MAGNETIC OBSERVATIONS. 355 



between the other two quantities. If d is taken as the constant, the equa- 

 tion represents a circle; if a, it represents a hyperbola. 



This equation may have a useful application in making it possible to 

 judge, in advance of actual test pitting, of the probable depth of surface 

 covering over a magnetic rock, for which the original assumptions are ful- 

 filled, and the numerical values of ^, a, and d are determinable. It will be 

 remembered that the assumptions upon which equation (13) rests are the 

 fundamental ones of Section III, and also that the rock has a uniform 

 strike. In practice, the uniformity of the strike can be established by other 

 traverses on each side of the one in question, and ^, the angle of dip, may 

 usually be determined by the outcrop of other formations in the same 

 series. 



For any practical application it is also necessary that a (half the 

 thickness of the rock) and d (half the distance between the stations at 

 which the horizontal component is a. maximum) should be known. From 

 an inspection of the equation it is evident that any close determination of 

 li, except for. great depths of covering, depends upon very precise knowl- 

 edge of the ratio between a and d. The practical difficulties in the way of 

 the measurement of a and the ever-present probability that the rock may 

 vary from point to point, not only in actual but in effective magnetic thick- 

 ness (which is what a actually signifies), make it clear that for the most 

 part h can only be found approximately. Also, in the case of a rock 

 striking due east and west the methods fail, from the fact that 2c? can not be 

 determined on the ground. 



The determination of li is therefore hedged in with important limita- 

 tions; yet in many cases the information supplied by the equation may be 

 very useful. The difficulties in the way of measuring a ai'e disposed of in 

 the event that along one traverse on the strike of the rock li is known, as it 

 may be, by the sinking of a test pit. This value of li at once gives a A^alue 

 of a, which may be used on other traverses across the same rock with much 

 more accurate results, in the lack of disturbing factors, than if a were 

 known only by measurement It should be added that when the traverse 

 crosses the strike of the magnetic rock at the angle 7, the distance d meas- 

 ured on the line of the traverse must be multiplied by sin y in order to get 

 the value of d to be used in the determination of /*, and also that li must be 

 corrected for the heigrht of the instrument. 



