598 Professor Ernest G. Coker [Feb. 18, 



more even distribution in the longitudinal section. The contour is 

 apparently not entirely satisfactory, as the head merges into the main 

 body in a somewhat abrupt manner, and suggests that a more satis- 

 factory solution would be obtained by more gradual transition curves 

 following one of the systems of curves of principal stress in a member 

 of rectangular form, and of considerable width. If this is carried 

 out as shown in the next model, you will, I think, observe that the 

 effect of this change is a beneficial one, and the lines of stress are 

 less curved, while there are no portions of the head which may be 

 looked upon as of doubtful utility. 



Economy in the use and distribution of material to resist stresses 

 in a structure, is clearly a most desirable end, and in perhaps no case 

 is this more necessary than in some of the latest developments of 

 modern engineering — the airship and the aeroplane — where weight 

 is a most important factor ; and tentative experiments upon models 

 of links used in these structures show that some help in the solution 

 of these new problems may possibly be afforded by optical investi- 

 gations. 



OVERSTRESSED MATERIALS. 



The behaviour of materials which are not stressed beyond the 

 elastic limit, suggests inquiry as to the nature of the stress distribu- 

 tion in a body which is overstressed at certain points. When this 

 occurs in a transparent material, the permanent strain produces such 

 a change in the structure that we can no longer depend upon the 

 laws of the optical behaviour of elastic material, but some further 

 knowledge may be gained if we take into account the stress strain 

 relations of overstressed material. In this respect we are fortunate 

 in having compounds of nitro -cellulose which show a marked 

 similarity to ductile materials like wrought-iron and structural steel ; 

 in fact, the stress strain properties are very similar to those of ductile 

 metals, and it seems a natural inference that the stress distributions 

 under similar conditions will correspond, although the metal is a 

 crystalline solid while the optical material is of a colloidal character. 



If, therefore, the stress distribution is determined so far as the 

 optical behaviour can be traced, the remaining effect may in many 

 cases be determined approximately from the stress strain relations. 



Usually the most convenient method of examining this latter is 

 by the measurement of the lateral changes, and the case of a tension 

 member with a central hole has been "examined by Mr. Y. Satake 

 and myself in the laboratory at University College. At the central 

 minimum section, for example, the sum of all the stresses across it 

 must equal the applied load both within and beyond the yield point of 

 the material, and when these stresses are determined, it is found that 

 the distribution is such that when the yield point is reached at the 



