354 MR WILLIAM SWAN ON OBSERVATIONS 



the magnet is also represented as in its erect position, but inaccurately so ; and 

 in fig. 6, it is represented as inaccurately inverted ; while in both figures the inter- 

 sections of the theodolite and magnet wires have been brought into optical coinci- 

 dence, in order to read off the magnetic declination. Since the optical axis of the 

 collimator coincides approximately with that of the cylinder we may assume that 

 the magnetic axis is turned round the line OB, fig. 1 ; and if, in figs. 4, 5, 6, loe 

 be an angle equal to the inclination of the planes AOB, BOZ, fig. 1, we may, since 

 the angle AZB is small, assume that loe is sensibly equal to the inclination of 

 the planes AOB, AOZ, or to ft* The angles Aoe, Boe will then, with sufficient 

 accuracy, represent the errors in the values of (3 in the different positions of the 

 magnet, and those angles may evidently be either estimated, or measured by means 

 of a position-micrometer. The micrometer I have employed for this purpose con- 

 sists of a piece of plate-glass, having on it a small circle about 0*25 inches in dia- 

 meter, divided to every five degrees, by means of a fine diamond point. The glass 

 is cemented with Canada-balsam to the flat surface of the field-lens of a Ramsden's 

 eye-piece, and its thickness is such, that when the diaphragm-wires are brought to 

 focus, the divided circle is so close to them as to be also very nearly in focus, so 

 that its divisions are sufficiently well defined. The angle AEO can then be easily 

 estimated to the nearest degree. 



In the usual position of the magnet, fig. 5, let 



AO I = ft , AO e = y 1 , eol = (3 , 

 Then ft = (3 + 7l . 



Similarly, when the magnet is inverted, fig. 6, reckoning the angle AO / in the 

 direction ACBD, let 



AO I = ft , BO e = 7 3 , 



Then ft = 180° + (3 + y 3 : 



where, as the angles ft and ft are measured always in the direction ACBD, the 

 angles y x and y 3 are to be reckoned positive or negative, according as they are 

 measured in the same or in the opposite direction. 



If, now, the magnet be inverted again and again, causing the lines 1 and 3 

 alternately to coincide with the line 0, and if, after each inversion, the cross- wires 

 of the theodolite be made to intersect those of the collimator, we shall obtain the 

 following series of readings : — 



] st, From the verniers of the horizontal limb of the theodolite, 



8 t = 8 + cfy 1 ; and 8 Z = 8 - <p 3 . 

 2dly, From those of the vertical limb, the zenith distances of the collimator-cross, 



180° - ^ ; 180° - 4,3 . 



* Supposing BAZ or /3=45°, AZ = 90°, and AZB=:1°, the error in the value of /3 introduced 

 by this supposition is only about 31", which would not appreciably affect the subsequent calculations ; 

 and as AZB need not exceed 5' or 10', the error in |S will generally be much smaller. 



