f 25* ] 
for x, is making every root ten times fmaller than 
it is. 
Thefe proportions are all taken from the writings 
of the algebraifts, or however are fuch as eafily fol- 
low from them, and therefore need not be demon- 
fixated here. 
The following is a defcription of a machine for 
regulating the motion of the abovementioned rulers, 
which I caufed to be made by an excellent workman 
in this town, and which I defire the fociety to accept 
of, to be kept as a fpecimen, for the infpection of 
any gentleman, who may chufe to have fuch made. 
It extends only to equations of two dimenfions ; 
but it is eafy to fee from it, how it may be carried 
to others of any number. A draft of it is exhibited 
in fig. 4. of the abovementioned table : where 
ABC D reprefen ts a frame of iron or fteel, confid- 
ing of four ftrait bars joined together at their ex- 
tremities, and forming a redtangular parallelogram 
about 1 2 inches long and 8 broad j into which at its 
four corners are fcrewed four perpendicular columns 
EF, GH, IK and LM, whofe lower ends ferve 
it as feet to ftand on. And on one of the aforefaid 
bars, viz. on A, is a moveable nut or Aider, which 
may be fcrewed to it at any point thereof ; it appears 
in the figure at N ; and on this nut, as a center, one 
end of the bar N O' turns, whofe other end is 
fcrewed down to the crofs bar P Q at R, which crofs 
bar is fcrewed down to the frame at P and Q, and 
may be let nearer or further from the end A at plea- 
fure : this bar reprefents the line RR in fig. 1. Then 
K k 2 on. 
