8 R. P. WILLIAMS ON 



in one plane. This is the " sine qua non" of the operation, which 

 it is the object of the constructors of such instruments to meet in 

 the most effective manner. Now a circular cutter fully meets these 

 requirements — as it can be made perfectly true, can be ground, 

 polished, and sharpened on the points, and in the position which it 

 will permanently occupy, and when made, can be submitted to a 

 rigid test in the following manner. 



Let the image of a small fixed object, reflected from the acting 

 part of the disc, which is highly polished, be observed during 

 revolution, at a moderate speed. If it has been worked to a true 

 figure, the image will appear as fixed as the object viewed, directly; 

 if, on the contrary, it be untrue, the extent of the error will be seen 

 at once, in the aberrations of the image. 



If a disc be executed so as to stand this test, then, the section 

 of its cutting edge will be represented by a right line ; that is to 

 say, its parts will lie evenly between its extremities, and it is only 

 necessary to make the object we desire to section move by 

 mechanical contrivances in a direction parallel (one plane of course 

 coinciding) with the plane of the cutter's motion, to have a 

 theoretically perfect section-cutting machine. 



I have sought to accomplish this in the machine before you, by 

 a screw underneath the plate, the circular motion of which is 

 made available by band and pulleys, for revolving the cutter, 

 which revolves in a vertical plane in the same direction as the 

 object is caused to move in, by means of the aforesaid screw. A 

 second sliding apparatus is securely screwed to the first mentioned 

 slide. This second slide is to advance the object for each succes- 

 sive section, and is furnished with a fine screw for that purpose, 

 with 100 threads to theinch. By the milled head and index, a further 

 division of a hundredth of that interval can be effected, so that the 

 finest setting possible, is the l0 ^ 00 , expressed decimally 0-0001 of 

 an inch. 



The slide to which the adjusting screw is attached, carries a 

 little block faced with ebonite, on which the head is placed for 

 sectioning. This block is capable of motion round its centre, for the 

 adjustment of the head in any vertical plane, and the frame carry- 

 ing the cutter being moveable, is set so as just to clear the cutter 

 of the ebonite, which provision also enables us to introduce cutters 

 of larger size. One turn of the traversing screw advances the 

 object through a space equal to -£$ of an inch, the cutter having 



