The Motion and Distribution of tlie Sun-spots 



27 



Having computed v,', V2', v./ and v/, the moments in reference to the mean are 

 given by 



(5) ; V3 = v.; — 3iv/ + 2h\ 



I V, = v; — Ahv^' -j- — ?,h\ 



in which formulae I liave written h in stead of v/. 



Lastly the characteristics are obtained from the relations 

 x^ = — 0.b + h, 



In the computation of these characteristics of the motions in longitude, the 

 material of observation brought together in table X, is divided into latitude-zones, 

 5° wide, in stead of 2°. 5, as is the case in the table. The results of these com- 

 putations are given in table XI. The latitude zones of the northern hemisphere 

 are designated by N^, N^, etc. and those of the southern hemisphere by S^, 

 , etc , and Sj being nearest tlie equator. 



Mean and Dispersion. In table XI, n represents in the first place the 

 number of cards, spot-days we may say, after the manner in which the material 

 of observation has been catalogized. The values of rr^ indicate the mean of the 

 motions of the spots in longitude, referred to the adopted system of co-ordinates. 

 The angular velocity of this system is 35'. 461 an hour, corresponding to a rotation 

 period of 25.38 days. From the values of the fact, discovered by Carrington, 

 of the angular velocity of the sun being diminished by increasing latitude, is 

 clearly proved. 



In a later section I shall compute the rotation period of different latitudes by 

 using the values of the characteristics given in this table. 



It may not be out of place to make a comment here. In the papers on the 

 motions of the sun-spots hitherto published, there are, as far as I can remember, 

 only the averages of the motions computed. On that account one gets no idea of 

 the accuracy by which the rotation period, for example, may be determined from 

 the observations of the spots. During the computations I have made in order to 

 determine the rotation period at different latitudes from this vast material, I was 

 greatly surprised at finding that this determination could only be made with con- 

 siderable uncertainty. An excellent measure of this uncertainty is the dispersion 

 a.j. If we designate the mean error of by s(,x\,), we have as is well known 



