1910-11.] Illustration of the Modus Operandi of the Prism. 293 
wave-crests. The tangent to an isophasal line at any point is parallel to 
the wave-crests and perpendicular to the line of advance of the waves in 
that neighbourhood. Taking v as the velocity of the ship along AO, the 
condition that the wave-pattern maintains the same position relative to the 
ship requires that the wave-crests moving forward in a direction inclined at 
angle \js to the line of motion of the ship should advance with velocity 
v cos \fs. Thus the velocity of the waves, and therefore the wave-length, 
varies according to the direction of the crest, being constant at all points 
where the tangents to the isophasal curves are parallel. As, according to 
the known results for ship-waves, the tangents to the isophasal curves are 
parallel at all points along any straight line through O such as OR, in 
fig. 3, the line OR is the locus of points where a constant wave-length is to 
he observed, and the crests of the whole group of waves having this wave- 
length are parallel to the tangent RD to the isophasal OC. The line AO, 
and the two lines CO in fig. 3 are reproduced from fig. 2. The group moves 
perpendicularly to RD. If we suppose the moving point-pressure to be 
first applied at P, then R marks the extreme rear of the group of the 
observed wave-length at the instant the pressure has reached O, which then 
marks the front of the same group. 
§ 5. For the application to the prism, OA in fig. 3 represents the side of 
the prism affected from P to O by the incident light pulse whose trace is 
TP when first it meets the prism at P : OB is the side at which the light 
emerges. PQ, being perpendicular to the tangent to the isophasal OC at R, 
indicates the direction of motion of the group whose crests lie along OR, 
and which we shall observe until it leaves the prism at Q. OS is per- 
pendicular to PR. 
Let t be the time taken by the pulse to pass from P to O ; then 
PS = v cos yfr . t, and PR = U£ according to the principle of stationary phase, 
where U is the group-velocity corresponding to the wave-velocity v cos \fs. 
For convenience we shall write V instead of v cos \[r to denote the wave- 
velocity in glass corresponding to wave-length A. in vacuo : and we 
shall take V 0 to denote the velocity of the waves in vacuo , and T as the 
greatest thickness of the prism traversed by the group under observation, 
i.e. T = PQ. The length of the group at time t is represented by RS, which 
is ( V — U)£. Immediately after time t the group begins to emerge from the 
prism at 0. 
§ 6. To follow the condition of the disturbance after complete emerg- 
ence, remark that the rear of the group advances at the group- velocity 
U, and that it will reach Q in a time t', reckoned from the time of 
the diagram, where 
