8 Mr. Smeaton’s Obfervatlom on the 
as I have been able to learn, the firft idea thereof. One end of 
the axis of this inftrument being the center of the meridian arc, 
and carrying its index, M. Roemer thereby avoided the errors 
arifing from the plane of the mural arc not being accurately a 
vertical plane; and which Mr. Flamsteed endeavoured to 
check, by obferving the paflage of known ftars nearly in the 
fame parallel of declination ; that is, pafling nearly over the 
fame part of the plane of the arc ; by which he was enabled to 
corredt or check the errors of the arc in right afcenfion. But 
it is the peculiar method in which Roemer divided his inftru- 
ments, that occafions him here to be introduced. 
Though it is a very fimple problem by which geometricians 
teach how to divide a given right line into any number of parts 
required ; yet it is frill a much more limple thing to fet off 
upon a given right line, from a point given, any number of 
equal parts required, where the total length is not exactly 
limited ; for this amounts to nothing more than affuming a 
convenient opening of the compaffes, and beginning at the 
point given, to fet off the opening of the compaffes as many 
times in fucceffion, as there are equal parts required ; which 
procefs is as applicable to the arch of a circle as it is to a right 
line. Of this fimple principle Roemer endeavoured to avail 
himfelf. 
For this purpofe M. Roemer took two ftiff, but very fine- 
pointed, pieces of fteel, and fixed them together, fo as to 
avoid, as much as pofiible, every degree of fpring that would 
neceffarily attend long-legged compaffes, or even thofe of the 
fhorteft and ftiffeft kind when the points are brought near toge- 
ther. The diftance of the points that he chofe was about the 
or -h-°f an inch. This, upon a radius of 2.f or three feet, 
would be about 10 minutes. With this opening, beginning 
at 
