The differences, using three terms in (lie equations, arc within the uncertainty 

 of the observed values. The probable error of a single representation is + ().(i scale 

 divisions, or 4^ 0.0000!) in the absolute scale. 



The curves show a double progression in the daily motion, with a principal 

 maximum of horizontal force in the morning, a principal minimum before noon, 

 and a secondary maximum in the afternoon ; the precise epochs (to the nearest five 

 minutes) and extreme values were computed by means of the preceding formula?. 



The secondary maximum is readied about 8" 30 m P. M. with a comparative!} 



small range. 



The mean value of the force is attained about 7 h 55™ A. M., and again about 

 l 1 ' 55 m P. M., with considerable regularity ; it is again reached at 6f b and ll^ h P. M., 

 though with less regularity. 



At Toronto (see Vol. II. of the Toronto Observations) the diurnal variation of 

 the horizontal force lias a principal maximum at a little after 4 P. M., and a prin- 

 cipal minimum at 10 or 11 A. M. ; the secondary maximum occurs about (i A. M. 

 There is, therefore 1 , this specific difference in the diurnal motion at these two 

 stations: in that at Philadelphia the morning maximum is the higher of the two, 

 while at Toronto it is the afternoon maximum. The difference between the two 

 maxima, as shown above, is almost nothing in the minimum year 1843-44, but 

 increases before (and after) this epoch in proportion to the interval. At Toronto 

 the daily range seems to be slightly greater. The secondary minimum at Toronto 

 occurs about 2 or 3 A. M., or about six hours later than at Philadelphia; this is a 

 second though less significant point of difference. 



The minimum daily range occurs in 1843-44; its value is then less than one-half 

 what it was in 1840-41. 



The following equation expresses the mean diurnal range in scale divisions: — 



R = + 19.68 — 3.78 (t — 1843) + 2.77 (t — 1843) 2 . 

 It represents the observed values as follows: — 



