DIP-NEEDLE ERRORS ARISING FROM MINUTE PIVOT-DEFECTS. 



By H. W. Fisk. 



The values of inclination presented in the tables of results of magnetic observations, 

 in Volumes I, II, III, and IV of the "Researches of the Department of Terrestrial Mag- 

 netism," have been determined mainly by dip circles, depending in general upon observa- 

 tions with four needles at each station. The development of the earth inductor is a 

 satisfactory field instrument has now been accomplished by the Department, and its 

 use in the field, as shown by tabulated results and reports in this volume, has been sufficient 

 under a variety of conditions to assure its success and remove all doubt as to the ex- 

 pediency of its general adoption. It has been amply demonstrated that the corrections 

 of earth inductors on an adopted standard remain practically constant for all inclina- 

 tions, and these corrections are known for the instruments in use certainly within 0'.5 

 and in general probably much nearer. With the dip circle on the other hand there is 

 always an uncertainty greater than this. The reduction to standard of a series of field 

 observations with a dip circle is one of the most tedious operations involved in the prep- 

 aration of observations for publication and at the same time the least secure. 



The methods heretofore followed in reductions for determination of corrections on 

 adopted standard have been described in Volume I, page 45, and in Volume II, page 17, 

 of the "Researches of the Department of Terrestrial Magnetism." The first method 

 involves adjustment of corrections determined for different values of inclination, /, by 

 use of the formula FI = x+z cos I+y sin / where F is the total intensity and x, z, 

 and y are coefficients obtained by least squares. It requires well-distributed comparisons 

 with a reliable standard and has given good results whenever such comparisons were 

 available; under these circumstances the method will control in a satisfactory way those 

 general changes in the correction for a given needle which are known to take place where 

 the instrument is used through widely varying inclinations. It does not take account 

 of certain other changes in correction, sometimes of considerable magnitude, which 

 persist only through limited ranges of inclination. The second method which, because 

 of lack of sufficient distribution of reliable comparison-data, from necessity has been 

 frequently used instead of the first, involves substantially an adjustment of needle- 

 differences and the rejection of those needles showing erratic behavior. The four mean 

 observed needle-differences for each group of several stations of nearly the same inclina- 

 tion are plotted and graphically adjusted so that the sum of any four corresponding 

 graph-values of successive needle-differences will be zero, thus [(a b) + (b c) + (c d)-f- 

 (d a)] = 0, the corresponding values of inclination by the four needles being a, b, c, 

 and d. Assuming that the mean correction for any one needle determined at one or 

 more base-stations remains constant throughout an expedition, corrections for the other 

 three needles at various inclinations are determined from the needle-difference graphs 

 and the process repeated in turn assuming each of the other needles constant. A crit- 

 ical examination of the needle-difference graphs and of the four series of corrections 

 obtained as above serves to reveal unusual accidental errors as well as those ranges 

 of inclination over which one or more of the needles behaved badly, either because of 

 pivot irregularities or deterioration. After rejecting such values, smoothed mean correc- 

 tion-curves are deduced. 



In the case of certain expeditions reported upon in this volume, and for which the 

 stations when arranged in the order of increasing inclination were densely distributed 

 throughout the range of inclination, it was discovered that certain well-marked, short- 



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