34 PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. 



meridian arc, and carrying its index, M. Roemer thus avoided the errors arising 

 from the plane of the mural arc not being accurately a vertical plane ; and 

 which Mr. Flamsteed endeavoured to check, by observing the passage of known 

 stars nearly in the same parallel of declination ; that is, passing nearly over the 

 same part of the plane of the arc ; by which he was enabled to correct or check 

 the errors of the arc in right ascension. But it is the peculiar method in which 

 Roemer divided his instruments, that occasions him here to be introduced. 



Though it is a very simple problem by which geometricians teach how to divide 

 a given right line into any number of parts required ; yet it is still a much more 

 simple thing to set off on 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 assuming a convenient opening of the com- 

 passes, and beginning at the point given, to set off the opening of the com- 

 passes as many times in succession, as there are equal parts required ; which 

 process is as applicable to the arch of a circle as it is to a right line. Of this 

 simple principle Roemer endeavoured to avail himself. For this purpose he took 

 2 stiff, but very fine-pointed pieces of steel, and fixed them together, so as to 

 avoid, as much as possible, every degree of spring that would necessarily attend 

 long-legged compasses, or even those of the shortest and stifFest kind when the 

 points are brought near together. The distance of the points that he chose was 

 about the ^ or -fV of an inch. This, on a radius of 2i- or 3 feet, would be 

 about 10 minutes. With this opening, beginning at the point given, he set off 

 equal spaces in succession to the end of his arch, which was about 75*^. Those 

 were distinguished on the limb of the instrument by very fine points, which were 

 referred to by a grosser division, the whole being properly numbered. The sub- 

 division of those arches of 10 minutes each was performed by a double micros- 

 cope, carried on the arm or radius of the instrument, the common focus being 

 furnished with parallel threads of single silk, of which ] I being disposed at 10 

 equal intervals, comprehending together one lO' division, the distance of the 

 nearest threads became a very visible space, answerable to 1 ' each, and therefore 

 capable of a much further subdivision by estimation. The divisions of this 

 instrument were therefore, properly speaking, not degrees and minutes ; but 

 yet, if exactly equal, would serve the purpose as well, when their true value was 

 found, which was done by comparison with larger instruments. 



Now, if it be considered, that in going step by step of lO' each, through a 

 space of 75° there will be a succession of 450 divisions, dependant on each 

 other ; if it be also considered, that the least degree of extuberance in the sur- 

 face of the metal, where each new point is set down, or the least hard particle 

 (with which all the base metals seem to abound) will cause a deviation in the 

 first impression of a taper point, and so produce an inequality in the division ; it 



