504 



Prof. B. Hopkinson. 



[Jan. 31, 



that the permanent extension produced on the 20 inches is negligible, 

 is fairly conclusive evidence that the theory is applicable in this case, 

 and that the material is almost perfectly elastic up to the highest 

 stress as calculated from the theory. The maximum strain at the top 

 of the wire is 2V/a, or 34-4/17 thousandths. The corresponding 

 tension is about 790 Ibs. To this must be added the 50 Ibs. steady 

 tension, making a total of 840 Ibs. as the maximum stress experienced 

 by any portion of the wire. The mean tension in the top 20 inches, 



where the extension is greatest, is {- - x 390 ) + 50, or 770 Ibs. 



\4rU,UUU / 



Now, after the completion of the experiments, the top 20 inches of 

 the wire were cut out and tested statically with a Swing's extenso- 

 meter. There was perceptible failure of elasticity at 500 Ibs., very 

 marked yielding at 700 Ibs. (which produced a permanent extension 

 of nearly 1 per cent.), and at 800 Ibs. the wire drew out very rapidly 

 and finally broke. 



With a fall of 10 feet and a steady tension (T) of 20 Ibs., the 

 calculated extension will be found to be 53 thousandths of an inch, 

 or 106 micrometer divisions. This, again, agrees very well with the 

 observed extension of 104 divisions. In this case the calculated 

 maximum tension at the top end is 1150 Ibs., and the mean tension 

 on the 20 inches about 1000 Ibs. Of this extension, however, about 

 11 per cent, is permanent, so that there is some failure of elasticity, 

 and it is improbable that the maximum stress quite reaches the calcu- 

 lated value. It is practically certain, however, that it exceeds the 

 mean stress corresponding to the elastic part of the maximum extension 

 in the top 20 inches, viz., about 900 Ibs. 



Next as regards the time for which these stresses are applied. 



The strain at the top of the wire is 2 e~v- at l yL , where t is the time which 



a 



has elapsed since the wire first arrived there. In the case of the 

 5-foot fall it will be found that the stress falls from 840 Ibs., its 

 initial and maximum value, to 500 Ibs., which may be taken as the 

 elastic limit, in about 0'8 thousandth of a second. 



These results were fully confirmed by a large number of experiments 

 in which different steady tensions were applied. The general con- 

 clusion is that in this material, which has an elastic limit of 40,000 Ibs., 

 or 17'8 tons per square inch, and breaks at 28'5 tons, a stress 

 momentarily exceeding 75,000 Ibs., or 33J tons, and exceeding the 

 static elastic limit for a time of the order of 1/1000 second, may be 

 applied without any very great failure of elasticity.* 



It may be further noted that a blow from a height of 10 feet, 



* The absolute stress is, as usual, calculated on the uncontracted area of the tebt- 

 piece. The statical breaking stress at the moment of breaking is, of course, greater 

 than this figure, but then the material is hardened by the drawing out. 



