368 
suppose the clock equally audible in every position of the te- 
lescope, and the observer able to observe in all with equal 
convenience, for personal discomfort will interfere with the 
attention). That arising from uncertainty in estimating the 
star’s place will vary inversely as the cosine of its declination. 
‘«* But there is yet another, arising from the actual dis- 
placement of the star’s image, by irregular changes im the re- 
fractive density of the atmosphere; the effect will, as the 
preceding, be inversely as the cosine of declination, but also 
directly as the magnitude of these changes. ‘This depends, 
in the first place, on the heterogeneity of the air as to heat 
and moisture; and in the second, on the quantity of dis- 
turbed medium through which the line of sight passes. The 
former scarcely admits of expression in terms of our present 
meteorological data, and we must be content to assume for it 
an average value. In respect to the other, as the disturbance 
takes place chiefly within a small distance of the earth’s sur- 
face, it will easily be seen that its amount is as the secant of 
zenith distance. If then we denote by u the probable error 
of the ear, by y that of the eye, and by z the atmospheric 
tremor at the zenith, we have, by the theory of these errors, 
for a star whose declination is 6, 
2 
cos’. 8 cos?d . cos? (i -—8) 
It is evident that z admits of a minimum in respect of é: let x 
be the tangent of /— 6, A that of latitude, and r= ; differen- 
tiating and equating to 0, we derive 
‘¢ Tf then we select three stars, properly differing in zenith 
distance, we can determine the three errors u, y, and z. We 
find « in the usual way, by comparing each wire of a set of x 
