1879.] Report to the Committee on Solar Physics. 



in 



9. A glance at the sums of this table for the whole 16 years will 

 suffice to show that 24*25 days does not correspond to the exact period 

 of any marked inequality. The sums are small, and we conclude there- 

 fore that we have not been fortunate in our chance selection of a period 

 to begin with ; but the peculiarity of our method is, that it will enable 

 us to ascertain the true position in the time-scale of the neighbouring- 

 prominent inequalities by means of the results of Table I. The method 

 of doing this can easily be rendered evident. Each horizontal row of 

 Table I consists of 24 numbers, and there are 16 years, beginning with 

 1858. We may, therefore, call the numbers of the first row (0) 5S , 

 ( 1 ) 5 8 ? ( 2 )ss> &c -> ( 2 3) 58 ; those of the second row (0) 59 , (1) 59 , (2) 59 , &c, 

 (23) 59 , and so on for each row. 



In this table, therefore, each vertical column consists of similar 

 numbers for the various years, adopting the notation now mentioned. 



Suppose, however, that we displace these values as follows : — 



1858 . . (0) M , (1) 58! (2) 58 . . (21) 58; (22) 58 , (23) 58 . 



1859 . . (1) 59 , (2) 69 , (3) 39 . . (22) 59 , (23) 59 , (0) 59 . 



1860 . . (2) 60 , (3) OT , (4) 00 . . (23) 60 , (0) 60 , (1) 60 . 



1873 . . (15) r3 , (16) 73; (15% ■ • (12) w , (13) 73 , (14) 78 . 



Now, if we add up the various vertical columns of this series the 

 sums will represent an inequality somewhat larger in period than 

 24*25 days. For it is manifest that if we have a regular series of 

 waves whose values we plot numerically after the manner of Table T, 

 the consequence of adopting too small a time scale will be to throw any 

 salient point of the wave, such as the crest, always further and further 

 to the right, and to correct this we should have to pull the whole 

 series a little to the left each time. Now, this is precisely what we~\ 

 have done in the above process, which will thus give us the representa- 

 tion of an inequality of larger period than 24*25 days. It is easy to 

 find the exact length of period which the above series represents. 

 We pull everything to the left nearly one day, but more accurately the 

 24th part of 24*25 days in one year. If, therefore, 365*25 days give 

 24* t/, 5 



— ~, what will 24*25 days give ? We find from this proportion that 



the period of the inequality indicated by performing the above process 



is 24*25+ ^ ^ — = 24*31 7 days. Again, we may pull things to the 



left two, three, or four divisions each year, and thus obtain the represen- 

 tation of inequalities with periods of 24*384, 24*451, or 24*518 days. 



Or we may perform the opposite operation of pushing things to the 

 right one division each year, and thus obtain the representation of an 

 inequality, having a period of 24*183 days, while 2, 3, or 4 such divisions 

 each year would give us periods of 24*116, 24*049, or 23*982 days. 



