264 



On the Contact of Conies with Surfaces, 



[Mar. 10, 



uamelv, that the time between a minimum and the next maximum is less 

 than that from the maximum to the next minimum. 



Thus the times from the minimum to the maximum are for the three 

 periods 3"0G, 4* 14, and 3'37, while those from the maximum to the 

 minimum are 6*75, 8'44, and 7*44 years. 



In all the three periods there are times of secondary maxima after the first 

 maximum ; and in order to exhibit this peculiarity, statistics are given of the 

 light-curve of R Sagittse and of /3 Lyra^, two variable stars which present 

 peculiarities similar to the sun. 



Finally, the results are tested to see whether they exhibit any trace of 

 planetary influence ; and for this purpose the conjunctions of Jupiter and 

 Venus, of Venus and Mercury, of Jupiter and Mercury, as well as the 

 varying distances of Mercury alone in its elliptical orbit, have been made 

 use of, and the united effect is exhibited in the following Table, the unit of 

 spotted area being one-millionth of the sun's visible hemisphere : — 







Excess or 



Deficiency. 





Angular 



Jupiter and 



Venus and 



Mercury alone 



Mercury and 



separation. 



Venus. 



Mercury. 



(Perihelion =0). 



Jupiter. 



0 to 30 



+ 881 



+ 1675 



- 380 



-227 



30 to GO 



- 60 



- 139 



-1188 



-317 



60 to 90 



- 452 



-1665 



-1287 



-594 



90 to 120 



- 579 



-2355 



-1262 



-714 



120 to 150 



- 705 



-2318 



-1208 



-508 



150 to 180 



— 759 



-1604 



-1027 



-491 



180 to 210 



- 893 



- 481 



— 519 



-416 



210 to 240 



- 752 



+ 547 



+ 430 



-189 



240 to 270 



- 263 



+ 431 



+ 1082 



- 25 



270 to 300 



+ 70 



+ 228 



+ 1436 



+ 154 



300 to 330 



+ 480 



+ 1318 



+ 1282 



+ 164 



330 to 0 



+ 1134 



+ 2283 



+ 586 



- 45 



IV. "On the Contact of Conies with Surfaces." By William 

 Spottiswoode, M.A., F.R.S. Received February 16, 1870. 



(Abstract.) 



It is well known that at every point of a surface two tangents, called 

 principal tangents, may be drawn having three-pointic contact with the 

 surface, i. e. having an intimacy exceeding by one degree that generally 

 enjoyed by a straight line and a surface. The object of the present paper 

 is to establish the corresponding theorem respecting tangent conies, viz. 

 that " at every point of a surface ten conies may be drawn having six- 

 pointic contact with the surface ;" these may be called Principal Tangent 

 Conies. In this investigation I have adopted a method analogous to that 

 employed in my paper " On the Sextactic Points of a Plane Curve" (Phil. 



