1869.] ^'^ [Kirkwood. 



has recently been discussed with great labor and ability by Professor 

 Spoerer, of Anclam, and Mr. Carrington, of England, who have shown 

 conclusively that the rapidity of movement varies regularly with the lati- 

 tude. The equatorial portions have the greatest angular velocity ; in 

 other words, the proper motion of the spots is in a direction contrary to 

 that of the sun' s rotation. The formula by which the astronomers named 

 express the law for the dependence of the sun' s apparent period of rota- 

 tion on the latitude are as follows : 



According to Carrington, ? = 865' — 165' sin I I . • . (l) 

 " " Spoerer, I = 16.°8475 — 3^3812 sin (41°13' +?,). (2) 



where ~ is the arc described in a solar day. The true time of rotation is 

 supposed to be that indicated by an equatorial s^jot ; and on this assump- 

 tion, (1) gives 



P = 24.^9711 = 241 2311 18m 23s (3) 



or, (2) gives 



P = 24.162447 = 24^ W^ 59™ 0^ . . . • • . . (4) 



The true value is probably between the results here given, 



(14.) But will this modifying element in the theory of planetary action 

 afford a satisfactory explanation of the periodic recurrence of maxima 

 and minima of solar spots ? Let us consider. 



(a.) The 11-Year Cycle. — The anomalistic period of Mercury is 87.1 

 9702, and 



87.19702 X 46 = 4046.16292 = ll.y077 = Tj . . . . (5) 

 This is very nearly equal to Wolf's value of the cycle, and agrees at 

 least equally well with recorded facts.* Again, 



— ^= 24.182594 = 241191^49^218 . . ,' . . (6) 



163 



which is nearly a mean between Spoerer' s and Carrington' s values of the 



sun's period of rotation. With this, therefore, as the time of the sun's 



axial revolution, we have 46 times the period of Mercury — equal to 163 



times that of the sun's rotation. The recurrence of maxima at mean 



intervals of 11.077 years would thus be accounted for.f Again, the 



epochs at which sun-spots were seen before the invention of the telescope 



may be presumed, with much probability, to have been nearly co-incident 



with the maxima epochs of Schwabe's cycle. Now, it is a remarkable 



* The following astronomical cycles are also nearly equal to this period 

 of variation : 



1. 18 periods of Venus:=11.0742/. 



2. 35 syn. per. of Mer.=:11.104 



3. 1 period of Jupiter.^11.860 



4. llt^—limQij 



5. 28i!,— 11.082 



6. 45«,=11.063, 



where <i=the syn. per. of Venus with respect to Jupiter; i.^^rsyn. per. of 

 Mercury with respect to Venus ; and ig^that of Mercury with respect to 

 Jupiter. 



t It is not probable that Mercury is on the meridian M precisely at the epoch of perihelion 

 passage. It is only necessary to suppose this coincidence to occur when the planet is near the 

 perihelion point. Even at the distance of 20° the diminution of the disturbing power would be 

 extremely small. 



