Prof. Balfour Stewart and Mr. \V. L. Carpenter. 



treatment of sun-spots as above described, and we have adopted a 

 similar plan with our terrestrial records. 



8. Thus at length by the means now described we obtain 36 

 yearly series corresponding to the years from 1832 to 1867 inclusive, 

 each series containing positive and negative quantities whose sums are 

 exactly equal. Let us represent these as follows : 



(1) (2) (3) a . . . (24) 32 



(1)33 (2)33 (3)33 - (24)33 



(1) 67 (2) 67 (3) 67 .. . . (24) 67 



Now if we allow these terms to stand as above and take the sums of 

 the various vertical columns, we shall obtain a result denoting (when 

 divided by 36) the final Inequality corresponding to 24 days 

 exactly as well as this can be represented by the whole body of 

 observations at our disposal. Suppose, however, we arrange the 

 horizontal lines in such a manner that (24)^ comes under (23) 35 , and 

 (1)^ under (24)^, and so on. If we then sum up the vertical lines 

 so arranged, the result will now represent an Inequality having a 

 period so much longer than 24 days, that the difference amounts to 

 one day in the course of a year. This period will easily.be found by 

 the following proportion. If in 365'25 days things advance 1 

 day, how much will they advance in 24 days ? The result is 



24 



=0*0657, and hence the period of the Inequality in question 

 365'25 



will be 24'0657 days. In the above example things have been pushed 

 each year one place backwards, that is to say, from right to left ; had 

 they been pushed one place forwards this would have denoted an 

 Inequality as much less in period than 24 days, as the one we have 

 now considered is greater, in other words, one with a period of 

 23-9343 days. So in like manner two or three places backwards each 

 year will denote Inequalities with periods of 24'1314 and 24'1971 

 days, and two or three places forwards inequalities with periods of 

 23-8086 and 23'8029 days and so on. Here the law is sufficiently 

 obvious. Tlie comparative magnitude of the final Inequality so 

 obtained may be found by simply adding together all its 24 terms 

 without respect of sign, the sum representing the total area of 

 departure from the mean, which the Inequality would have exhibited 

 had it been put into a graphical form. 



9. To obtain the proper phase of the Inequality let us arrange 

 oui- series of individual observations so that the first begins with 

 January 1, 1832, and let us suppose, for instance, that we are dealing 



