132 



Mr. A. Mallock. 



[Dec. 8 y 



The advance of the tool violently distorts the material in its neigh- 

 bourhood, and presently along the line ec the distortion becomes too 

 great for the substance to preserve its continuity (Note 2), the lamina 

 ECec then begins to slide on ec, and its base Ee to move up the 

 face of the tool, while the point of the tool is repeating the distortion 

 and separation on fresh material ahead. 



This in all the cases I have examined is the manner in which all 

 tools, except those with very acute angles, act. 



The curvature of shavings appears to be due to the crushing of the 

 base of the lamina? while passing over the face of the tool, thus 

 making them thicker at that end than at the outer surface. 



The effect of the friction between the laminae and the tool has the 

 opposite tendency of thinning out the ends of the laminae and preventing 

 the curvature, so that when from want of lubrication or the nature 

 of the material the friction becomes excessive, the shavings are 

 nearly straight. 



The shaving is generally shorter than the path of the tool, which 

 shows that BED is less than 45°. 



I will now attempt to take account of the forces which are brought 

 into play by the action of the tool. 



These are due to (1) elastic distortion, (2) elastic bending, (3) per- 

 manent distortion, (4) permanent bending, (5) internal friction, i.e., 

 the friction of the laminae sliding over one another, (6) the friction of 

 the material on the tool, and (7) if the tool is not considered as being 

 perfectly sharp, the radius of curvature of the edge will appear in a 

 term giving the limit to the rate of distortion in its neighbourhood. 



If the tool is perfectly sharp the rate of distortion at the edge is in- 

 finite, and the material at the edge can offer no resistance to its pro- 

 gress unless capable of infinite distortion without rupture. 



This is easily seen to be the case by the following considerations : — 



Fig. 10. 



a B t 



I) 



L 



Let ABCD (fig. 10) be the section of a parallelopiped of any mate- 

 rial, and let it be distorted as shown by the dotted lines until rupture 

 takes place. The work expended in bringing it to its distorted state 

 depends on Bb, i.e., the distance AD must be moved before the limit of 

 distortion is reached, and this is simply proportional to BD, the 



