Mr. Troughton on dividing Instruments. 135 
proper vertical position, as the work proceeds. The above 
may suffice, for the present, to gratify those who feel them- 
selves interested upon a subject which will be better under- 
stood, if I should hereafter have the honour of laying before 
the Royal Society a particular description of the instrument 
here alluded to ; a task which I mean to undertake, when, 
after being fixed in the place designed for it, which I hope 
will be effected at no very distant period, it shall be found 
completely to answer the purposes intended. 
Should it be required to divide a circle according to the 
centesimal division of the quadrant, as now recommended 
and used in France, we shall have no difficulty. The ioo° of 
the quadrant may be conveniently subdivided into 10 each, 
making 4000 divisions in the whole round. The 2 56 bisec- 
tional intervals, the two tables of errors, and the manner of 
proceeding and acting upon them will be exactly the same as 
before, until we come to cut the divisions ; and for this pur- 
pose we must have another line divided upon the sector. For 
~ 4-ooo P art °f circle being equal to 5' ,4 of the usual angu- 
lar measure — = i,5f divisions ; and just so many will 
be equivalent to one of the intervals of the circle. The value 
of one of the great divisions of the sector will be i° 26' 24", 
and that of the ~ parts, which are to be annexed to the right 
and left as before, will be to' 48", therefore divisible by the 
engine. Should any astronomer choose to have both gradua- 
tions upon his instrument, the additional cost would be a mere 
trifle, provided both were done at the same time. 
It must already have been anticipated, that dividing by the 
eye is equally applicable to straight lines as it is to circles. 
