THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[SIXTH SERIES ] 

 DECEMBER 191(5. 



LIX. On Convection Currents in a Horizontal Layer of 

 Fluid, when the Higher Temperature is on the Cinder Side. 

 By Lord Ratleigh, O.M., F.R.S.* 



THE present is an attempt to examine how far the inter- 

 esting results obtained by Benard t in his careful and 

 skilful experiments can be explained theoretically. Benard 

 worked with very thin layers, only about 1 mm. deep, standing 

 on a levelled metallic plate which was maintained at a uni- 

 form temperature. The upper surface was usually free, and 

 being in contact with the air was at a lower temperature. 

 Various liquids were employed — some, indeed, which would 

 be solids under ordinary conditions. 



The layer rapidly resolves itself into a number of cells, the 

 motion being an ascension in the middle of a cell and a 

 descension at the common boundary between a cell and its 

 neighbours. Two phases are distinguished, of unequal dura- 

 tion, the first being relatively very short. The limit of 

 the first phase is described as the " semi-regular cellular 

 regime " ; in this state all the cells have already acquired 

 surfaces nearly identical, their forms being nearly regular 

 convex polygons of, in general, 4 to 7 sides! The boundaries 



* Communicated by the Author. 



t Revue generate des Sciences, vol. xii. pp. 1261, 1309 (1900); Ann. d. 

 Chimie et de Physique, t. xxiii. p. 02 (1901 ). M. Benard does not appear 

 to be acquainted with James Thomson's paper " On a Cham>:ng Tesselated 

 Structure in certain Liquids" (Proc. Glasgow Phil. Soc. 1S81-2), where 

 a like structure is described in much thicker layers of soapy water cooling 

 from the surface. 



Phil May. S. 6. Vol. 32. No. 192. Dee. 1910. 2 O 



