DIURNAL RANGES OF MAGNETIC DECLINATION. 65 



calculated minimum points of declination-range, while the 

 spaces between the two lines may be taken to denote the 

 calculated capacities for declination-range. 



It will be found that the observed and calculated range- 

 capacities agree well together; nevertheless there is this 

 peculiarity about the observed results. There appears to 

 be an exaltation of the observed zero or base-line when the 

 range is great, and a depression of the same when the range 

 is small. 



12. This is a phenomenon which we might expect from 

 the facts connected with smaller periods. Let us take the 

 eleven-yearly period (as it is called) whether for sun-spots 

 or declination-ranges. It is well known that the short- 

 period oscillations (those of perhaps two or three months) 

 are much more pronounced in both cases at epochs of 

 maximum than at epochs of minimum. In fine, we are 

 here imagining something analogous to musical beats, in 

 virtue of which more especially the two periods iof and 12 

 years alternately produce a state of exaltation and depres- 

 sion. Indeed we may even imagine that these two ine- 

 qualities of 1 of and 12 years themselves represent the 

 beat-period of some shorter disturbance. 



13. We have therefore endeavoured to give a variable 

 zero to our calculated ranges, on the supposition which 

 follows — namely, observed zero = x + y x calculated range. 



Now the observed zero for each year may be obtained 

 by taking a point midway between the two observed curves, 

 while the calculated ranges may be obtained from the 

 second set of curves. We shall thus get a series of equa- 

 tions of the above type, one for each year ; and by making 

 use of these we may obtain the values of x and y. By this 

 means we have found x= 19*07, ^ = 0-54. 



14. Having thus obtained our three periods and a means 

 of calculating the position of the variable zero, we may 



SER. III. VOL. VIII. F 



