1870.] 



and Horizontal Force at Kew Observatory, 



235 



superimposed variation is very visible, so that the yearly values of the 

 inclination appear to increase up to the period of maximum disturbance 

 and to decrease after it. At Kew, the general effect of disturbances 

 is probably the same as at Toronto, that is to say, tending to increase 

 the inclination ; but the secular change being considerable, and tending 

 to decrease the inclination, the joint effect of the secular change and the 

 superimposed variation might be expected to appear in a diminution of the 

 yearly secular change for those years during which the disturbances are 

 increasing from their minimum to their maximum value, and in an increase 

 of the yearly secular change for those years during which the disturbances 

 are decreasing from their maximum to their minimum. 



The law of diminution of the dip at Kew due to the conjoint action of 

 these two causes, may thus be graphically represented in the following 

 exaggerated curve — 



c i> 



where B represents the epoch of maximum, and C that of minimum 

 disturbance. 



Also, we may regard ABE as denoting the first six years' results, and 

 E C D those of the second six years, the epoch of maximum approximately 

 falling about the middle of the first six years' observations, and the epoch 

 of minimum about the middle of the second. 



Now the slope of the line AED represents the average secular change, 

 also (1) represents the mean of dips deduced from the first series of 

 six years, and (2) the mean of those deduced from the second series, 

 (1) being above the line of average dip, and (2) being below it. From 

 this it is evident that, in order to bring (1) to the same epoch as (2), we 

 should have to apply to (1) a greater than the average secular change. 

 But before this reasoning can be used to account for the difference of 

 l'*69, we must examine whether, as a matter of fact, in the Kew observa- 

 tions the secular change is less than the mean during periods of increasing 

 disturbance, and greater than the mean when the disturbances are 

 decreasing. 



9. Taking the two series of six years as comprising the most regular and 

 reliable observations made at Kew, and deducting the mean dip for 1857, 

 in the Table prepared by Sir E. Sabine, from that for 1868 in Table I. of 

 this paper, we find a mean secular change of 2 f, 07. 



On the other hand, the actual yearly changes and their differences from 

 the mean are as follows : — 



