Downloaded from MARCH 1921. CONTACT PRESSURES AND STRESSES. 367The stress function x = c . r 6 sin 6 is a solution of the general This is substantially found to be the case. equation ' = o (1) for plane stress, and from it we obtain : rl 6 . (a) at The University of Auckland Library on June 5, 2016 pme.sagepub.com Downloaded from bfARCH 1091. CONTACT PRESSURE8 AND STRE8SES. 369 rr = a p 1. = a constant = c,. r Ro Downloaded from P m = o , S r 8 = o and 388 = -2 c x = a constant of value sayp.Also, as can be easily verified, there is no stress over the rest Hence the stress function of the boundary, while at infinity all stress vanishes. (7)corresponds to the case of a normal pressure uniformly applied to a limited portion of the plane boundary of a semi-infinite plate.The stress at any point C having co-ordinates T~, el, r,, O, , with reference to the origins A, B, is obtainable by integrating the effect 'of all the elemental loads on the boundary A B. At any point D the load intensityp on an element dz of the boundary gives a radial stress at C of where r,e are the co-ordinates of C with reference to D as origin.As will appear immediately, it is convenient to reckon the stress produced at C with reference to an origin D (r, +) having a vector C D bisecting the angle A C B.The normal, tangential, and shear stresses at C, due t o the distributed load pax, are then

Ilztroductiim.-The mode of action of cutting tools has been the subject of much investigation on account of its great importance t o mechanical engineers, who carry out a very large proportion of their work by aid of machinery designed to provide the most efficient action of various tools for shaping metals and other materials, but so far it has apparently not been studied by photoelastic methods. As a preliminary to the description of some experiments which have been made by aid of polarized light at the suggestion of the Cutting Tools Research Committee, it may be of interest to recall, very briefly, the principles upon which such experiments are based. Nearly all transparent bodies when loaded become doubly refractive, and a ray of ordinary light passing through the material in a state of stress is subjected to a selective retardation whereby its transverse vibrations lag one behind the other. No effect is visible to the eye, since ordinarylight consists of such a complex system of transverse vibrations that the eye is unable to detect what is going on, but if ordinary light is, as it were, strained through some kind of sieve whereby a homogeneous character of a particular kind is imparted to it, the effect of stress in the material becomes apparent. The most convenient apparatus for obtaining the homogeneous light mentioned above is a crystal of transparent calcium carbonate, cut in a special way, invented by an Edinburgh r h I E I.MEcH.E.] at UNIV NEBRASKA LIBRARIES on June 4, 2016 pme.sagepub.com Downloaded from ACTION OF CUTTING TOOLS. APRIL 1922. ACTION OF CUTTING TOOLS. APRIL 1922. * Contribution B l'Btu.de de la Deformation hwtique des Solides. A. Mesnager. Annales des Ponts et Chaussbes, 1901. DISCUSSION ON APML 1923. * '' Photo-Elastic Measurements of the Stress Distribution in Tension Members used in the Testing of Materials." Appendix, Section A.

The physical characteristics of transparent bodies capable of resisting stress have been the subject of much investigation, and in particular the properties of various glasses have been studied with much thoroughness since these latter have an extensive use both for commercial and scientific purposes. In recent years many new forms of optical materials have found an industrial use, and especially nitro-cellulose compounds, which are valuable in cases where glass is not suitable. In recent years many new forms of optical materials have found an industrial use and especially nitro-cellulose compounds, which are valuable in cases where glass is not suitable.