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, doe 
be an angle equal to the inclination of the planes AOB, BOZ, fig. 1, we may, since 
the angle AZB is small, assume that /o¢ is sensibly equal to the inclination of 
the planes AOB, AOZ, or to 6.* The angles Aoe, Boe will then, with sufficient 
accuracy, represent the errors in the values of @ 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 
ROVE". NOVA = G4. 5 eol=8, 
Then Bh =B+%- 
Similarly, when the magnet is inverted, fig. 6, reckoning the angle AO/ in the 
direction ACBD, let 
LN) = 18h. BOs —atyer. 
Then 8, = 180° + B + 4,: 
where, as the angles @, and @, are measured always in the direction ACBD, the 
angles ‘y, and yy, 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 :— 
lst, From the verniers of the horizontal limb of the theodolite, 
6, = 6+ 9,3; and d,=0- @,: 
2dly, From those of the vertical limb, the zenith distances of the collimator-cross, 
180° — y,; 180° — ¥,. 
* Supposing BAZ or B=45°, AZ=90°, and AZB=1°, the error in the value of 8 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 f will generally be much smaller. 
hind 
