315 
Captain Kater's floating collimator , &c. 
be considered that each is a single observation, not the mean 
of two ; and with reference to the collimator, the errors of 
division have necessarily, and may also with respect to the 
star, have contrary effects. Add to these the sources of error 
arising from inexact bisection of the plumb-line dot, from the 
bisection of the star from reading off ; and, in so large an 
instrument as the Dublin circle, from the effects of unequal 
temperature, to which may be also added the irregularities 
of refraction ; and then we may rather wonder greater dis- 
cordances are not sometimes to be found. The deviation 
from the mean very rarely indeed mounts to 3" ; and it is 
to be remembered, that a second in the circle is only about 
ToVo °f an inch. It may be objected, that with reference to 
mural circles, in which the reversing principle cannot be 
applied, the effect of the errors of division on the index cor- 
rection cannot be done away. In mural circles the principal 
means of obtaining the index correction are observations of 
the pole star above and below the pole, and by observing by 
reflection. The difficulties that occur in the practice of these 
two methods, when contrasted with the use of the collimator, 
are surely not compensated by the advantage of obtaining 
perhaps the index correction more free from the errors of 
division. When we consider Mr. Troughton’s improved 
method of dividing, and the application of six microscopes to 
a mural circle, we need not fear any appreciable error in de- 
termining by the floating collimator the index correction. 
Besides, as Captain Kater has pointed out, we may by 
changing the inclination of the collimators bring into use 
different parts of the circle, and so avoid the effect of errors 
of division. 
