— _ 
7 
meridian. ‘This position, I soon perceived, was less advanta- 
geous than that described above ; and it was accordingly aban- 
doned in all the instruments subsequently constructed for other 
observatories. In the Dublin Observatory, however, I pre- 
ferred the continuance of the less perfect arrangement to the 
interruption of the series of observations consequent upon its 
alteration ; and I have been thus compelled to re-discuss the 
theory of the instrument, which is rendered much more com- 
plicated in this form. 
‘* It was natural to suppose that the moment of the force 
exerted by the iron bar upon the suspended magnet was of the 
form MUcosu, U and u denoting as before; so that the 
equation of equilibrium should be, simply, 
U= X tanu. 
Differentiating, and dividing by Y = X tan 0, and denoting (as 
before) the change of U produced by a small change of the 
vertical component of the earth’s force by Vé Y, we have 
bY. (sec? uu + tan u®*) 
yY ma 2 8 be i > 
in which p = V-! cotan 0. 
‘«* This formula, however, is only an approximate one. The 
expression for the moment of the force exerted by the iron bar 
upon the suspended magnet, in this case, is not, strictly, of the 
form supposed above; and it becomes necessary to seek the 
exact form, and to examine in what manner the formula of re- 
duction is modified. 
‘¢Let CP be the freely suspended 
horizontal magnet ; C’P’ the verti- 
cal iron bar; and O the point in 
which it intersects the horizontal 
plane passing through CP. Also, 
let dm and dm’ denote the elements 
of free magnetism at P and P’, and 
p the distance PP’. Then the 
force exerted by dm’ on dm is 
