PREFACE. Vll 



" Gardens nous de croire qu'une science soit faite quand on 1'a 

 reduite a des formules analytiques." I have endeavoured to make 

 the analytical results as intelligible as possible, by numerical 

 illustrations, which it is hoped will be found correct, and by the 

 insertion of a number of diagrams of stream-lines and other 

 curves, drawn to scale, and reduced by photography. Some of 

 these cases have, of course, been figured by previous writers, but 

 many are new, and in every instance the curves have been 

 calculated and drawn independently for the purposes of this work. 



I am much indebted to various friends who have kindly taken 

 an interest in the book, and have helped in various ways, but who 

 would not care to be specially named. I cannot refrain, however, 

 from expressing my obligations to those who have shared in the 

 tedious labour of reading the proof sheets. Mr H. M. Taylor has 

 increased the debt I was under in respect of the former treatise by 

 giving me the benefit, so long as he was able, of his vigilant 

 criticism. On his enforced retirement his place was kindly taken 

 by Mr R. F. Gwyther, whose care has enabled me to correct many 

 errors. Mr J. Larmor has read the book throughout, and has 

 freely placed his great knowledge of the subject at my 

 disposal ; I owe to him many valuable suggestions. Finally, I 

 have had the advantage, in the revision of the last chapter, of 

 Mr A. E. H. Love's special acquaintance with the problems there 

 treated. 



Notwithstanding so much friendly help I cannot hope to have 

 escaped numerous errors, in addition to the few which have been 

 detected. I shall esteem myself fortunate if those which remain 

 should prove to relate merely to points of detail and not of 

 principle. In any case I shall be glad to have my attention called 

 to them. 



HORACE LAMB. 



May, 1895. 



