1865.] On the Sextactic Points of a Plane Curve. 349 



being to the north of them is a sufficient reason why the wind does not 

 change to south of west. The polar-wind gales which are experienced in 

 these high latitudes, seem to derive their air from that upper current 

 returning from the pole, part of which sometimes makes its downward way 

 to the surface in high latitudes, especially in spring. 



The gales of the southern hemisphere, just remarked upon, have their 

 exact counterpart in the high latitudes of the northern hemisphere, though 

 I have not noticed them to be so constant, perhaps on account of there 

 being much more land in the northern hemisphere. Still all seamen know 

 how, after getting north of the N.E. trades, we look for the wind to come 

 from S., S.W., and W., with warm air and rain. 



These curves, and the arguments deduced from them, seem to favour 

 Maurv's theory of the circulation of the air ; where he supposes two 

 rising currents we have a low barometer, and where he supposes two 

 descending currents we find a high barometer ; but they are also sug- 

 gestive, and a series made with standard instruments for each month in 

 the year might lead to most useful discoveries as to the normal circulation, 

 and its disturbance by the effect of land. How strikingly these curves prove 

 the uniform state of the atmosphere in those parts of the Atlantic between 

 the trades, at the same seasons of the year! especially in contrast with their 

 sudden distortions on the polar side of the trades, where their irregularities 

 resemble the waves of the sea in the same latitudes, which may in fact be 

 called the resultants of these distortions. Similar curves, outward and 

 homeward, deduced from the same logs, between the latitudes of 40 South 

 to 20 North, in the Indian Ocean and Bay of Bengal, would, I think, give 

 interesting results, and I hope some day to work at them. 



A track-chart accompanies these remarks, showing the routes inside and 

 outside the Cape Verde Islands, together with a homeward-bound route, 

 thus showing the longitude in which each degree of latitude has been 

 crossed. 



X. "On the Sextactic Points of a Plane Curve." By WILLIAM 

 SPOTTISWOODE, M.A., F.R.S., &c. Received June 15, 1865. 

 (Abstract.) 



The beautiful result given by Professor Cayley in the Proceedings of 

 the Royal Society (vol. xiii. p. 553), and deduced, as I understand, by 

 the methods of his memoir " On the Conic of Five-pointic Contact" (Philoso- 

 phical Transactions, vol. cxlix. p. 3/1), led me to inquire how far the for- 

 mulae of my own memoir " On the Contact of Plane Curves " (Philosophical 

 Transactions, vol. clii. p. 41) were applicable to the solution of the pre- 

 sent problem. 



The formulae in question are as follows : if U=0 be the equation of the 

 curve, H its Hessian, and V=(a, b, c,f, g, h~Jj>e, y, ^) 2 =0 that of the conic 

 of five-pointic contact ; and if, moreover, a, ft, y being arbitrary constants. 



