THE RAMSDEN DIVIDING ENGINE. 733 



tionand description of his engine for dividing mathematical iustriiments 

 (accompanied with proper drawings) and of the manner of usiug the 

 same, and also of the engine by which the endless screw, being a prin- 

 cipal part of the said dividing engine, was made, and upon agreeing 

 and entering into articles with them for assigning over the right and 

 property of the said engine to them for the use of the public, and 

 engaging himself to give to the said commissioners and such other per- 

 sons, being mathematical instrument makers, not exceeding ten, as 

 shall be appointed by them during the space of 2 years, from the 28th of 

 October, 1775, to the 28th of October, 1777, such instruction and informa- 

 tion with regard to the making and using of the said engine, as may be 

 fully sufficient to enable any intelligent workman to construct and use 

 other engines of the same kind, and also binding himself to divide all 

 octants and sextants by the said engine which shall be brought to him 

 by any mathematical instrument makers for that purpose at the rate of 

 3 shillings for each octant and at the rate of 6 shillings for each brass 

 sextant, with nonius divisions to half minutes, for so long a time as the 

 said commissioners shall think proper to permit the said engine to re- 

 main in his possession. Of which sum of £615 paid to the said Mr. 

 Ramsden, £300 was given him as a reward for the improvement made 

 by him in the art of dividing instruments by means of the said dividing 

 engine and for discovering the same, and the remaing£3i5 in considera- 

 tion of his making over the property in the said engine to the commis- 

 sioners of longitude, for the use of the public, and for the other consid- 

 erations before mentioned. 



" In order to render this instrument more extensively useful, the com- 

 missioners of longitude ordered the written explanations, with drawings, 

 of the dividing engine to be prepared for publication, and it is now pub- 

 lished accordingly." 



Plate II is from a lithograph in Ramsden's publication, and illustrates 

 the machine as originally constructed. 



Mr. Ramsden states in his pamphlet that " the teeth on the circum- 

 ference of the wheel were cut by the following method : 



"Having considered what number of teeth on the circumference 

 would be the most convenient, which in this engine is 2,160, or 360 multi- 

 plied by 6, I made two screws of the same dimensions of tempered steel, 

 in the manner hereafter described, the interval between the threads being 

 such as I knew by calculation would come within the limits of what 

 might be turned off the circumference of the wheel. One of these screws, 

 which was intended for ratching or cutting the teeth, was notched 

 across the threads, so that the screw, when pressed against the edge of 

 the wheel and turned round, cut in the manner of a saw. Then, having 

 a segment of a circle a little greater than 60 degrees, of about the same 

 radius with the wheel, and the circumference made true, from a very 

 fine center, I described an arch near the edge, and set off the chord of 

 60 degrees on this arch. This segment was put in the place of the 



