S?3 On the improved Dividing Engine. 



one half of the teeth to different situations, while under the 

 operation of the cutter, and finally producing full sound and 

 complete teeth all round, is a self-evident proof of its supe- 

 rior accuracy. This I have done, after shifting it to oppo- 

 site quarters and eighths, perhaps not less than 30 limes, 

 while under the cutter, and finally the teeth are complete. 



The last time that I shifted it was the 10th of last June, 

 which was one-eighth. I then cut a line on the one side, 

 half on the solid wheel and another on the ring, with the 

 dividing point, which is fixed to have no other motion but 

 to and from the centre of the wheel. I then turned the screw 

 720 times, which is one half of the number of teeth in the 

 wheel. I then cut a similar line with the same fixed point, 

 and then withdrew the 24 bending screws, and shifted the 

 rinf half round. Of course the lines now stand in an op- 

 posite situation to what they were when cut, yet they are 

 good coincidents. 



The anonymous critic, above alluded to, may, when- 

 ever he pleases, satisl'y himself as to the accuracy of the 

 coincidence of the lines, by a personal inspection of the 

 engine — which will, I think, put an end to all his suppo- 

 sititious cases respecting the shifting of the ring having a 

 tendency to diminish the teeth. He calls me an obscure 

 individual : the charge is certainly true; and had he added, 

 that mv obscurity is the cause that my invention has not 

 been more noticed, it would have been equally true. But 

 of this I am confident, that however obscure I may re- 

 main, my invention will continue to live as long as mathe- 

 matical dividing engines continue to be used ; and little as 

 he yet knows of the value of my discovery, I have no hesi- 

 tation in asserting mv opinion, that there never was (nor 

 ever will be) a dividing engine cut on the single edge, in 

 the old way, but would, could the teeth be reversed as in 

 my invention, exhibit considerable errors. — Let any person 

 but make the experinjent, and he will be compelled to ac- 

 knowledge the truth of my statement. 



Those w ho have seen circles divided by my engine, and 

 who aic competent judges, all approve of their accuracy. 

 The author oi:' the observations which have appeared in Dr. 

 Rees's Cyclopedia states, that he has seen one of my im- 

 proved refioc'iing circles well divided. I have received 

 testimonies to the same effect from a Captain M'Lennan, 

 from Souih America, and from Lieutenant l^hij^ps, of His 

 Majesty's ship Bellerophon ; and at this moment I am busy 

 with another reflecting circle, which 1 hope will be divided 



soon. 



