4H 
An Account of the Measurement 
upper and under thermometers ; and as, in the course of the 
time specified, I had various opportunities of satisfying myself 
on this point, I desisted from making any farther use of it. For 
the purpose of ascertaining the limits of the errors likely to result 
from the cause now spoken of, it will be right to institute some 
little inquiry into its mode of operation. 
In Plate XVI. Fig. i, let CD be the line passing through the 
centre of the sectorial tube, brought into any position for obser- 
vation ; the angle made with the zenith being ACB, and C A the 
consequent direction of the plumb-line. CB and BA may there- 
fore represent the radius and arch of tfie sector, when in a 
state of uniform temperature throughout. 
Now, at any time, let the thermometer at the top C, indicate 
a degree of heat superior to that shewn by the other at B ; and 
let it also be supposed, that the difference between those degrees 
of heat, at any intermediate point, is directly as the distance of 
that point from C or B; and farther, let the tube CB be extended 
to D, while the arch AB continues of the same length. 
If the line CA be extended to F, and the line AE be drawn 
parallel to BD, meeting the arch FD in E, then will the small 
space FE measure the error in the observed zenith distance of 
the star. 
As the angle ACB must in all cases be small, ACB and EF 
may be considered as two similar sectors of circles ; under which 
supposition, we get FE = - ; and, applying this to an ex- 
treme case occurring at Arbury Hill, on the 12th of September, 
As few of the stars selected for observation were, at either of 
■, hence FE = 
5 0 . x 0,0001 237 x 6®. 26' 
2x1 2 ’ 
