730 THE RAMSDEN DIVIDING ENGINE. 



Having marked the four points 0°, 30°, 60°, and 90°, the mode of pro- 

 cedure was as follows : The chord of 15° laid off backward from 90° 

 gave 750. From 75° the chord of 10° 20' was laid off forward, giving 

 85° 20', and from 90° the chord of 4° 40' laid off backward gave the 

 same point. 



85° 20'= 5,120' or 1,024 chords of 5' each, and 1,024=2'*' (2 carried to 

 the tenth power), so that by continual bisections the arcs of 5' were ac- 

 curately marked. 



In order to divide the circle beyond the 85° 20' into arcs of 5' each, 

 an arc of 40' (or eight 5' divisions) was laid oft' backwards to 84° 40', 

 thus leaving an arc of 320' or 64 arcs of 5' each between these two 

 points. These 5' arcs were laid oft' by continual bisections. Thus Bird 

 was able to check accurately the original arcs of 15°, 30°, 60°, 75°, 

 and 90°. 



ORIGIN OF THE DIVIDING ENGINE— CUTTING ENGINES FOR CLOCK 



WHEELS. 



To the clock-maker, more than any other mechanic, we are indebted 

 for the origin of the dividing engine. 



" While the art of clock-making was in its rude state the dividing of 

 a wheel into a number of parts and cutting away notches of spaces was 

 done by manual operation with a file. This was not only a tedious but 

 a very imperfect way of obtaining a desired result, since the unequal 

 lines in the size and shape of the tools prevented it from trfinsmitting 

 applied force in an equable manner. 



" To facilitate the manual operation of cutting wheels by a file the 

 sample platform was invented (described by Father Alexander in his 

 book on clock-making), which was a circular plate of brass from 10 inches 

 to a foot or more in diameter, with as many concentric circles thereon 

 as the usual number of teeth in the wheels and pinions of clockwork 

 required to be divided into corresponding parts of a circle. In the center 

 of this platform was fixed a stem or fast arbor, around which an alidade, 

 ruler, or index, with a straight edge pointing to the center, turned freely 

 into any given point of a required circle, by means of which the divisions 

 of any given circle were transferred to a wheel placed on the side stem 

 under the side index by a marking point. At length a little frame was 

 mounted on the index, which was contrived to direct and confine the 

 file in such a way as to cut the notches of a wheel placed over the in- 

 dex with less deviation from the truth than could be managed by mere 

 manual dexterity. This addition, no doubt, led to the adoption of a 

 circular file, or cutter, and of such other appendages as completed the 

 construction of the simple cutting machine."* 



It is asserted in '■'■ Etrennes Ghronornetriques^^ par M. Julian le Roy, 

 "that Dr. Hooke was the first person who contrived, about 1675, such 

 an arrangement as could merit the name of a cutting engine (machine a 



See Rees' Encyclopsedia, vol. 11 : " Gutting engines," 



