740 Prof. E. G. Coker on the J 



Or, geometrically, 



cos 7 -cos (ft cos t|t _ XW _ E Wi _ EXx X t Wi 

 ^ 6) sin </> sin^r ~ AY * AE ~ AE + AE 



= A0Aa|t -f k 2 sin (/> sin -^ cos 7, 



. Ay-Afoty _ X1W1 _ DW _ DX XW 



( ^ /c 2 sin sin yfr ~ AW/ ~ AD ~ AD + AD 



= cos <ft cos -^ 4- sin <j> sin i^Ay, 



equivalent to (11) and (12) above. 



So also the formula for sin y=sn w can be interpreted. 



LXXXII. The Optical Determination of Stress. By E. G. 

 Coker, M.A., JJ.Sc, Professor of Mechanical Engineering, 

 ("il;i and Guilds of London Technical College, Finsbury*. 



THE principal advances in our experimental knowledge 

 of the strength and properties of materials have been 

 made by the use of mechanical apparatus for applying stress 

 and measuring strain, and instruments of this class are now 

 in general use possessing a sufficient degree of accuracy for 

 the most refined measurements, but whatever applications 

 purely mechanical methods may have, they possess a common 

 characteristic feature that measurements must be taken over 

 a definite length, area, or volume maintained in a standard 

 condition throughout in order that the state of stress or strain 

 may be referred to some standard measure possessed by the 

 instrument, or by which it is calibrated. Whatever the 

 arrangement may be, it is not in general possible to measure 

 the stress or strain at a point, if the body is subjected to 

 stress varying from point to point. 



This defect in purely mechanical devices is one which from 

 the nature of the case is hardly likely to be overcome entirely, 

 yet in the great majority of the problems which arise in 

 practice the stresses change very rapidly from point to 

 point, and experimental information, if it exists, has almost 

 invariably been obtained by using mechanical apparatus 

 incapable of determining the stress at a point. Mathematical 

 researches of the state of stress and strain in bodies give 

 exact solutions of a variety of complicated problems ; but 

 some of the simplest forms of practical construction offer 

 problems of the greatest difficulty, as for example the deter- 

 mination of the stresses in hooks, chain links, and rivetted 



* Communicated by the Author: read in abstract at the British 

 Association, Sheffield. 



