118 



Prof. B. Stewart and W. Dodgson. [May 29, 



It will at once be seen from this curve that it exhibits very nearly 

 the same positions for maximum inequalities as those shown in 

 % I- 



Thus, by selecting at random the period 24" 25 days we are by our 

 method referred to nearly the true positions of the various maximum 

 inequalities, and it might then be well to construct a separate book for 

 each of these, as we have done for the large inequality corresponding 

 to 24 days nearly. 



17. While this method has succeeded in bringing before us the 

 hitherto unknown inequalities of the Kew declination-range, it might 

 yet be imagined that the results obtained are of a local or semi-local, 

 and not of a truly cosmical nature. To test this we have compared 

 together the daily declination-ranges as recorded at Trevandrum by 

 Mr. Broun during the years 1858-64, with the corresponding por- 

 tions of the Kew series. Plotting these in series of 24 days each 

 we have obtained by the method already described the following- 

 results : — 



Table V. — Comparing together by the above method 7 years of 

 Trevandrum and 7 years of Kew Declination-range. 



Divisions 



Exact period 



from normal. 



in days. 



-2-0 



23 -8686 



-15 



, . 23 -9014 



-1 -o 



23 -9343 



-0'5 



23 -9671 



Normal 



24 -0000 



+ 0-5 



, 24 -0329 



+ 1-0 .... 



24 '0657 



+ 1-5 .... 



24 -0986 



+ 2-0 



. . 24 1314 



Magnitude of 



inequality. 



Kew. 



Trevandrum. 



925 



. 1235 



1206 .... 



1301 



1633 



1809 



1774 .... 



2245 



1687 



. 2507 



1546 



2448 



1425 



2123 



1322 



1662 



1085 . , 



. . 1489 



The results of Table V are exhibited graphically in Diagram II, 

 figs. V, VI, No. V denoting the Kew, and No. VI the Trevandrum 

 inequality. 



18. We see from Table V that the maximum inequality occurs for 

 these 7 years, both for Kew and Trevandrum, at points not far 

 distant from 24*00 days. There are thus exhibited signs of repetition 

 in this Kew .inequality, as well as evidences of its cosmical nature, 

 inasmuch as Trevandrum gives results similar to Kew as far asjperiod 

 is concerned. 



19. We shall now compare together the forms of the inequalities in 

 these two places. 



