1869.] iUl [Kirkwoorl. 



The observations of recent years seem to render it probable, moreover, 

 that the epocli of extraordinary activity is passing away. The number 

 of nevr groups in 1867 was less than in any other year since the com- 

 mencement of Schwabe's observations; while the whole number counted 

 during the 11 years from 1857 to 1867 inclusive, as compared with that of 

 the 11 years immediately preceding, was as 1483 to 1715. 



(17.) The Great Irregularity of the 11-Year Cycle from 1828 to I860.— 

 Mercury was in perihelion about 1838.277, and this was probably the 

 maximum epoch depending on Mercury alone. But the observed epoch of 

 greatest disturbance was about 1837.2. Let us, then, inquire whether 

 any configuration of the disturbing planets will account for this marked 

 deviation from regularity. 



Mercury and Venus had the same mean longitude (343°) near the 1st of 

 April, 1837, or, about 1837.247*, when Mercury was at less than its mean 

 distance from the sun. If this conjunction occurred on, or very near, the 

 solar meridian M, an extraordinary disturbance of the photosphere would 

 evidently result. Now, the interval from 1837.247 to 1838.277 was 

 376.r'2075, dui'ing which time the sun would have performed 15 entire 

 rotations; also the arc between longitude 343° and 75°, (that of Mercury's 

 perihelion,) is 92°. The daily motion of Mercury, moreover, when nearest 

 the sun is about 5°. If, then, the conjunction of 1837.247 occurred over 

 the solar meridian M, and if we represent by t the number of days from 

 1838.277 till Mercury was on the same solar meridian, we shall have, 

 taking the sun's period of rotation as adopted in (6) 



376.2075 j_^ ^ ,^^,^ 



11-92x0^ 

 15 + ci 



360 



whence t = ^A 8 +, and 5° x i^ = ^9° + (10) 



Hence the longitude of Mercury when on the solar meridian M in 1838, 

 and at other recent maximum epochs, was 94°, or 19° from the perihelion. 

 Again, the interval between two consecutive conjunctions of Mercury and 

 Venus is 144^.5651, and 



144.d 5651 X 28 = 4047.d 8228, 

 exceeding the period of 163 solar rotations by 1.^119. It is easy to see, 

 therefore, that when the mean longitudes of the planets were the same 

 (about 348°) in 1848.328, the ecliptical longitude of the solar meridian M 

 was 12° in advance, and that the disturbing effect would consequently be 

 diminished, although still sufficient to fix the maximum in 1848 instead 

 of 1849. In like manner the further decrease of solar activity in 1859 — 60, 

 as well as the observed increase from 1828 to 1837, is readily accounted 

 for. 



(18.) Mercury and the earth had the same mean longitude, 0°, ± about 

 1837.726. 



Mercury and Venus, " " 343° ± " 



1837.247. 



* This is not tlie precise epocli of conjunction ; we may adopt it, liowever, without material error. 

 It may be remarised that a great disturbance of the photosphere would also be produced by the 

 passage of the planets successively over the meridian M, shortly before the time of actual con- 

 junction. 



