[ 426 ] 

 LI. Intelligence and Miscellaneous Articles. 



ON A RELATION BETWEEN THE SUN-SPOT PERIOD AND THE 

 PLANETARY ELEMENTS. BY CHARLES DAVISON, M.A., MATHE- 

 MATICAL MASTER AT KING EDWARD^ HIGH SCHOOL, BIR- 

 MINGHAM. 



HPHE length of the sun-spot period was first estimated by its 

 -*- discoverer, Schwabe, at about ten years. Some years later, 

 Kudolf Wolf, making use of a much more extensive series of ob- 

 servations, determined the mean period to be 11*111 years, with 

 an uncertainty of 0*307 year. The period of Jupiter being 11-86 

 years, it was at first surmised that there might be some connexion 

 between the two. But the idea was soon abandoned, partly on 

 account of the obviously considerable difference between the two 

 periods. 



A close approximation to the sun-spot period is, however, ob- 

 tained by taking the average of the periods of all the known planets 

 in the solar system, on the supposition that the determining effect 

 of each planet is directly proportional to its mass and inversely 

 proportional to the square of its distance from the sun. If m be 

 the mass of a planet, d its distance from the sun, P its period, the 

 average to be determined is 



S(Pm/^)-rS(m/cl 2 ). 



In the following Table the values of m, d, and P are taken from 

 Herschel's 'Outlines of Astronomy' (1873); the corresponding 

 elements for the satellites and minor planets being omitted as 

 unknown or unimportant. 



Planet. 



Mass. 



Distance. 



Period, 

 in days. 



m/d 2 . 



~Pm/d 2 . 



Mercury 



0-074 



0-895 



1-000 



0-134 



343125 



102-682 



17-565 



19-145 



0-387 

 0-723 

 1-000 

 1-524 

 5-203 

 9-539 

 19-182 

 30-057 



88 



225 



365 



687 



4333 



10759 



30687 



60187 



0-494 

 1-711 

 1-000 

 0-058 

 12-676 

 1-128 

 0-048 

 0021 



43 



386 



365 



40 



54925 



12136 



1473 



1264 



Earth 



Mars , 









Neptune 



Prom these values we find that 



2(m/d 2 ) =17*136, 

 2(Pm/rf 2 )=70632, 

 and 



2(Pm/d 2 )-r2(m/d 2 )=4122 da J s * or n ' 29 years. 

 If the elements be those given in Newcomb's ' Popular Astro- 

 nomy' (1878), the value of this average is 11*27 years. The 

 effect of taking the moon into account is to reduce both these 

 estimates by 0*01 year. In either case the average is well within 

 the limiting values given by Wolf for the sun-spot period, namely 

 11-111+ 0*307 years. 



