OF THE MAGNETIC FORCE. 25 



Observed range. Computed range. 



January, 1841 38.8 38.3 



1842 . 23.8 26.2 



1843 . 24.1 19.7 



1844 . .... 15.2 18.7 

 1845 24.2 23.2 



The minimum range as given by the formula is in September, 1843. In Part I. 

 of the discussion we found the minimum range of the declination in May, 1843, 

 and the minimum from the disturbances of the declination in August, 1843. 



Before proceeding to the discussion of the disturbances in the horizontal force, 

 the formulae given for the diurnal variation require to be put in a different form for 

 future use and for convenience of comparison with other places. 



The scale divisions were multiplied by the value of one division of the scale 

 (0.0000365), and again by the value of A' found for the year; the numerical constant 

 was replaced by JTand the angular quantities were changed by 180 so as to make 

 increasing numbers correspond to increase of force ; we then obtain in absolute 

 measure the following expressions for the regular solar-diurnal variation of the 

 horizontal force at the Girard College: 



Year 1840-41 H = 4.178 + 0.00091 sin (9 + 72 3 14') + 0.00178 sin (28 + 301 16') + 0.00090 sin (38 + 134 42') 

 " 1841-12 H = 4.175 + 0.000(51 sin (9+64 07 ) + 0.00100 sin (2 8 + 311 32 ) + 0.00069 sin (3 8 + 132 19 ) 

 " 1842-43 H = 4.173 + 0.00063 sin (8+70 06 ) + 0.00108 sin (2 + 312 24 ) + 0.00057 sin (38 + 143 06 ) 

 " 1843-44 H = 4.170 + 0.00033 sin (8 + 93 55 ) + 0.00078 sin (28 + 308 58 ) + 0.00036 sin (38 + 137 58 ) 

 " 1844-45 H = 4.168 + 0.00067 sin (8+91 13 )+ 0.00104 sin (2 8 + 303 25 ) + 0.00063 sin (38 + 141 26 ) 

 The angle 9 counts from midnight ; the middle epoch to which each equation refers is January. 



Investigation of the Eleven (Ten?) Year Inequality in tlie Disturbances of the 

 Horizontal Magnetic Force. In Table VI. the number of disturbances in each month 

 has been given as found from the observations ; these numbers are, however, not 

 directly comparable with one another, first, on account of some omissions in the 

 record, and secondly, on account of the change from a bi-hourly to an hourly series. 

 For any incomplete month the number of disturbances for the whole month is 

 obtained by simple proportion from the number during the part of the month re- 

 corded; for January, 1841, the total number becomes 35, for June, 1841 the total 

 number is 18. For January, February, and March, 1843, the mean total number 

 of the disturbances, as found in the same months in the preceding and follow- 

 ing year, was substituted ; this mean gave 8, 20, and 20, respectively. The num- 

 ber of disturbances after October, 1843, were halved to make them comparable 

 with the bi-hourly series. There were two anomalous months, July and December, 

 1840, in which the disturbances amount to 165 and 120, with an annual mean of 

 64, whereas in the same months in the following year they only amount to 26 and 

 26 respectively, with an annual mean of 27 ; the mean annual difference 37 was 

 applied to the numbers found in 1841, which give 63 and 63 as a substitute for the 

 anomalous values in July and December, 1840. This anomaly does not exist in 

 the phenomenon itself, but is unquestionably due to the irregularity in the pro- 

 gressive change. 



Table IX. contains the number of disturbances as distributed over the several 

 years and months, all referred to a uniform series of bi-hourly observations. To 



