74 Prof. C. G. Knott on Reflexion and Refraction of 



The chief peculiarities embodied in these tables are shown 

 graphically in the corresponding curves (figs. 5 and 6, 

 p. 86). Any one curve represents the manner in which 

 the energy of each wave depends on the angle of incidence. 

 The angles of incidence are measured off along the horizontal 

 line ; and the corresponding energies are represented by the 

 ordinates perpendicular thereto. The energy of the incident 

 wave is of course represented by a straight line at unit 

 distance from the line along which the angles of incidence are 

 measured off. 



The first set of curves shows the state of things for an 

 incident condensational wave. For the sake of brevity, we shall 

 occasionally refer to the different waves by the letters A Aj A' 

 B B x chosen to represent their energies. At perpendicular 

 incidence condensational waves only are started at the bound- 

 ing surface ; and as the angle of incidence increases the 

 energies of both of these diminish. A', which we may also call 

 the water wave, seems to fall off continuously until it vanishes 

 at grazing incidence. The A-wave, however, vanishes at two 

 distinct incidences, and after 80° is reached begins to increase 

 till at 90° it attains unity. The behaviour of this reflected 

 condensational wave is extremely curious, the wave being 

 practically non-existent for incidences between 50° and 80°. 

 The greater part of the energy of the incident wave is then 

 accounted for by the B x or reflected distortional wave. For 

 incidences higher than 45°, three-quarters of the whole 

 incident energy is so transformed. It will be noticed that 

 up to pretty high angles of incidence the energy of the water- 

 wave does not suffer any very great falling off'. 



Turning now to the second set of curves, which show the 

 state of things for an incident distortional wave, we meet with 

 some very curious relations. For reasons already discussed, 

 the A-wave cannot exist for incidences higher than a certain 

 critical value, which depends only on the rock itself. The 

 energy of this wave, however, attains a considerable maximum 

 value for an angle of incidence slightly below this critical 

 value. Almost for the same incidence, the energy of the 

 Bj-wave falls to a very low minimum, almost vanishing 

 indeed. Comparing this first portion of the second set of 

 curves with the first set of curves as a whole, we see a 

 general resemblance between the two. That is, the energy 

 of the reflected wave of the same type as the incident wave 

 rapidly falls off to a minimum as the angle of incidence 

 grows, while that of the reflected wave of the other type 

 rapidly increases to a maximum. Finally the energy of the 

 reflected wave of the same type, in both cases quite abruptly, 



