12 DISCUSSION OF THE VERTICAL FORCE. 



Corrections for jirocjrcsske and irregtdar changes. — The difficulty of fully elimi- 

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

 the first year (1841), demanded the a^jplication of a secondary process analogovis to 

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

 progressive change in the readings of the vertical force is less decided aiid 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 montlis it Avas 

 applied very sparingly. 



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

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

 ances. The indiA-idual figiu'es thus corrected were inserted in blue ink in the 

 manuscript tables. 



EecognitioH and separcdion of the larger distm-hances. — Peirce's Criterion for the 

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

 years, and commencing with Jidy, 1841, in the following order: July 0\ August 2", 

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

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

 1\ August 3", September S*", etc. I'he 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 finally 

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

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

 able to imperfection in the corrections for temperatm-e 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 

 liour, wiU 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 o\qx 30 divisions from the mean were marked, and a new mean 

 was taken, the hourly observations Avere again compared Avith this ncAV mean, and 



' 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. 



