parallax of certain fixed stars . 281 
take place in winter. Hence an uncertainty in the index error, 
which as deduced from Procyon, might occasion a difference 
in the zenith distance of (ex. gr.) a lyr^ in summer and winter, 
= i",i6, bearing a considerable proportion to the supposed 
discordance in summer and winter. This is an extreme 
case : the index correction, as deduced from other stars, 
would not be so much affected. The polar star below the 
pole, is likely to be often used, and might occasion an uncer- 
tainty of about 1" under similar circumstances. 
When I call this uncertainty, I suppose the matter is en- 
tirely doubtful as to the preference to be given to either of 
the formulas. 
Bradley's law of change from temperature was deduced 
from his astronomical observations, but other astronomical 
observations do not contradict the law of the French formula ; 
which has also been confirmed by physical experiments, and 
seems more to be depended on. 
It appears then that an incorrect law may materially affect 
the index error, and occasion incorrect results. 
It therefore seems of the first importance with respect to a 
mural circle, to ascertain with exactness the law of variation 
of refraction from change of temperature ; otherwise errors 
will be mixed up in all the conclusions. 
It will not be possible to deduce easily, by the results from 
Bradley’s refractions, the results that the French refractions 
would give. 
For this purpose it will be necessary not only to know the 
mean temperature at the observations of the star, whose 
north polar distance is required, but also the temperature at 
the observations of stars by which the index error is com- 
