THE POLARISCOPE. 
155 
at corresponding points; and then the waves ah'c'df and a"h"c"d" 
are to be reckoned in the same phase. So that two equal waves, 
one positive and one negative, in the same phase produce dark- 
ness or rest. 
Suppose we wish to find the effect of a given set of positive 
waves together with an equal set of negative waves, the latter 
^ wave-length behind the former. Draw the positive set 
a h"cf'd", and another positive set, a h"'c"'d"'^ \ wave-length 
behind the first. The latter are to be reckoned negative, and 
we must therefore subtract the motion caused by the second 
from that caused by the first. 
To find the resultant, consider the particle 6. The first 
positive wave would raise it to h" ; the second wave, if positive, 
would raise it to h'" ; if the second set is to be reckoned nega- 
tive, we must raise the particle to h", and then lower it to 6^, 
where is equal to h h'". The resultant wave is . . . 
Therefore a positive wave, together with a negative wave \ 
wave-length behind, produce a positive wave 1*4 times higher 
than either, and J of wave-length before the first, or we may call 
it a negative wave f of a wave-length behind the first. 
This case is important for this reason. We shall have to con- 
sider cases of this kind. 
Waves travel in one medium, so that the motion of every par- 
ticle is parallel to of (fig. 5). Suppose of the height of the 
waves. They then enter a medium in which the motion must 
be parallel to either of the two lines o 6 or o 6'. The wave, 
the vibrations of which are along o /, will, on entering the 
medium, be broken up into two waves, the vibrations in which 
will be equal to o m or o n, and parallel to these lines. These 
will travel on independently of each other. Now, suppose they 
meet with another medium, in which the vibrations must be 
parallel to m' n' perpendicular to of. Draw m m', nn\ per- 
pendicular to m' n' . The motion in the third medium will be 
the sum of the two waves whose heights are m m' and n nf. 
mm' and nn' are equal, and in opposite directions. They will 
therefore produce darkness unless the waves om^ on have tra- 
velled with different speeds, so that one of them is behind the 
other on reaching the third medium. In that case we have seen 
that the light may have any intensity between darkness and the 
sum of the light due to each set of waves. For we should have 
stated that the intensity of light is proportional to the square of 
the extent of vibration of each particle, or, which is the same 
thing, to the square of the light of the wave. 
When a ray of light enters any crystal not of the cubical 
system, it is divided into two rays which pursue different paths. 
One of these rays is refracted according to the same laws as hold 
for glass, water, &c. This is called the ordinary ray. The other is 
VOL. VII. — NO. XXVII. M 
