December 30, 1922] 



NA TURE 



875 



able for examination, it is clear that the Dehra Dun 

 value of g should be strengthened by a new direct 

 determination of the difference Kew — Dehra Dun. 



This could be made by sending the Indian pendulums 

 back to Kew for a further set of observations to be 

 made there, or, if the use of Invar pendulums is con- 

 templated, then the new set of pendulums could be 

 employed for this purpose. It is imperative that the 

 value of g at Dehra Dun should be established so 

 thoroughly as to be unimpeachable. 



G. P. Lenox-Conyngham. 



Trinity College, Cambridge, 

 November 29. 



The remarks by Mr. Oldham in Nature of November 

 18, p. 665, relating to a suggested variation in gravity, 

 are of great interest. As a result of measurements 

 of g at Melbourne in 191 3, a doubt as to the invari- 

 ability of g relative to that at Potsdam was forcibly 

 borne to mind. The report (Gravity Observations, 

 British Antarctic Expedition, 1910-1913) which 

 gives the results of the Melbourne measurements, 

 has been delayed in the press, but it is felt that there 

 is some evidence in this case of a lack of constancy 

 in the value of g relative to Potsdam. 



The problem is discussed in greater detail from 

 another point of view in the Glaciological Report 

 (Wright and Priestley), which is due to appear 

 shortly. C. S. Wright. 



Wey Lodge, Portmore Park, Weybridge, 

 November 20. 



Action of Cutting Tools. 



In the interesting letters by Mr. Mallock and Prof. 

 Coker which have recently appeared in Nature, some 

 points of importance to the elucidation of the action 

 of a tool when operating on materials have been 

 raised. 



Mr. Mallock appears to adhere to the view expressed 

 in his paper of 1881 that the action is simply a 

 phenomenon of shear. H. Tresca, however, two years 

 after Mr. Mallock's paper showed in his classical and 

 extensive " Memoire sur le rabotage des metaux " 

 (Memoires presentes par divers savants a V Academic 

 des Sciences de I'lnstitut de France. Tome 27, No. 1, 



D, as it approaches the tool begins to flow in region 

 IS, which is Tresca's zone d'activite. The flow reaches 

 a maximum in the region C from which the chip or 

 jet of metal D emerges, and Tresca in the light of the 

 results of his remarkable and historical investigations 

 on the flow and deformation of solids likens the action 

 to the flow of the metal through a tube of shape ABC 

 with its orifice open horizontally at the top part of 

 C. Since no change in the density takes place the 

 product of the co-ordinates xy (where the origin is at 

 the tool edge) of a point on any surface in B and C 

 continuous with a horizontal plane in A must be 

 constant, so that the traces of these surfaces in the 

 sides and also the free edges of B are hyperbolas. 



This zone B can be seen in some of the beautiful 

 photographs of cutting tools published by Mr. J. F. 

 Brooks (Proc. Inst. Mech. Engrs., 1905, p. 365) and 

 more especially in the last photograph of Plate 10. 

 If now vertical lines be scribed upon the sides, the 

 state of affairs during flow of a material which does 

 not rupture for large body-shifts, such as lead, is 

 represented by Tresca in Fig. 2. 



that the phenomenon was primarily one of 

 plastic flow. The periodic rupture of the chip which 

 takes place is subsequent to the plastic flow stage 

 and depends upon the nature of the material being 

 operated upon, the angle the tool face presents to 

 the advancing stream of material, and the velocity 

 with which the material moves relative to the tool. 



This stage of the action is complex and does not 

 appear to be understood fully. The plastic flow 

 stage, however, is comparatively simple. 



In the diagram (Fig. 1) suppose that the tool T 

 presents a plane face square to the advancing material. 

 The portion A, which will ultimately form the chip 



NO. 2774, VOL. I iol 



Here the maximum slide velocity is at the edge of 

 the tool and in the horizontal plane through the edge. 

 But one of the two important principles enunciated 

 by Tresca is that during flow the maximum shear 

 and maximum slide velocity are co-directional. We 

 should therefore expect the material to rupture along 

 this horizontal plane, and I think this can clearly be 

 seen in Plate 1 1 of Brooks's photographs of the tool in 

 action on mild steel. 



Turning now to Prof. J. T. Nicolson's and Dempster 

 Smith's experiments (Engineer, 1905, p. 358) and their 

 diagram of the formation of a chip (Fig. 9), it may be 

 seen that though the diagram is complicated by 

 rupture phenomena and by the fact that the tool is 

 acting on a wedge-shaped part of the forging, Tresca's 

 representation of the plastic phenomena is well sub- 

 stantiated and the maximum shear is clearly seen in 

 the initial stages. 



The start of rupture along the horizontal plane is 

 also clearly shown by Frederick Tavlor in his presi- 

 dential address before the American Society of 

 Mechanical Engineers in 1906 (vol. 28), which is a 

 monumental work on " The Art of Cutting Metals." 



The same views are expressed by C. Codron in his 

 extensive series of " Experiences sur le travail des 

 machines-outils pour les metaux," published in the 



Bulletin de la Societe d' Encouragement pour I' Industrie 

 Nationale," 1 903-1 905. 



The second important principle enunciated by 

 Tresca, namely, the maximum shear across any face of 

 a small right six face is a constant = K (Tresca's plastic 

 modulus), together with the one already mentioned, 

 enabled Saint Venant to develop the general equa- 

 tions of plastico-dynamics. If the mathematicians 



