1876.] Rainfall in connexion with Sun-spots. 383 



from this equation we obtain a mean annual difference of 5*03 inches in 

 favour of the years of maximum sun-spot. 



(16.) A similar comparison of Ar with AD (differences of river- 

 depths from the mean) also gives favourable results. The 116 years of 

 river-depths (1756 to 1871) compared with the relative numbers of sun- 

 spots for the same years give the equations AD = + 0*17322 Ar and 

 A D = -f- 042266 Ar. According to these equations the depth in the 

 years of most sun-spot should exceed the depth in the years of least sun- 

 spot by an annual average of 12-69 inches. For all, except three, of the 

 11 sub-periods into which the 116 years are divided the values of / are 

 favourable, and they would no doubt be found favourable as far back as 

 the observations of river-depths extend (1728), if we had the sun-spot 

 numbers for those years. 



(17.) Sun-spot, rainfall, and river curves laid down from the Tables 

 have, notwithstanding some exceptions, a general resemblance, which 

 cannot, I think, be ascribed to chance. The resemblance, as might 

 be expected, is greatest in the case of the rainfall curve for the globe. 

 Here, with the exception of two or three years in the period 1765 to 

 1776, for which there are only three stations, and of three years in the 

 period 1832 to 1841, the resemblance is very strong. 



(18.) Of the seven entire sun-spot periods of rainfall for the globe, 

 the mean values of six can be compared with the mean values of "Wolf's 

 relative numbers by placing the maxima years near the middle and the 

 minima years at the beginning and end of each period, so as to have 

 nearly all the maxima years in one horizontal line, and the minima 

 years in other horizontal lines. This is done in one of the Tables. 

 The river-depths for the same six periods are similarly arranged in 

 another Table. Then, applying Bessel's formula, we get three equa- 

 tions, the second terms of which enable us to lay down three curves 

 showing the general progression of sun-spot, rainfall, and river-depths. 

 The modification of these curves by the third terms of the equations is 

 shown by dotted curves. In a similar way we obtain three other equa- 

 tions and curves for five sun-spot periods, in which the minima years of 

 sun-spot are placed near the middle and the maxima years at the com- 

 mencement and end. The resemblance of the curves to one another is 

 very striking. 



(19.) According to the terms containing 6 and 2 6 in the first three 

 equations the three cycles have nearly the same lengths. The rainfall 

 maximum occurs 4-8 months after the sun-spot maximum, and the river 

 maximum 9*6 months after the rainfall maximum. According to the 

 second three equations the rainfall minimum occurs 10 # 8 months after 

 the sun-spot minimum, and the river minimum 3*6 months after the 

 rainfall minimum. The mean range of rainfall variation is 6*19 inches, 

 and of river-depth variation 16-73 inches. The intervals from the 

 minima to the maxima epochs are in every case less than those from 



