the Royal Society’s Injlruments . 397 
needle is drawn out of its true polition in thefe two fitua- 
tions, in confequence of its not being truly balanced, is 
accurately the fame ; and the mean between the two ob- 
ferved dips is very nearly the fame, as if the center of 
gravity was at m. But if the center of gravity is at m, 
the dip will be very nearly as much too great in the pre- 
fent Rate of the needle, as it will be too little when the 
poles are reverfed. Therefore, the mean of the obferved 
dips in thefe four lituations will be very nearly the fame 
as if the needle was truly balanced. 
Secondly, if the planes on which the axis rolls are not 
horizontal, the dip will be very nearly as much greater 
than it would otherwife be, when one face is turned to 
the Welt, as it is lefs when the other is ; for if thefe planes 
dip towards the South in one cafe, they will dip as much 
towards the North in the other, fuppoling the levels by 
which the inftrument is fet to remain unaltered. Con- 
fequently, the mean of the two obfervations will be very 
nearly the fame as if they were placed truly horizontal. 
Thirdly, by the fame method of reafoning it appears, 
that the mean of the two abovementioned obfervations 
will be not at all altered, though the line, joining the 
mark on that end of the needle by which we obferve, 
with the axis of motion, is not parallel to the direction of 
magnetifm in the needle; that is, though the mark does 
not coincide with the point a or b, or though the line 
joining the two divifions of 90° is not perpendicular to 
the horizon, or though the axis of motion does not pafs 
through the center of the divided circle, provided it is in 
G gg 2 the 
