San-spot Areas and Diurnal Temperature- Ranges. 291) 



The temperature-range Inequalities around 26 days have been dealt 

 with in a similar manner, except that (B) is a mean of 3 not 4 sums 

 of (A), and (C) a mean of 3 not 4 sums of (B). Here, too, it is the 

 series (C) which is ultimately used. 



13. These smoothed series have then been treated exactly after the 

 manner in which we have treated the sun-spot series, and with them 

 too the first term of each Inequality represents the phase of that 

 Inequality which would have corresponded to January 1, 1832, 

 provided the terrestrial records had extended back to that date. 

 Thus the phases of the celestial and terrestrial Inequalities both 

 start from the same epoch, and are in this respect strictly comparable 

 with one another. 



Limits of Accuracy of this Method. 



14. It is obvious that the method now described can only be con- 

 sidered as correct for periods not far removed on either side from that 

 for which the series was originally framed. Thus in the case of 

 24 days it is apparent that 12 places pushed backwards every year 

 would imply the same setting as 12 places pushed forwards, and also 

 for 26 days 13 places pushed backwards each year would yield the 

 same result as 13 places pushed forwards ; it will not, therefore, do 

 to extend the method nearly so far. It is imagined that four days a 

 year on each side will form a legitimate boundary, or, adopting the 

 notation of Art. 10, that the region between the limits 48 and +48 

 will not be seriously open to objection. Considering it, however, 

 desirable that this point should be verified by some kind of actual 

 trial, we have adopted the results deduced from a series of observa- 

 tions of Diurnal Declination-ranges at Kew excluding disturbances 

 ( u Proc. Boy. Soc.," May 15, 1879). These observations extend from 

 1858 to 1873 inclusive, forming a series of 16 years, and they have 

 been arranged as follows : 



a. In yearly series representing 24 days in length, beginning 

 January 1, 1858. 



y3. In yearly series representing 24 - 25 days in length, beginning 

 January 1, 1858. 



Both of these series have been treated according to the method 

 described above, and settings have been made at distances denoting 

 half a day in a year, and extended on each side to lengths which 

 are probably beyond the limits of safety. The magnitudes of the 

 Inequalities represented by the various settings have been obtained 

 by summing up the positive and negative departures, and the results 

 are exhibited graphically in the following diagram in which abscissae 

 represent periods, while the ordinates represent corresponding In- 

 equalities. 



VOL. XXXVII. X 



