ANALYSIS 



DISTURBANCES OF THE DIP AND TOTAL FORCE. 



IN the preceding discussion of the disturbances of the horizontal and vertical 

 components of the magnetic force at the Girard College Observatory, the laws of 

 their variations, as far as they have been recognizable from the series, were brought 

 out and discussed, and this suffices, perhaps, in most cases, for any future applica- 

 tion of theory, or for the purpose of testing hypotheses ; but as it is also desirable 

 for other comparisons to deduce the corresponding results for dip and total force 

 from previous researches, it is proposed here to present the results of this combina- 

 tion numerically and in tabular form. 



This combination is effected by the formulae: 



/AY AJTx A* AY AX 



Av = sin cos 6 ( -^ v~ ) and = sin 2 6 -^ + cos 2 dv~ 



\ i .A I <p JL 



which expressions have already been used in the preceding part. 



A strict treatment of the disturbances of either the dip or total force would 

 require the formation of the difference of each observation of the vertical and hori- 

 zontal force from its normal value (corresponding to the hour, month, and year), the 

 conversion of these differences from units of scale value into parts of the respective 

 force, and finally the numerical combination of the contemporaneous values of the 

 two instruments by means of the above formulae. To treat over 44,000 observa- 

 tions in this manner is impracticably laborious, and makes it desirable to substitute 

 in its place another process less cumbrous, but, as regards results, equally effective. 

 The method adopted avoids also the labor of forming normals, and especially that 

 of separating the disturbances anew for each element. The method pursued in the 

 discussion of the Toronto observations answers all purposes, and has also been 

 adopted for the Philadelphia series; a more distinct idea, however, is here given for 

 the limiting value beyond which disturbances are recognized. The method is as 

 follows : Returning to the manuscript tables which contain the observations reduced 

 to a uniform temperature and corrected for progressive change, as far as this was 

 practicable, each observation marked there as a disturbance, that is, which differed 

 as much or more than + 30 scale divisions from the normal of the vertical force, 

 and as much or more than + 33 from the normal of the horizontal force, was tran- 

 scribed and at once converted into its equivalent in parts of the force to which it 

 respectively belonged. One scale division of the vortical force magnetometer equals 

 0.000033 parts, and of the horizontal force magnetometer 0.0000365 parts of the 



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