476 



PROFESSOE KNOTT ON THE STRAINS PRODUCED IN IRON, 



We may take, for rough estimation, E = 2x 10 12 and n='8 x 10 12 in both metals,* 

 giving the following values in kilogrammes per square centimetre for the stresses 

 corresponding to the mean strains in the foregoing table, if we consider these strains 

 to be purely elastic. 



Principal Mean Stresses in Iron and Nickel Tubes B V. in Kgms. ter sq. cm. 





Field 



= 190. 



Field 



= 310. 



Field 



= 500. 





Iron. 



Nickel. 



Iron. 



Nickel. 



Iron. 



Nickel. 



-20 



+ 7 

 + 13 



p 



Q 



R 



+ 1-8 

 -TO 

 - -6 



-13 



+ 4 

 + 9 



+ •08 

 -• 1 

 + • 3 



-18 

 + 6 

 + 12 



-1-6 



+ -8 

 + 1-2 



From these numbers we may calculate for each state the quantity 



| (PA + Qm + Ri>) = \n {S 2 + 2 (X 2 + M 2 + v 2 )} 



which measures the potential energy stored up in unit volume of an elastic substance 

 strained to the extent and in the manner indicated by the ratios A, m, v. We find, then, 

 for the potential energy of strain in the three fields named, the quantities 



5 "3, 0*2, and 6*1 ergs in iron. 

 327 , 595 , ,, 766 „ „ nickel. 



These are calculated by taking into account only the final values. But there is a 

 fundamental difference between the manner in which the magnetic force of, say, 310 

 carries the iron through its intermediate conditions of strain, and the manner in which 

 an application of surface tractions effects the same succession of states. At every 

 stage in the process, whether the strain coefficients be increasing or decreasing, the 

 magnetizing force is producing a change which we must suppose to be always resisted 

 by the elastic forces — that is to say, between the field corresponding to the maximum 

 elongation in iron and the zero elongation, there is no real assisting of the forces which 

 arc producing the strain. We have, in short, no warrant in assuming a giving back of 

 energy by the strained metal during this stage, which, in the purely elastic problem, 

 answers to a condition of work done by the substance as it recovers. Since the clastic 

 constants are not appreciably changed by magnetization, we may plausibly enough 

 assume the work done during the second half of the positive elongation stage to be 

 equal to the work done during the first half. Consequently, instead of 0"2 erg being 

 the amount of work done against the elastic forces in the Field 310, we should take 

 1 0'6 + 0*2 ( = 10*8) as in all probability the better value. 



* Mr Mitchell, a student in the Physical Laboratory, Edinburgh University, determined for me the value of 

 Young's modulus by flexure experiments on the nickel sheets from which the coiled Tubes C 2 C 3 had been formed. 

 The values found were respectively i'i x lO la and 2'5 X 10 12 in C.G.S. units. 



