312 Sir William Herschei/s observations and experiments 
In the calculation of a set of apertures for the intended 
purpose, I admitted none that gave less than i of the light ; 
for by a greater contraction of the aperture of the mirror, an 
increase of the spurious diameters would render a judgment 
of equality liable to deception ;-f* when therefore a star of the 
third order of distances was to be found, I rejected the direct 
way of reducing a star of the first order to ± of its light, but 
selected a star previously ascertained to be of the second 
order ; and by taking of its light, the equalising telescope, 
with all its light, was used to examine all such stars as 
appeared likely to give the required equality, till one of them 
was found ; nor was it necessary to have a great number of 
limiting apertures, as it soon appeared that with eight or ten 
of them I could have many different gradations of light, which 
would ascertain even fractional degrees, and reach as far as 
the stars of any order of distances I could expect to be visible 
to the unassisted eye. 
This method of equalising the light of the stars, easy as it 
may appear, is nevertheless subject to great difficulties ; for 
as the brightness of a star is affected by its situation, with 
regard to the ambient light of the heavens, the stars to be 
equalised should, if possible, be in nearly the same region. 
When the sun is deep under the horizon, this is however not 
of so much consequence as the altitude of the star to be equa- 
f This was fully proved by the following experiment. July 27, 1813,! viewed 
Arcturus in a to feet reflector ; first with all its light ; next with circular diaphragms, 
which confined its aperture to T * T , -J T , and ^ of it ; but 1 found that the 
different spurious diameters, arising from the smallness of the apertures, made esti- 
mations of what is generally called the magnitude of the stars impossible. 
See also experiments on the spurious diameters of the celestial objects, Phil. Trans, 
for 1805, page 40. 
