ON DIVIDING INSTRUMENTS. g 



by any means apply the principle of turning to the art of 

 dividing instrunr)ents, the tools liable to objection mit^ht be 

 dispensed with. The means of doing this were first sug- Application of 

 gested by seeing the action of the perambulator, or mea- marking divi^ 

 suring wheel; the surface of the Earth presenting itself as sions. 

 the edge of the instrument to be divided, and the wheel of ^ 



the perambulator as a narrow roller acting on that edge ; 

 and hence arose an idea, that some easy contrivance might 

 be devised, for marking off the revolutions and parts of the 

 roller upon the instrument. Since the year above-men- 

 tioned, several persons have proposed to me, as new, divid- 

 ing by the roller, and I have been told, that it also occurred 

 long ago to Hook, SissonPaud others ; but, as Hatton on 

 watch-making says, " I do not consider the man an in- 

 ** ventor, who merely thinks of a thing; to be an inventor, 

 ** in ray opinion, he must act successfully upon the thought, 

 ** so as to make it useful." I had no occasion, however, to 

 have made an apology for acting upon a thought, which, 

 unknown to me, had been previously conceived by others; 

 for it will be seen in the sequel, how little the roller has to 

 do in the result, and with what extreme caution it is found 

 necessary to employ it. 



When a roller is properly proportioned to the radius of When most 

 the circle to be divided, and with its edge made a small mat- |ectlve^' ^'^ 

 ter conical, so that one side may be too great, and the other 

 side too little, it may be adjusted so exactly, that it may be 

 carried several times around the circle, without the errour 

 of a single second ; and it acts with so much iteadiness, 

 that it may not unaptly be considered as a wheel and pinion 

 of indefinitely high numbers. Yet, such is the imperfec- 

 tion of the edges of the circle and roller, that, when worked 

 with the greatest care, the intermediate parts, on a radius 

 of two feet, will sometimes be unequal to the value of half 

 SI minute or more. After having found the terminating 

 point of a quadrant or circle so permanent, although I was 

 not prepared to expect perfect equality throughout, yet I 

 was much mortified to find the errours so great, at least ten 

 times as much as I expected ; which fact indicated, beyond 

 a doubt, that if the roller is to be trusted at all, it must only 

 be trusted through a very short arc. Had there been any 

 B 2 thin^ 



