Reductions to Standard Instruments 71 



2^ 



By differentiation of the formula tan / = t> 



/I 



A^ sin 7 , ^Z cos 7 



^^ = F— + ^7^ 



substituting tiie values of AT/ and AZ as above determined 



. ^ _ _ xF _ yTT sin 7 zZ cos 7 



Whence . ^ ?/~-2 • <^t 



A7 = - .T - ^^-^sm 27 



But if the effects arise chiefly from induction, it is quite probable that x = y - z, and 

 hence, A7 = — x, which is the correction if the error be caused entirely by a homogenous 

 magnetic induction of the various parts of the dip ckcle. In general, this correction must 

 be small for dip circles in which the movable part is relatively small. 



Supposing there is a permanent magnetization of the instrument parts, and that we 

 have h and z arising from (a) and /from (6), then siniilai'ly, 



77' = 77 + A/7 = 77 + /i +/ sin 7 Z' = Z + AZ = Z + 2 -/ cos 7 



Whence . ^ / _ h sin 7 z cos 7 



F F F 



In general, the first two terms may be eUminated by reversal of microscopes, reversal of 



instrument, and by various orientations of the f ootscrews during observations, and only the 



last term would remain. Thus r 



, , z cos 1 



^=-F~ 



That part of the error caused by irregularity of the bearing pivot^sections of the needles 

 can be expressed by some empirical function, such as 



A7 = X + y sin 7 + z cos 7 + . . } 



From the above considerations it follows that the general formula 



FM = X + z cos 7 + 2/ sin 7 



will express the variation of the needle-correction with changes in total intensity and 

 inclination. The observed values of A7 for each needle and circle, obtained from compari- 

 sons with standardized instruments at shore stations and at observatories during the 

 Galilee work, were adjusted by the method of least squares in accordance with that fommla. 

 The importance of the variation in A7 with change in F and 7, particularly for the sea dip- 

 circles, is shown by inspection of the values of coefficients x, y, and z given on pages 66-69. 

 Since, for even the best land dip-circles, the variations in the needle-corrections are of 

 an order equal to or greater than the actual error of observation, the determination of a 

 standard value for inclination at any station is a difficult question. The numerous com- 

 parisons made with earth inductors by the observers of the Department of Terrestrial Mag- 

 netism in various regions of the globe have indicated that the correction of an earth inductor 

 on standard is subject to practically no change with variation in magnetic field. For the 

 preliminary adjustments of the corrections of the land circles used in standardizing shore 

 observations, reliance was, therefore, placed chiefly on the values of A7 obtained by compari- 

 sons with earth inductors; successive and final least-square adjustments were then made, 

 using all the shore data, improved by the preliminary adjustments. As will readily be 

 seen, the compilations and reductions necessary for each needle and circle are long and 

 laborious, particularly so when no field earth-inductor was available, as was the case for the 

 Galilee work.^ 



'C/. Chauvenet, W. Manual of spherical and practical astronomy, v. II (33). 



'In view of the experience gained on the Galilee and in the land work, a field earth-inductor was added to the equipment 

 of the Carnegie at the earliest possible time, viz, in September 1910. 



