12 DISCUSSION OF THE VERTICAL FORCE. 



Corrections for progressive and irregular changes. The difficulty of fully elimi- 

 nating all effects of changes of temperature, and adjustment, particularly during 

 the first year (1841), demanded the application of a secondary process analogous to 

 that used in the reduction of the horizontal force for progressive change. The 

 progressive change in the readings of the vertical force is less decided and more 

 fluctuating than in the horizontal force. Half monthly means, and in special cases, 

 means of even less periods of time, have been taken and were compared with the 

 monthly mean, the differences were applied either progressively (increasing or 

 diminishing) or as constants, as the case seemed to demand. 



Seventeen months required no such correction, and in many months it was 

 applied very sparingly. 



The process leaves the diurnal variation, relatively, undisturbed, and prepares 

 the series for the application of Peirce's Criterion for the recognition of the disturb- 

 ances. The individual figures thus corrected were inserted in blue ink in the 

 manuscript tables. 



Recognition and separation of the larger disturbances. Peirce's Criterion for the 

 recognition of the disturbances was applied to the observations extending over four 

 years, and commencing with July, 1841, in the following order: July O h , August 2'', 

 September 4 h , October 6 h , November 8 h , December 10 h , January (1842) 12 h , etc. 

 The odd hours were selected from July, 1844, to the close of the series, thus July 

 l h , August 3 h , September 5 h , etc. The following limits of separation, in scale 

 divisions, have been found for each year : 



July, 1841 June, 1842, limit, 52 



1842 " 1843, " 46 



" 1843- " 1844, " 40 



" 1844 " 1845, " 33 



Average limit, 43 



As this limit would only separate 1 in every 34 observations, and would not 

 furnish a sufficient number of disturbances to investigate their laws to advantage, 

 it was necessary to contract the above limit, and 30 scale divisions were finaDy 

 selected. There can be no doubt that the limiting number as found by the use of 

 the criterion is too high, owing to the unavoidable presence of irregularities ascrib- 

 able to imperfection in the corrections for temperature in some cases, and in others 

 due to apparently fitful changes in the instrument. 30 scale divisions =0.00099 

 parts of the vertical force =0.0127' in absolute measure, adopted as limit of devia- 

 tion of any observation from its corresponding mean monthly value for the same 

 hour, will furnish an average value for the ratio of the number of disturbances to 

 the whole number of observations. The ratio of a disturbance to the whole force 

 is also nearly the same for the horizontal and vertical component. 



All deviations over 30 divisions from the mean were marked, and a new mean 

 was taken, the hourly observations were again compared with this new mean, and 



1 The vertical force, in absolute measure, is on the average, between 1841 and 1845, equal to 12.84 

 (English units), as stated in a subsequent number of this discussion. 



