C 255 ] 
ther, if that coefficient is affirmative, otherwife nearer 
to it : for which purpofe the end A of the frame, 
and the bars ST, UX, YZ and the crofs bar PQ^ 
fhould all be graduated, beginning at the front of the 
frame D. They are graduated on the machine itfelf 
in a manner fomewhat different, but it is found not 
fo convenient for ufe. Then the feveral diftances 
upon the cord ej f where the pencil or pin 6, 7, 
fhall crofs it, being reckoned from the pricked line 
upon the upper bar U X, and mealured upon a fcale, 
on which the diftance of the crofs bar PQ^ from a 
line drawn along the middle of the end A, from EF 
to GH, is unity (the reafon of which appears from 
the foregoing demonftration, where Do or O T in 
fig. 1. and which anfwers to the diftance of this line 
PQfrom the bar A, was pat equal to unity) fhall 
give the required roots. And if the cord ej is re- 
moved, and a piece of pafteboard put over the ma- 
chine, on the two upper bars UX and Y Z, having a 
ftrait line drawn on its under fide,reprefenting the cord 
ef and a pencil with its point upwards be put in 
the place of the pin 7, that pencil will defcribe on 
the under fide of the pafteboard a curve, which 
with the faid right line fhall conftrutt the equation 
propoled : and the larger the coefficients of the 
equation are (which coefficients may be made as 
large as you pleafe without altering the roots, by 
multiplying them by any number at pleafure) the 
larger will be the angles at which the curve and 
the (trait line fhall cut each other; which in the 
conftrudtion of equations is a very defireable cir- 
cumftance. And as it appears from the foregoing 
demon- 
