the 'Trigonometrical Operation. 235 
But befides the important bufmefs of the triangles, which 
engrofled alrnoft our whole attention, it is fufficiently obvious, 
that, in order to have been enabled to make conclufive obferva- 
tions, the relative heights of the ftations fhould in ftri&nefs 
all have been afcertained by levelling : for purpofes of this fort 
geometrical determinations, however good in other reflects 
they may be, Ihould not here be admitted, becaufe they in- 
volve the very point in queftion, that is, the height, which 
fhould be obtained independently of angular meafurement. 
Befides barometers and thermometers at both ftations, two ob- 
fervers and two inftruments of the fame kind would have been 
neceffary, for taking at the fame inftant the reciprocal angle of 
elevation and depreffion 
Although, therefore, in our fituation the circumftances did 
not admit of conclufive obfervations on terreftrial refraction, 
confidered either by the mean or its extremes ; neverthelefs, 
fince in a variety of cafes angles both of elevation and depref- 
fion were reciprocally obtained at the fame ftations, but at dif- 
ferent times, it is hoped, fuch new light will be thrown on the 
% Dr. Maskelyne, in a letter that I lately received from him, remarks, that it 
would be of ufe to have a perfon to note the thermometer at the object as well as at 
the ftation of the obferver, whereby (if niceties of this fort were of confequence) 
the refraction might be more accurately computed by the application of a new cor- 
rection Thus, calling r zr — z= Toth of the arc of diftance ; h — the height of 
IO 
the uniform atmofphere ; t ~ the difference of the thermometers at the two 
ftations ; writhe difference of altitude of the two ftations above a common level : 
the correction would then be — ; and the true or whole refraCtion would 
40 ox 
be zrrrp according as the thermometer flood lower or higher at the upper 
400* & 11 
ftation. 
H h 2 
matter 
