their position 
of rest. If a wave of light polarized in a plane through ahc, 
perpendicular to the plane of the paper, be set up, the particles 
will, after a has performed a whole number of oscillations, lie 
in the line ah' c' .. . li a had not begun to move until half the 
time of a vibration after it really started, the particles would 
have occupied the position a h"c" ... 
The case we shall have most frequently to examine is that in 
which two causes exist, each of which would alone produce a 
set of waves such as ah'c' , , ,, of the same length and of the 
same height. In this case the effect of the two causes together 
is sum of the three separate effects. That is to say, if the two 
causes coexist, one of which would throw the particles into the 
position ah'c' . , . at a given time, and the other would throw 
them at the same time into the position a h"(f' . . . , the effect of 
the two causes together is to leave them all in their original 
position, ahc , . . For the position of any one, as d, is found 
thus : — The first wave would lower d to df, the second would 
raise it to d " ; the two together bring it into a position found 
by first drawing a line upwards as high as dd", and then 
measuring downwards a distance d"d, equal to d d". It is clear 
that, as d d' is equal to d d", and e e' equal to e e" , all the par- 
ticles will, at every moment, be in the position of rest. 
The wave ah''c"d" is said to be retarded by half a wave 
length, that is to say, to be half a wave length behind ah'c'd '. . . 
It is sufficiently clear that if a h"c"d" is moved forwards half a 
wave length, that is, this distance a, the curve a h"d'd" would 
cover the curve a h"c"d" at every point. 
We see then that two waves, one of which is retarded by half 
a wave length, produce rest, or, in the case of light, darkness. 
A more exact representation of the case most frequently 
occurring is this : — The wave a h'c'd' differs from a h"c"d" only 
in depressions in one existing instead of the elevation in the 
other. We may look on the three waves in two lights ; either 
we may say that they are both similar waves, one of which is 
behind the other (in a different 'phase), or we may say that one 
is a positive wave (producing elevations and depressions), and 
the other a negative wave producing depressions and elevations 
