436 EEPOKT--1891. 



of the ductility of the material. The term " modulus of elas- 

 ticity " is used to denote the result found by multiplying the 

 stress per square inch by the original length of the specimen, 

 and dividing by the elongation. Thus, we have seen that a 

 stress of 1 ton per square inch will produce an elongation of 

 T¥ooo P^^^ ^^ ^^^6 length of a piece of iron, or for a length of 

 lOin. y-gLj^in.: this gives the modulus of elasticity as 26,880,0001b. 

 per square inch. The modulus of elasticity may also be defined 

 as the ideal stress which would be capable of stretching a per- 

 fectly elastic bar to double its length ; it may be calculated 



WL 



from the following formula : E = —^^-, where E = the modulus 



of elasticity, W = the load producing elongation /, k ~ area in 

 square inches, L = original length of specimen. 



The modulus of elasticity is an important factor in all 

 calculations where the stress is determined from the strain, 

 as, for example, in the deflection of beams ; and it should be 

 noted that an error in measurement of the elongation of the 

 specimen of YQi-ooin., with a load gradually increasing up to 10 

 tons per square inch, would mean an error of 2 per cent, in the 

 modulus of elasticity ; and, in trying to determine the exten- 

 sions from ton to ton, an error of j-yyi^oin. would mean an 

 error of 20 per cent, in the extension per ton. It is therefore 

 evident that very delicate instruments are necessary in order to 

 measure these minute elongations. Several ingenious pieces of 

 apparatus have been devised from time to time, among the best 

 of which are those used by Professors Unwin and Kennedy. 



Professor Kennedy's apparatus consists of a light lever mul- 

 tiplying the elongations of the specimen from a hundred to 

 two hundred times, according to the degree of accuracy desired. 

 These extensions are measured between two small holes in the 

 test-piece, which are generally lOin. apart. Two steel points- 

 fit into these holes, one of which is fixed, and the other mov- 

 able by the stretching of the specimen. The whole apparatus 

 is slung on the test-piece, and is totally unaffected by its mo- 

 tions as a whole, and, of course, by any change of form in the 

 frame of the machine. The instrument can be easily calibrated 

 from time to time by means of Vernier callipers. This appa- 

 ratus has been in use for the last five years at the University 

 of Sydney. Professor Unwin uses a screw^ micrometer exten- 

 someter, also a roller and mirror extensometer ; while Professor 

 Bauschinger uses still more delicate appliances. 



The foregoing considerations show that delicate instruments 

 are necessary in order to determine accurately the elastic limit 

 and modulus of elasticity ; but other difiiculties exist, which will 

 now be considered more closely. The method described for 

 determining the elastic limit is that usually adopted in the 



