PREFACE. Vii 



sented by equations formed by equating to unity the sums of 

 the squares of the n variables, each divided by an appropriate 

 coefficient. It is of course possible to adapt the formula of this 

 paper to the case of nature by supposing n = 3. 



The next paper, "On the Motion of Waves in a variable 

 canal of small depth and width," though short, is interesting. 

 It was read before the Cambridge Philosophical Society, on 

 May 15, 1837, and a Supplement to it on Feb. 18, 1839. 

 On Dec. 11, 1837, were communicated two of his most valuable 

 memoirs, "On the Reflexion and Refraction of Sound," and 

 " On the Reflexion and Refraction of Light at the common 

 surface of two non-crystallized media." These two papers 

 should be studied together. The question discussed in the first 

 is, in fact, that of the propagation of normal vibrations through 

 a fluid. Particular attention should be paid to the mode in 

 which, from the differential equations of motion, is deduced an 

 explanation of a phenomenon analogous to that known in 

 Optics as Total internal reflection when the angle of incidence 

 exceeds the critical angle. By supposing that there are pro- 

 pagated, in the second medium, vibrations which rapidly dimi- 

 nish in intensity, and become evanescent at sensible distances, 

 the change of phase which accompanies this phenomenon is 

 clearly brought into view. 



The immediate object of the next paper, " On the Reflexion 

 and Refraction of Light at the common surface of two non- 

 crystalline media," is to do for the theory of light what in the 

 former paper has been done for that of sound. This is done in 

 a manner which will present little difficulty to one who has 

 mastered the former paper. But this paper has an interest 

 extending far beyond this subject. For the purpose of explain- 



