734 THE liAMSDEN DIVIDING ENGINE. 



wlieel, the edge of it was ratclied, and the number of revolutions and 

 parts of the screw contained between the interval of the (K) degrees were 

 counted. Tlie radius was corrected in the proi)ortion of 300 revolu- 

 tions, which ought to have been in 60 degrees, to the number actually 

 found, and the radius, so corrected, was taken in a pair of beam com- 

 passes while the wheel was on the lath, one foot of the compasses was 

 put in the center and with the other a circle was described on the ring ; 

 then half the depth of the threads of the screw being taken in dividers 

 was set from this circle outwards and another circle was described, cut- 

 ting this point; a hollow was then turned on the edge of the wheel of 

 the same curvature as that of the screw at the bottom of the threads ; 

 the bottom of this hollow was turned to the same radius or distance 

 from the center of the wheel as the outward of the two circles before 

 mentioned. 



" The wheel was now taken off the lathe, the bell-metal i)iece (7>) was 

 screwed on as before directed, which after this ought not to be removed. 



"From a very exact center a circle was described on the ring C, about 

 four-tenths of an inch within where the bottom of the teeth would 

 come. This circle was divided with the greatest exactness I was capa- 

 ble of, first into 5 parts and each of these into 3. These parts were 

 then bisected 4 times, that is to say, supposing the whole circumfer- 

 ence of the wheel to contain 2,1()0 teeth, this being divided into 3 parts, 

 each of them would contain 144, and this space bisected 4 times would 

 give 72, 36^ 18, and 9; therefore each of the last divisions would con- 

 tain 9 teeth. But, as I was apprehensive some error might arise from 

 quinquesectiou and trisectiou, in order to examine the accuracy of the 

 divisions I described another circle on the ring C, one-tenth inch within 

 the former, and divided it by continual bisections, as 2,160, 1,080, 540, 

 270, 135, 67i, and 33^ ; and, as the fixed wire (to be described presently) 

 crossed both the circles, I could examine their agreement at every 135 

 revolutions (after ratching could examine it at every 33^) ; but not 

 finding any sensible difference between the two sets of divisions, I, for 

 ratching, made choice of the former; and, as the coincidence of the 

 fixed wire with an intersection could be more exactly determined than 

 with a dot or division, I therefore made use of intersections in both 

 circles before described. 



"The arms of the frame were connected b}' a thin piece of brass of 

 three-fourths of an inch broad, having a hole in the middle of four tenths 

 of an inch in diameter; across this hole a silver wire was fixed exactly 

 in a line to the center of the wheel; the coincidence of this wire with 

 the intersections was examined by a lens seven-tenths inch focus, fixed 

 in a tube which was attached to one of the arms. 



" Now a handle or winch being fixed on the end of the screw, the 

 division marked 10 on the circle was set to its index, and, by means 

 of a clamp and adjusting screw for that purpose, the intersection 

 was set exactly to coincide with the fixed wire; the screw was then 



