3 77 
1907-8.] On the Cohesion of Steel, and Yield Points. 
then the normal stress on the surface of slipping at the instant when 
yielding begins must also be the same for each, since this is 1/ft times the 
limiting friction. 
Let the value of the normal stress at the moment when slipping 
commences be n. 
For tension, the surface of slipping is inclined to the axis of the bar at 
an angle (45° + 0/2), and the normal stress on this surface at the yield 
point is 
n = t . sin 2 (45° + 0/2) = t/2 . (1 + sin 0). 
For compression, the surface of slipping is inclined at an angle (45° — 0/2), 
and the normal stress on this surface at the yield point is 
n = c . sin 2 (45° - 0/2) = c/ 2.(1- sin 0). 
Hence tj 2.(1+ sin 0) = c/2 . (1 - sin 0). 
And 
t 1 — sin 0 
c 1 + sin 0 
Or, since tan 0 = ft , sin 0 = — JL=- . 
J i+A 2 
And* — ■= \/l + f^ 2 — ft # 
G + /X 2 + ft 
Since 0 is a small angle, sin 0 = tan 0 nearly, and the result may he 
simplified to 
t 1 — ft 
C 1 + ft 
As mentioned above, the value of ft for mild steel is +176. The corre- 
sponding ratio t/c is 0‘705, or, if the approximate expression be used, +701. 
Some measurements were taken on six pieces cut from a j-inch 
round bar of mild steel. Three of the pieces gave a yield point in tension 
of 18 ‘5 tons per square inch, and the other three a yield point in com- 
pression of 19 '9 tons per square inch. The values corresponding with these 
figures are 
t/c = 0*93 
ft = 0’036 
0 = 2° 4' 
a = 46°, and /3 = 44°, approximately, 
which do not accord well with those just deduced. 
* Since the above was written, the author has found that the same result has been 
obtained by Mesnager, Comptes Rendus, vol. cxxvi., p. 515. 
