396 REPORTS ON THE STATE OF SCIENCE, ETC. 
found under torsional alternating cycles, and then the full alternating torque was 
applied for a large number of cycles. The elastic limits of the other two were not 
found; alternating torque of one constant range only was applied and continued 
until the test was completed. In all four tests a constant range of strain was attained 
long before the cycles of torque were discontinued or long before the specimen broke, 
as the case might be. It will be observed that one hollow and one solid specimen 
fractured, and that the limiting fatigue range must presumably lie between the real 
stress of the unbroken and the broken specimens. 
What will be called, provisionally, the ‘real’ stress at the skin of the hollow 
specimens was calculated by a method similar to that employed (see p. 389) for the 
other hollow specimens (see Appendix I.), the only difference between the methods 
being that various values of the ratio rom (p. 392) were now taken, and a position 
of the RS line (see fig. 19) was found by equating the range of resisting moment, for 
each value of a ; to the range of the applied torque. Any one of the RS lines so found 
satisfies the essential condition of equality of range of applied torque and range of 
resisting moment; but, of course, the values of (a) the ultimate range of ‘ real’ 
stress and (b) the range of elastic limit stress at the internal surface of elastic break- 
, 
down vary widely according to the value of ues The values of (a) and (b) are given 
C 
respectively in Tables IV. and V. An examination of these tables leads to the con- 
clusion that the most probable value of - for this steel is about 0-30, because this 
value of - makes the ultimate ranges of stress of the fractured hollow and solid 
specimens agree, and it makes the highest ranges of the unbroken hollow and solid 
specimens also very close (Table IV.). This value of = also (see Table V.) brings 
the stresses in the solid specimens at the locality R, where the modulus changes, 
approximately to the elastic limit 7-0 tons per sq. in. observed during two of the 
tests. Thus the stress at R for the broken solid specimen appears as +7-25 tons 
per sq. in., and the stress at R for the unbroken solid one as -- 6-82 tons per sq. in. 
C ; : ; : 2 
Thus the value € =0-30 brings the tests of hollow and solid specimens into substantial 
correspondence with each other. Table IV. gives the comparison of the ultimate 
ranges of stress for the torsion specimens for various values of = , and Table V. gives 
the stresses at the point R for these various values of = It appears that the value 
0-18 for 2 previously obtained is the most probable value a for the steel of 0-12 per 
/ 
cent. carbon. It will be observed that not only does the value C7 0-18 make the ulti- 
mate and elastic limit ranges of stress very approximately the same for A7 as for 
the hollow specimens of the same material, but that the curves of distribution of stress 
at the ultimate range for A7 and the hollow specimens, while not in exact coincidence, 
are in fair agreement. 
The author thinks these results confirm in a rather striking manner the validity 
of the assumption provisionally adopted as to the distribution of stress in a round 
bar under alternating torsion when the range of strain has become constant. 
It is of some interest to compare for the three solid specimens the ratio of the 
ultimate stresses (a) calculated on the author’s assumption of stress distribution 
and (6) calculated on the assumption of perfect elasticity. 
C’ stress (a) 6:14 
A7. 0-12 t. C broken= =0- eben pe adie) — 7: 
per cen roken 0-18 streas (6) 7-49 = 9 83 
C’ 8-67 
0-1. 0:35 t. C unbroken = = 0- = =0: 
per cent. C unbroken 0-30 “0 10-0> 0° 865 
y C’ 9-09 
1-2. 0:3 t. © br kk fan 0s —) ——— — ie 
5 per cen roken 0-30 * 10-5 =9 865 
7 
