Sun-spot Areas and Diurnal Temperature-Ranges. 297 



with an Inequality which exceeds the 24-day period by six days in one 

 year. Our object is to represent this and all other Inequalities with 

 the phase they have in the beginning of 1832, that is to say, to 

 represent each by a row of 24 figures (plus and minus), the first of 

 which denotes the phase on January 1, 1832. Now, since the parti- 

 cular Inequality in question is larger in period than 24 days, corre- 

 sponding phases will gradually advance to the right, and hence the 

 mean phase for 1832, which is denoted by the true phase for July 1 of 

 that year, will be three (i.e., one-half of six) divisions to the right as 

 regards the phase for January 1. Hence it will be necessary, in 

 order to represent this Inequality as it was on January 1, 1832, to 

 push the 1832 series three places to the left, and then each successive 

 yearly series six places to the left of the one before it. The method 

 of setting for a difference representing an exact number of days in 

 each year is thus obvious. 



It is equally easy to set for differences representing not only whole 

 days, but also fractional parts of days. For instance, let it be 

 required to set for an Inequality greater than 24 days by 3'75 days 

 each year. Bearing in mind from what we have said that the mean 



3"75 



of 1832 is days wrong,~we have as follows : 



2 



Phase lias gone Phase has to be pulled 

 Year. to right. to left (nearest whole number). 



1832 1-875 2 



1833 5-625 6 



1834 9-375 9 



1835 13-125 13 



1836 16-875 17 



and so on. and so on. 



10. Having thus explained our principle of setting we shall now 

 briefly describe the practice which it has been found most convenient 

 to adopt. The whole number of yearly series is regarded as being 

 made up of three sets of 12 years each, namely, 1832-43, 1844-55, 

 1856-67, and Inequalities are obtained representing 1, 2, 3, 4, &c., 

 days' difference plus or minus in 12 years. Thus 24_ 39 or simply 

 39 represents, according to our notation, an Inequality whose 

 period falls short of 24 days by 39 days in 12 years, and so on. 



It has not been deemed necessary to make separate and complete 

 settings for each of the small stages indicated above, but only for 

 every third. Thus, for instance, we should make separate and com- 

 plete settings for 42, 39, 36, &c., obtaining in each case three 

 partial sums of 12 years each, the sum of which would represent the 

 final Inequality. But with regard to the Inequality 41 we should 

 esteem it sufficiently accurate if the first set of 12 years for 42 be 





