TOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. SQ 



perceived, in common with all preceding artists, how very much more qasy a 

 given line was to bisect, than to trisect, or quinquisect : and therefore the g6 

 arc which proceeded by bisections only, or by laying off the same identical 

 openings, which, as already shown, is still more simple and unexceptionable, 

 was wholly intended by him by way of checking the division of the arc of QO, 

 which required trisections and quinquisections. But experience soon showed the 

 superior advantage of it so strongly, that the use of the QO arc is now wholly set 

 aside, where accuracy is required ; whereas th^ ingenuity of Mr. Bird having 

 shown a way to produce the 90 arc by bisection, when this is really pursued 

 quite through the piece, by rejecting all divisions derived from any other origin, 

 the 90 arc will have nothing in it to prevent its being equally unexceptionable 

 with the 96 arc ; and consequently if, instead of the 96 arc, another arc of 90 

 was laid down, which being on a different radius, its divisions will stand totally 

 unconnected with the former, then these two arcs would in reality be a check on 

 each other ; for being of equal validity, the mean might be taken : and if, in- 

 stead of vernier divisions, strokes at the distance of any odd number, as 7, 9, 

 11, or 13, are marked on, and carried along with the index plate; these will 

 produce a check on neighbouring divisions ; and the angle may then be deduced 

 irom the medium of no less than 4 readings. 



The last works that have been made known to the public in the line of 

 graduation, so far as have come to my knowledge, are those of the very ingenious 

 Mr. Ramsden, which were published, by order of the Board of Longitude, in 

 the year 1777. From his own information I learn, that in the year 1760 he 

 turned his thoughts towards making an engine for dividing mathematical instru- 

 ments ; and this he did in consequence of a reward offered by the Board of 

 Longitude to Mr. Bird, for publishing his method of graduating quadrants ; for 

 as several years previous to that period, he had taken great pains to accomplish 

 himself in the art of hand-dividing, in which line Mr. Bird had acquired his 

 eminence, he conceived by this publication of Mr. Bird's he should be reduced 

 to the same standard of performance with the rest of the trade. He therefore, 

 partly to save time, and that kind of weariness to an ingenious mind that ever 

 must attend the endless repetition of the same thing from morning to night ; 

 partly still to preserve the pre-eminence he had then gained ; and partly to pro- 

 cure dispatch in the great increase of demand for Hadley's sextants and octants, 

 in consequence of the successful application of the moon's motion to the purpose 

 of ascertaining the longitude at sea, which instruments for this purpose required 

 a degree of accuracy and certainty in the division, by no means necessary when 

 applied to the simple purpose of observing latitudes ; I say,, for these considera- 

 tions, Mr. Ramsden determined to set about something in the instrumental way, 

 that should be sufficient effectually to answer these purposes. 



