242 Mr. Lax on a Method of examining 
we may guard it against the effects of unequal expansion or 
contraction in the metal, by means of the apparatus which I 
have described : for we have only to measure the arc which 
has been determined by the observation against the whole 
circle, or against the multiple of it, which approaches nearest 
to the circle, and from thence to deduce its value in the man- 
ner explained above, and we shall either have entirely ex- 
cluded the error which we apprehended, or have rendered it 
too small to be of any importance. Suppose, for instance, that 
the arc determined by the observation was 48° ; then by mea- 
suring it against the whole circumference increased by an 
arc of 24 0 , we shall obtain a result free from any greater 
error of unequal temperature, than one eighth of the increase 
or decrease of this arc of 24 0 beyond a due proportion to that 
of the circle itself. 
This expedient gives us all the advantages of the French 
circle of repetition, without the inconvenience arising from 
being obliged to turn the instrument, and move the telescope, 
so many times in the course of the observation. Nay, I am 
persuaded, that the result may be made more accurate in this 
way, than by the French method, because not only can the 
object be more frequently observed, but the contacts or bisec- 
tions, it may be presumed, will be more exact when the ob- 
server is not disturbed by the hurry attendant upon the use 
of the repeating circle ; and with respect to any error in the 
instrument, from whatever cause it may arise, it will be as 
effectually excluded by the process which I recommend, as 
by moving the telescope round the circle. Besides this me- 
thod is applicable either to the azimuth or altitude circle, or 
indeed to any circle which turns upon its own axis, whereas 
