MAGNETIC OBSERVATIONS. 59 



so as to bring its face to the east, and the horizontal circle again clamped. The 

 face of the needle now being towards the west, its north and south ends were read. 

 Let these readings be designated respectively as \)/ and ^". 10°. The needle was 

 reversed upon the agate planes, so as to bring its face towards the cast, and its 

 north and south ends were read. Let these readings be designated respectively as 

 V" and V 1 "- 



At the first few stations each of the readings <p', $", <p'" <|> r/ ",ij/, ij/', i]/". . . .ij/'", 



was repeated three times, the Y's being raised and lowered again between each 

 repetition; but after some experience I became convinced that the increase of 

 accuracy obtained by three repetitions, over that obtained by a single careful read- 

 ing, was not sufficient to warrant the greatly increased expenditure of time, and 

 accordingly the repetitions were abandoned. 



The needle A 2 proved to be well balanced, and the observations made with it 

 were therefore reduced by the usual formula, namely 



<p' + <p" + <l>'" + <l> ,r + <P r + <p VI + <p VII + <P TI "_ IL 

 8 ~ a 



% V + y ~\~ y + ^ Ir + ^ r + V 1 + ^ T " + 'V 1 " _ o 



8 _ _P 



where is the magnetic inclination or dip. 



The needle A 1 proved not to be well balanced, which was shown by the great 

 difference between the values of a and 3 obtained with it in low magnetic lati- 

 tudes ; although they agreed well enough at places where the dip was large. An 

 examination of all the observations showed that in every case 



ft' + ^ + ^ + ^^ + ^ + ^ + fl™ 7 

 4 ~" 4 



and 



y+y+y+f _ V' + ^ + V' + V 1 " 



4 ~ 4 



at least within about one degree. It therefore followed that, although the centre 

 of gravity of the needle did not lie in its axle, it did lie somewhere in the line 

 joining the two extremities of the needle, and passing through its axle. In such 

 cases we have 



. tan a 4- tan 3 

 tan = i — 



and by that formula all the observations made with this needle were reduced. 



At St. Thomas some observations of dip were made with the plane of the verti- 

 cal circle out of the magnetic meridian. They were reduced by the formula 



tan 6 = tan 6' cos a 

 where is the true dip, and 6' the dip observed with the vertical circle in a plane 

 whose azimuth, measured from the magnetic meridian, was a. 



