1880.] Mr. R. C. Rowe. Memoir on Abel's Theorem. 



bib 



We may, therefore, expect that whenever the viscous effect is great 

 relatively to the hardening effect, a wire will show to greater advan- 

 tage as regards its breaking strength, and to less advantage as 

 regards its elongation, when tested quickly than when tested slowly. 

 This is probably the case with tin, copper, and other metals in which 

 the viscous effect is great, [I have not tested tin wires, but copper 

 and also brass wires show a perceptible hardening effect under con- 

 stant stress, much less, however, than that shown by soft iron.] 



When, on the contrary, the hardening effect is great relatively to 

 the viscous effect, a wire will show to greater advantage as regards 

 breaking strength, and to less advantage as regards elongation the 

 more slowly it is tested. This is the case with soft iron, at least in 

 circumstances like those of the above experiments. 



The experiments show that even such variations in the rate of 

 applying stress, or such intermissions of stress as are liable to occur 

 in practical testing, are sufficient to affect most materially the results 

 of the test. 



A batch of specimens cut from the same coil, and similarly treated 

 in every way, give very closely accordant results when tested with the 

 same rate of increment of stress. The examples quoted above are all 

 taken from the same batch of specimens. One peculiarity is common 

 to them and to all the other specimens in the same batch, namely, the 

 double curvature, which appears in the diagrams soon after the limit 

 of elasticity has been passed. On the other hand, other specimens cat 

 from the same bundle of wire, but annealed at another time, do not 

 show this peculiarity. 



The examples given may fairly be taken as representative of a large 

 number of tests. I am now extending the experiments ; but it appeared 

 to me that the results already arrived at were of sufficient interest to 

 excuse their presentation in this somewhat crude form. 



VIII. "Memoir on Abels Theorem." By R. C. Rowe, Fellow of 

 Trinity College, Cambridge. Communicated by A. CAYLEY, 

 LL.D.j F.R.S., Sadlerian Professor of Pure Mathematics in 

 the University of Cambridge. Received May 27, 1880. 



(Abstract.) 



The object of this paper is to present in a shortened and simplified 

 form the processes and the results of Abel's famous memoir, " Sur 

 une propriete generale d'une classe tres-etendue de fonctions trans- 

 cendantes," composed and offered to the French Institute in 1826, 

 but first published in the " Memoires des Savans Etrangers " for 

 1841. 



VOL. XXX. 2 



