DISCirSSION OF THE VERTICAL FORCE 



19 



principal minimum at Toronto 10 A.M., at Philadelphia 9| A.M.; the epochs of 

 the early mornmg inflection are also about 3| hours later at Toronto. The curves 

 exhibit also a difference in the amplitude, at Toronto, Vol. Ill, the diurnal range 

 is 0.00019 parts, whereas at Philadelphia we found it much larger. 



The special study of the solar diurnal variation of the vertical force is reserved 

 for Part VIII. 



The minimum diurnal range occurred in 1842-43, on the average, therefore, we 

 may assume May, 1843, as the epoch of the minimum range in the eleven (or ten) 

 year period, resulting from the discussion of the declination, horizontal and vertical 

 force observations. 



To facilitate the comparison with similar expressions at other stations, the pre- 

 ceding equations of the diurnal variation are also presented, expressed in parts of 

 the vertical force. The angles have been changed 180° to reverse the order of 

 progression of the scale numbers. 



1841-42 V = + 0.00034 sin (a -j- 2860 40') + 0.00010 sin (29-1- 180 25') + 0.00006 sin (39+700) 

 1842-i3 V = + 0.00025 «n (9-1-249 17 ) + 0.00010 sra (29 + 16 48 ) -^ 0.00004 sm (39+ 15 ) 

 1843-44 V = + 0.00036 Sin (9 + 259 54) + 0.00011 sw (29+46 29 ) + 0.00002 sm (39+225) 

 1844-45 V = + 0.00030 sin (9 + 263 40 ) -j- 0.00014 sin (29 + 53 41 ) -i- 0.00004 sin (39 -j- 181) 



The constant terms and numerical coefficients when expressed in absolute measure 

 (English units) are as follows : — 





Y 



Term involving 1 



6 



29 



39 



1841-42 

 1842-43 

 1843-44 

 1844-45 



12.85 

 12.84 

 12.83 

 12.83 



0.00441 

 0.00322 

 0.00468 

 0.00388 



0.00131 

 0.00123 

 0.00144 

 0.00172 



0.00072 

 0.00055 

 0.00025 

 0.00047 



The angle counts from midnight. 



Investigation of the Eleven {or ten) Year Inequality in the Disturbances, and General 

 Analysis of the Disturbances of the Vertical Force. — By means of Table V, a new 

 table was formed of the number of disturbances in each month for the years 1841-42, 

 1842-43, 1843-44, 1844-45, commencing with July, and all referred to a uniform 

 series of bi-hourly observations ; the numbers for and after October, 1 843, were 

 halved. The number of disturbances for January, February, and March, 1843, are 

 the means between the same months in the preceding and following year. The 

 annual means of this Table (VII) are as follows : — 



Mean number of Disturbances. 



In 1841-42 . . . . c . . 51 



" 1842-43 ....... 34 



" 1848-44 ....... 25 



" 1844-45 ....... 16 



This seems to indicate the end of the year 1844 as the epoch of the minimum 

 number of disturbances in the eleven year period, taking the numbers collectively 

 for declination, horizontal and vertical force, the minimum probably took place in 

 the spring of 1844. 



