Mr. Moon on Fresners Theory of Double Refraction. 559 



approximate values substituted for Wj and w', it is assumed that 

 h is small with respect to u, or that the distances between the 

 particles are small compared with their actual motions, a sup- 

 position entirely at variance with the assumed data of the pro- 

 blem. Hence it is plain that this supposed illustration is for 

 every purpose entirely worthless. 



Thus as we were compelled to assume the existence of the 

 axes of elasticity, not only in the default, but in the face of evi- 

 dence, so we are compelled to assume this rule as to the mode of 

 calculating the velocity on a bare analogy to a case presenting 

 the most striking difference from that under consideration, 

 namely that of the direct transmission of an undulation when 

 the vibrations are in the direction of transmission. We are 

 not only compelled to assume the existence of undulations con- 

 sisting of vibrations executed in directions perpendicular to 

 the course of the wave, — respecting which it is not too much 

 to say, that it is impossible for the mind to conceive the possi- 

 bility of their existence, — but we are to suppose ourselves ac- 

 quainted with an exact law to which they are subject*. Of 

 the worth of such a theory I leave my readers to judge. The 

 discussion of the remaining portion of it I must defer to an- 

 other opportunity. ti^ ioi gnbiuH 



Liverpool, November 8, ] 845. ~ -}- A '— — — a 



* It is easy to conceive of transversal as the consequence of direct vibra- 

 tion, but I confess myself unable to conceive the possibility of there being 

 a surface of transversal vibrations in the same phase — that of a sphere for 

 example. The case of a stretched cord affords no analogy to guide us, for 

 there the wave is in the direction of the motion. At all events, if the hypo- 

 thesis of transversal vibration is to hold its ground, it must have much more 

 thought bestowed upon it than it has yet received. The most painful cir- 

 cumstance connected with the later history of the undulatory theory, is the 

 manner in which ideas, in themselves perhaps valuable as hints, have been 

 dressed up into a settled theory. A truly philosophical mind, to which the 

 idea of transversal vibrations had once suggested itself, would have set itself 

 to work to discover, if possible, some method by which such motion could be 

 conceived, and would not have rested satisfied so long as a doubt existed as 

 to the perfect feasibility of the scheme. Thus it is that we may account for 

 Young not having attempted to carry his first notion any further. He saw, 

 no doubt, the difficulties by which the idea of transversal vibrations was be- 

 set, and was well-aware that till these were got over, it was hopeless to at- 

 tempt to enter with any chance of success into the discussion of their na- 

 ture and consequences. Fresnel, on the contrary, was satisfied with a series 

 of possibilities, upon which he has built a theory, not only of no value in 

 itself, as having nothing solid to rest upon, but from its crudity and manifold 

 errors discreditable to himself and to the age by which it has been received. 



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