ON THE MAGNETIC SURVEY OP SCOTLAND. 



173 



It is now necessary that these observations be combined together by the 

 method of least squares. This method is described by General Sabine, in 

 discussing the Magnetic Observations in Scotland, in the volume of Reports 

 of the British Association for 1836. 



We are thus enabled to determine the most probable values of three un- 

 known' quantities ; viz. of ci = the dip at the central position; «=-the angle 

 which the isoclinal line passing through the central position makes with the 

 meridian ; and ? - =the coefficient, determining the rate of increase of the dip 

 in the normal direction, or that direction which is at right angles to the 

 isoclinal lines. 



Using all the stations except Tobermorie (where the dip seems to be 

 much increased by local attraction), we obtain the following values of S, u 

 and r; <5=71°'45' ( which represents the most probable value of the dip at 

 the central station, lat. 56° 48' N., long. 4° 19' W. ; u, or the angle which the 

 isoclinal line makes with the meridian, = — 71° 29', or its direction is from N. 

 71° 29' E. to S., 71° 29' W. ; and r, or the rate of increase of dip in the 

 normal direction, = 0' - 556 for each geographical mile, or 53 - 95 such miles 

 for each half degree of dip. 



The dip observations made use of in the previous survey of twenty years 

 ago consist of two sets (see Eighth Report of British Association, pp. 88-90). 



1 . Observations were made at ten stations by Sir James Ross ; these give 

 2=72° 40'-8 at the mean geographical position, 57° 20' N., and 3° 08' W., 

 and at the mean epoch, August 18, 1838 ; also u= — 62° 39' ; r=0'-545. 



2. Observations were made at thirty-six stations by General Sabine and 

 Mr. Fox ; these give w=— 54° 20' ; r=0'-550 ; 2=72° 13'*2 at the mean 

 geographical position 56° 18' N., and 4° 10' W. at the epoch, September 1, 

 1836. 



Let us regard these results as each possessing a weight proportional to 

 the number of stations made use of in obtaining it, and let us reduce them 

 to the epoch 1st January, 1837, by assuming the approximate yearly 

 decrement of dip to be 2', and the similar increment of the angle — u to 

 be 44' ; also let us reduce h to the central station, lat. 56° 48' N., 

 long. 4° 19' W. 



This station being the same as that used in the present survey, we have 

 thus the means of comparing the results of both surveys in the following 

 Table:— 



Table V. 



We thus see that in twenty-one years the dip at the central station has 

 diminished 46' - 9, or its yearly rate of decrease is 2'*23 ; the value of — u, on 

 the other hand, has beeu increased by 15° 26', or the isoclinal lines are so 

 much more nearly horizontal than they were in 1837 ; while r, or the co- 

 efficient which denotes the change of dip in a normal direction, has altered 

 very little*. 



* These changes will be rendered obvious by referring to a map appended to this Re- 

 port (Plate 6), in which the isoclinal lines for the two surveys are compared together. 



