244 Mr. A. Mallock. The Physical [June 6, 



Both torsional measures give n greater for the soft grey than for 

 the red, whereas by the measures of Young's modulus, which should 

 be very nearly equal to 3n, n is considerably greater for the red. 



It is possible that there may be a kind of " grain " in the sheets of 

 the soft grey india-rubber, and that as the distortion produced by the 

 extension in Experiments (1) and (2) is not in the same direction as 

 that due to the torsion in Experiments (3), (4), the origin of the 

 difference is to be looked for in this quarter. 



(5.) Young's Modulus for Large Extensions. 



Diagram III gives the results of these experiments. They were 

 made with the apparatus shown in fig. 1. The actual measures were 

 made on strips of (§-) 2 inch section, which were cut from the larger 

 pieces in a planing machine by a sharp thin knife, wetted with dilute 

 caustic soda. The sectional area of the strips so cut was exceedingly 

 uniform, and its smallness was convenient, as it allowed of moderate 

 forces being used to produce the required strains, which were increased 

 until the breaking strain was reached. 



In the diagram the results are reduced to what they would have 

 been had the piece of india-rubber operated upon been a cube of one 

 inch when unstrained. 



The ordinates of the curves A, B, B', C, C, are the lengths which 

 such cubes of soft grey, red, and hard grey india-rubber would respec- 

 tively assume when stretched by forces represented by the abscissae. 

 In the curves B, 0, the readings were taken as rapidly as possible, 

 while in B', 0', an interval of two minutes was allowed between each 

 successive addition to the strain. 



There were from thirty to fifty observations made for each curve. 

 In the case of the soft grey, it did not seem to make much difference 

 whether the readings were taken quickly or otherwise. 



Let x and I be the strained and natural lengths of the india-rubber, 

 and y the stretching force, then q = ldy/s f dx, and if the material is 

 incompressible, q = I'dy/sdx. 



By this equation the curves E, F, Gr were deduced from A, B, C, 

 to show the variation of q with the extension. It is worth while to 

 observe that since if q remain constant for all extensions, 



r ?*A 

 1 - P^-T' 



so that with q constant, if a stretching force be applied equal per unit 

 area to Young's modulus, the extension will be infinite. 



