L891.] 



Young's Modulus for Crystals, 



385 



is a constant for each beam, and R/w is the inclination of the 

 straight line passing through the plotted observations to the axis 



Hence putting 



, 



A for -J , 

 Sr 



B for 



-- , , 

 ot 3 



and 



C f or W , 



n 



Log q = log A + log B + log C. 

 The numerical values of quantities involved in A were as follows : 



Focal length of collimator, / = 8'87 inches. 

 Length between knife-edges, K 1} K 2 , I = 0'3422 inch. 

 Distance between division of scale 8 = O'Ol. 

 Distance between knife-edges K 4 , K 5 = I/O. 



The values employed for & and t varied between O'l and O'Ol inch, 

 id for W from 0'02 to 0*25 pound. The chief and indeed the only 

 jnsiderable source of error in these experiments is in the measure- 

 lent of t. The measures were made with a screw micrometer 

 ling to O'OOOl by estimation. 



The average value of t was between 0'03 and 0'04, so that the 

 leasurement was probably accurate to something like 1 in 400. 

 Eence, there may be an error in t 3 approaching 1 per cent. 



In the case of crystalline substances, beams cut from the same 

 leighbourhood of the same crystals exhibit a constancy, in the results 

 obtained from them, of this order, but in passing to other specimens 

 lore difference was observed. 



In many substances, and notably in the case of zinc, lead, and white 



irble, it was found that the full deflection due to a given load was 



lot reached until a considerable time had elapsed, and experiments 



nth such substances would of course lead to different values for 



foung's modulus, according as the observations were made in rapid 



iccession or slowly. 



The behaviour of zinc in this respect was so marked, that a 

 sparate set of observations were made with that material, the results 

 )f which are shown in diagrams (10) and (11), pp. 394-395. 



It will be seen on examining these diagrams that, starting with a 



2shly annealed piece of rolled zinc (and similar results were ob- 



lined from a beam cut from a large crystal of cast zinc), that, on the 



irst application of the force, the bending immediately produced con- 



inues to increase for many minutes, and that, when the load is 



amoved, the beam does not recover itself all at once, and also that 



permanent set has taken place. 



On the second application of the force, however, if the force is not 

 iter than that first applied, the behaviour of the zinc is quite 



ferent. It now very rapidly assumes its maximum deflection and 



