Dr. Rankine on Isoperimetric Regular Polygons. 365 



gitude 27° 27' W., approaching to the parallel of the islands 

 Trinidada and Martin Vas. The wind now permitted our steer- 

 ing well to the eastward of south After crossing the tro- 

 pic of Cancer [on the 12th] the wind became very variable, as 

 well in point of strength as in direction, so that on the 28th 

 we had only advanced to the latitude of 31° 56' S., longitude 

 4° 18' W.» 



I submit, then, that there are well-founded reasons for be- 

 lieving that in the South Atlantic, as in the North, the general 

 tendency of the atmospheric currents is to circle round a central 

 region in which calms and irregular winds prevail, and that 

 in neither the South nor the North Atlantic is there any zone or 

 belt of such calms extending over the whole width of the ocean. 



In the Pacific the steady winds from the south-west down the 

 coast of Chili or Peru, and from the north-west down the coast 

 of California — winds which in both hemispheres veer through 

 the bearing of their respective poles towards east, till on ap- 

 proaching the equator and at some distance from the coast they 

 become the regular trades — seem at first to point to the conclu- 

 sion that the atmosphere there also moves round in a pair of 

 circles ; but I have no evidence which will confirm such an idea 

 by the completion of the circles on the western side of that vast 

 ocean or over the continent of Asia. It would be foreign to my 

 present purpose to enter into the peculiar nature of the winds 

 that blow as well in the Western Pacific as in the Indian Ocean ; 

 but a very cursory examination will suggest that the same cause 

 which produces the monsoons — which is, in fact, strong enough 

 to divert the trades from their regular course — may also be strong 

 enough to prevent their recurving in a manner similar to that 

 which the concurrent testimony of many competent witnesses 

 shows to take place in the North and South Atlantics ; but as I 

 have wished throughout this paper to base my argument entirely 

 on positive evidence of facts actually experienced, rather than on 

 any theory which might explain how or why such facts occur, or 

 might say what might or ought to occur, I shrink from entering 

 at present on this part of the question. 



XLVI. On Isoperimetric Regular Polygons. By W. J. Mac- 

 quorn Rankine, C.E., LL.D., F.R.SS.L.fyE. #c* 



1. HPHE process described in this paper may afford to stu- 



J- dents of mathematics an additional elementary method 



of testing for themselves the accuracy of the ordinary approxi- 



* Communicated by the Author. 



