DIURNAL RANGES OF MAGNETIC DECLINATION. 55 



those of solar activity, so that to analyze the former is 

 probably equivalent to analyzing the latter. 



2. Our method of analysis is not new. The peculiar 

 treatment which we adopted in a previous communication 

 (Proc. Roy. Soc. May 29, 1879), and which had the ad- 

 vantage of enabling us to analyze with comparatively little 

 trouble a very long series of observations, is here unneces- 

 sary. The system which we have here pursued is, in fact, 

 that pursued by Baxendell and other astronomers with 

 observations of variable stars ; and it will be best under- 

 stood by means of an example. We shall select this ex- 

 ample from a preliminary paper by one of us, in which the 

 long-period inequality in rainfall was roughly analyzed as 

 well as these very declination-ranges which we are here 

 treating in a more laborious and accurate manner (Proc. 

 Lit. & Phil. Soc. Manchester, Feb. 24, 1880). 



The Paris rainfall-records arranged so as to exhibit an 

 8 -years series give us the following numbers : — 



5 S '4» 47'5» 457. 48*7, 5 ri > 49*8, 4 6 '5, 47% 

 the mean being 48*5 . From these we obtain the following 

 series of differences : — 



4-2-9, — I-O, —2*8, +0'2, +2-6, +1*3, — 2'0, —I'3. 



If we now add these together without respect of sign, and 

 divide by their number (8), we obtain 176 as the mean 

 departure from the mean of the whole. It is, in fine, mean 

 departures of this kind for periods of varying lengths 

 which we wish to obtain in our present communication. 



3. The observations at our disposal are those which have 

 been used by Prof. Elias Loomis in his " Comparison of 

 the mean daily Range of the Magnetic declination with the 

 Extent of the Black Spots on the Surface of the Sun " 

 (American Journal of Science and Arts, vol. 1. No. cxlix.) . 

 They are as follows : — 



