242 Mr. J. Croll on the ' Challenger's' Crucial Test of the 



of it in treatises on differential equations ; but I can scarcely 

 think it probable that in some form or other it is not known to 

 mathematicians who have occupied themselves with this subject. 

 Known or unknown, it is of exceeding value and beauty as a 

 purely mathematical method. As to Laplace's Dynamical Theory 

 of Tides in general, I have much pleasure in concluding with 

 a warmly appreciative statement by Airy which I find in his 

 < Tides and Waves/ art. (117) . 



" If, now, putting from our thoughts the details of the inves- 

 " tigation, we consider its general plan and objects, we must allow 

 " it to be one of the most splendid works of the greatest mathe- 

 u matician of the past age. To appreciate this, the reader must 

 " consider, first, the boldness of the writer who, having a clear 

 " understanding of the gross imperfection of the methods of his 

 " predecessors, had also the courage deliberately to take up the 

 " problem on grounds fundamentally correct (however it might be 

 " limited by suppositions afterwards introduced) ; secondly, the 

 (i general difficulty of treating the motions of fluids ; thirdly, the 

 " peculiar difficulty of treating the motions when the fluids cover 

 " an area which is not plane, but convex ; and, fourthly, the saga- 

 " city of perceiving that it was necessary to consider the earth as 

 " a revolving body, and the skill of correctly introducing this 

 " consideration. The last point alone, in our opinion, gives a 

 " greater claim for reputation than the boasted explanation of 

 " the long inequality of Jupiter and Saturn." 



Yacht < Lalla Rookh/ 

 Frith of Lorn, August 11, 1875. 



XXVI. The 'Challenger's' Crucial Test of the Wind and Gravita- 

 tion Theories of Oceanic Circulation. By James Croll, of 

 H. M. Geological Survey*. 



'ftJORTH Atlantic. — Perhaps the most remarkable result yet 

 obtained from the temperature-soundings of the ' Challen- 

 ger ' Expedition is the unexpected proof which they afford of the 

 physical impossibility, so far as the North Atlantic is concerned, 

 of any general interchange of equatorial and polar water due to 

 gravitation. 



It is a condition absolutely essential to the gravitation theory 

 that the surface of the ocean should be highest in equatorial 

 regions and slope downwards to either pole. Were water abso- 

 lutely frictionless, an incline, however small, would be sufficient 



* Communicated by the Author, having been read before the British 



Association, August 18/5. 



