of Edinburgh, Session 1869 - 70 . 
183 
position as if the grating were removed, which proves that a con- 
centric spherical wave is formed by the union of the fragmentary 
parts of the incident wave which the grating has allowed to pass, 
or at least the fragmentary parts distributed over the spherical 
surface produce the same effect upon our sense of vision as if the 
surface were occupied by an unbroken wave. If the grating be 
sufficiently fine, and the luminous source not too near, we see not 
only the source in its proper position, but also images of it on 
both sides in the direction at right angles to the wires or dark 
lines of the grating. If the light of the source be homogeneous, 
that is, the same as we find at any point of a pure spectrum, these 
lateral images are counterparts of the true image, of various in- 
tensities. If the source emit white light, it is exhibited in each 
of these images separated into its component colours, the image 
being spread out so as to form a spectrum, with the violet extremity 
nearest to the central image. 
In order to understand the origin of these lateral images, first 
suppose the transparent intervals to he of infinitely small width, 
and separated by dark spaces of finite and equal breadth. Suppose 
light coming from a distant source to be incident upon them in a 
direction perpendicular to their plane. The space occupied by the 
system of lines and spaces being very small, the surface of an 
incident wave may be considered as coinciding with their plane, 
so that a similar phase of vibration passes at all points of the 
transparent lines at the same instant. Each of these lines thus 
becomes the axis of a system of cylindrical waves behind the 
grating, and at any instant the same phase of vibration is found in 
each system at the same distance from the axis. 
Suppose the dark lines in the figure to represent sections of 
these cylindrical surfaces in the same phase of vibration. Upon 
the surfaces which envelope a succession of these surfaces of similar 
phase, in a direction parallel to AB, are formed a system of waves 
by which we see the true image in its real position ; similarly, by 
a system of waves which envelope surfaces of similar phase, in a 
direction parallel to CD, we see the first lateral image to the right ; 
by a system of waves parallel to EC, we see the second image, and 
so on. If we denote by a the distance between the transparent 
lines, and by D, the angular deviation of the first lateral image, 
