ON DIVIDING ASTRONOMICAL INSTRUMENTS. 107 



roller, being elevated or depressed, may be adjusted to the 



commensurate radius without beiuf^ made conical, as was 



necessary in the o^her rase. The apparatus, similar to the 



other, must here be fixed immovably to the frame which 



supports the circle; its position must be at the vertex, 



where also I must have my station ; and the instrument 



itself must be turned around its axis, in its proper vertical 



position, as the work proceeds, 'i'he above may suffice, for 



the present, to' gratify those who feel themselves interested 



upon a subject, which will be better Understood, if I should 



hereafter have the honour of laying before the Royal Society 



a particular descvi._,t;oa of the instrument here alluded to; 



a taskwhich 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 complelely to 



answer the purposes iateiided. 



Should it be required to divide a circle according to the -^ circle may 

 I 1- ■ • <■ I 1 11 readily b'- di- 



centesimal division oi tiie quadrent, as now recommended viti-d cemie.i- 



and used in France, we sliall have no difficulty. The 100" mdliy, 



of tliC quadrent may be conveniently subdivided into 10 



each, making 4000 divisions in the whole round. The "256 



bisectional intervals, the two tables of errouvs, nud the 



manner of proceeding and acting upon them will be exactly 



the satiie as before, until we come to cut the divisions ; and 



for this purpose we muvt have another line divided upon the 



sector. For part of the circle being equal to 5''4 of 



4000 ' 



r24'2>2"-5 ,. . . 



the usual angular measure = 151- divisions; and 



^ 5-4 



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 1° '26' 24", and that of the I parts, which are 

 to be annexed to the right and left as before, will be 10' 48", 

 therefore divisible by the engine. Should asiy astronomer and in the 

 choose to have both graduations upon his instrument, the common way 



I 1- • , 1 fi. ^ a I ■ 1 L ^L at the same 



additional cost would be a mere tritie, provictea both were ti,^e. 



done at the same time. 



It must already have been anticipated, that dividing by Straight lines- 

 the eye is equally applicable to strait lines as it is to circles, dedonthe 

 An apparatus for this purpose should consist of a bar of same princi- 



brass, ^ 



