48 
Mr. Pond on the changes in the 
ing the double of their zenith distances, if he does not find 
the same zenith point with different stars ( provided the in- 
strument be well divided) he may be sure that flexure takes 
place ; but he cannot infer the converse, that flexure does 
not take place, from his obtaining with all the stars the same 
error in the line of collimation. For if the flexure be the 
same on both sides of the zenith, a supposition by no means 
improbable, the observer will then have no indication of flex- 
ure by the usual method of determining the error of collima- 
tion by stars of different altitudes. Let us suppose that, with 
an instrument liable to flexure, it is required to measure by 
both methods the meridional distance of any two stars. The 
angular distance of the direct images will ( as we have already 
seen ) be affected by the difference, or by the sum of two flex- 
ures, according as the stars are placed on the same, or on 
opposite sides of the zenith. In viewing the reflected images, 
the instrument receiving two new positions, will be subject to 
two new flexures, by the sum or difference of which (as it 
may happen) the angular distance of the reflected images 
will be affected. 
The most probable supposition to be made concerning the 
flexures is, that at equal inclinations with the horizon, above 
and below it, they will be the same nearly both in direction 
and degree, and therefore that the two images below the 
horizon will approach by nearly the same quantity that the 
direct images receded, or vice versa. With an instrument 
therefore having such a system of flexures, the double altitude 
of each star will be correctly ascertained ; but stars of different 
altitudes will give different determinations of the horizontal 
point. From observations thus obtained, a near approxima- 
