319 



mean of two observations of the needle, first in its usual position, 

 and then inverted, will be affected with a residual error due to im- 

 perfect inversion of the needle. The present investigation refers 

 chiefly to that form of declinometer magnet, in which the magnet is 

 converted into a collimator by attaching to it a lens and cross fibres 

 or a divided glass scale, in the principal focus of the lens. 



It is shown that the errors due to imperfect inversion may be 

 computed, provided the magnet is observed, not only in its usual 

 position, and then inverted, — that is turned 180° round its axis, — 

 but also, when turned round 90° and 270°. 



Putting d for the correct reading, for the magnetic meridian on the 

 limb of the theodolite, used in observing the magnet ; d^, 3^, d.^, d^, for 

 the readings, when the magnet is turned through 0°, 90°, 270°, 

 360° respectively ; and g for the correction to be applied to the value 

 of the magnetic declination got from the mean of the readings in 

 the erect and inverted positions of the magnet, 



The value of g in seconds of arc may then be computed with suf- 

 ficient accuracy by the following formulae — 



^ sin 4- (d, — ^..) 

 tan/3 = -^f^^4- 



sin if a, -a.) sini(a^-aj 



sm 13 cos ^ 



_ sJ" « cos ^ (/3 ^ + /g g) sin ^ ((3^ — ^.^) 

 '' = sb^l'^^sTn ^|. cos 1 (a, - d.,) 



g _ ^ g cos ^ ('v^^ + 43 ) ^^" 2 (-4 ^1-4.3) 

 ^ sin I" sin -vj/^ sin ^/.^ cos J [^d^ — d^) 



Where /3,=:/3 + 7i; /3a = ^+73; 

 7v 73' '^v "^3 ^"^ "^J ^6'"g angles found by actual observation. 



3. On the Accuracy attainable by means of Multiplied 

 Observations. By Edward Sang, Esq. 



On opening any astronomical work of the present day, we are at 

 first startled by, and then familiarized with, the excessive precision 

 of the numbers set down. In our Nautical Almanac, for example, 



