DISCUSSION OF THE VERTICAL FORCE. 



17 



The following formulae of the mean diurnal variation of the vertical force were 

 deduced from the above tabular values. The angle 6 counts from midnight at the 

 rate of 15 an hour. 



1841-42 V = 641 d + 10 1 " .4 sin (8 + lOtiO 40') + 3\l sin (28 +198 25') + I 4 . 7 sin (38 -f- 250) 

 1842-43 V=697 + 7.6 (9+ 69 17 ) + 2.9 sin (29+196 48)+ 1.3 sin (38 + 195 ) 

 1843_44 V = 730 + 11.0 sin (9+ 79 54) + 3.4 sin (28+226 29)+ 0.6 sin (39+ 45 ) 

 1844-45 V = 756 + 9.2 tin (8 + 83 40) + 4.3 in (28+233 41) + 1.1 sin (38+ 1 ) 



In the construction of the equation for 1843-44 weighted normals were used, 

 those of the even hours have the weight 4, of the odd hours the weight 3. 



To show the degree of accordance in the expressions when deduced from the 

 even and odd hours separately, the resulting equations for the last year are added: 



Even hours: V = 756 + 9.32 sin (8+ 84O45') + 4.07 sin (28 + 235O17') + 1.2 sin (39 + 353O) 

 Odd " V = 756 + 8.99 sin (8 + 82 36, ) + 4.52 tin (28 + 232 05) + 1.0 sin (38 + 10 ) 



The observed and computed values compare as follows. The differences, observed 

 less computed, are expressed in scale divisions : 



The graphical representation of the observed and computed values exhibits a 

 maximum of the vertical force between 1 and 2 P. M., and a minimum of force 

 between 83 and 10| A. M. ; the diagrams also show a tendency of a secondary 

 maximum about two hours after midnight followed by a secondary minimum about 

 two hours later, with a range probably less than two scale divisions (0.000066 parts 

 of the force, or 0.00085 in absolute measure). This small nocturnal inequality is 

 only exhibited by one of the formulae, in 1842-43, when it has its greatest value ; 

 in the preceding year there is but a faint trace of it, in the two succeeding years it 

 is indicated in the diagram by dashes. The average diurnal range is nearly 22 scale 

 divisions (0.00073 parts of the vertical force, or 0.00932 in absolute measure). 



