ON THE MAGNETIC SURVEY OF SCOTLAND. 187 



In 1858 the declination was observed by means of an instrument of a dif- 

 ferent kind. This was invented by Dr. Lloyd, and it is described by him in 

 the Proceedings of the Royal Irish Academy, January 11, 1858. In this 

 instrument the telescope is horizontal, and there is a mirror by which the sun 

 may be reflected into the telescope, and its azimuth determined. The mirror 

 being adapted to the telescope by which the scale of the magnets is observed, 

 the same horizontal circle is made to serve for determining everything, and 

 thus the theodolite and additional tripod are dispensed with, while the alti- 

 tudes of the sun are determined by means of a small sextant and artificial 

 horizon. A considerable reduction in the observer's travelling equipment is 

 thus obtained. 



In Dr. Lloyd's instrument three adjustments are required. 



1. The axis of the mirror must be horizontal. This is tested by a small 

 riding level. 



2. The plane of the mirror must be parallel to the axis. Should this not 

 be exactly the case, the error is eliminated by first observing, then reversing 

 the axle in its Y s > observing again, and taking a mean of the two readings. 



3. The line of collimation of the telescope must be perpendicular to the 

 axis of the mirror. The error produced by want of a perfect adjustment of 

 tins nature may be got rid of by viewing the sun (1°) direct, or facing the 

 south, (2°) backwards, or facing the north. 



For, let 2 denote the error of azimuth in a direct observation, $' the same 

 in a back observation ; then it may be shown that 



sin 2 i alt. 



3=+C 



cos alt. 



w — p cos 2 | alt t 



cos alt. 

 where C is a constant quantity. 



Hence if A, B denote the readings of the circle in the fore and back obser- 

 vations, we have in the fore observation c= + {180° — (A — B)} sin 2 1 alt., 

 the sign of § being such that the truth lies between the results given by the 

 two observations. 



Before the commencement of the second year's survey, the axis of the 

 mirror had been accurately adjusted so as to be at right angles to the line of 

 collimation of the telescope, but on July 20, at Bridgend, the axis was found 

 to be very much out. A plumb line was suspended, which was viewed by 

 direct vision, and backwards by reflection. When viewed by direct vision, the 

 circle reading was 348° 18', while by back reflection it was 350° 20', the angle 

 of inclination of the mirror to the horizon in the back observation being about 



„_ r cos 2 10° 



& 



80°; the formula 122'=C gives C=118', — a large amount. In con- 

 cos 20° 5 B 



sequence of this, it has been thought advisable to reject all the observations 

 before Bridgend. At Bridgend the mirror was readjusted, and for all the ob- 

 servations afterwards, with the exception of two, the sun was observed both 

 by direct and by back reflection. The following Table exhibits the values of 

 S and C at the various stations, where both fore and back observations were 

 taken : — 



