8 PREFACE. 



aid MM. CAUGHT and PoiSSON have been enabled to give the 

 complete theory of the motion of the waves in an indefinitely 

 extended fluid. The same formulae have also put us in posses- 

 sion of the solutions of many other interesting problems, too 

 numerous to be detailed here. It must certainly be regarded as 

 a pleasing prospect to analysts, that at a time when astronomy, 

 from the state of perfection to which it has attained, leaves little 

 room for farther applications of their art, the rest of the physical 

 sciences should show themselves daily more and more willing to 

 submit to it ; and, amongst other things, probably the theory 

 that supposes light to depend on the undulations of a luminiferous 

 fluid, and to which the celebrated Dr T. YOUNG has given such 

 plausibility, may furnish a useful subject of research, by afford- 

 ing new opportunities of applying the general theory of the 

 motion of fluids. The number of these opportunities can scarcely 

 be too great, as it must be evident to those who have examined 

 the subject, that, although we have long been in possession of 

 the general equations on which this kind of motion depends, we 

 are not yet well acquainted with the various limitations it will 

 be necessary to introduce, in order to adapt them to the different 

 physical circumstances which may occur. 



Should the present Essay tend in any way to facilitate the 

 application of analysis to one of the most interesting of the 

 physical sciences, the author will deem himself amply repaid 

 for any labour he may have bestowed upon it ; and it is hoped 

 the difficulty of the subject will incline mathematicians to read 

 this work with indulgence, more particularly when they are 

 informed that it was written by a young man, who has been 

 obliged to obtain the little knowledge he possesses, at such 

 intervals and by such means, as other indispensable avoca- 

 tions which offer but few opportunities of mental improvement, 

 afforded. 



