oii 
F(t) = F(1 -=) H(t) - F(l -=) H(t - @) (I-26) 
Since this consideration arises at values of 9 lower than those 
normally encountered in the use of ball crusher gauges, the solution will 
not be carried out at this time. 
A generalized plot of ¥ and wt, /n vs. @ is given in Fig. I-4. Plots 
of ¥ and t, vse © for 5/32 in. and 3/8 in. balls (used under water) are given 
in Figs. I-5 and I-6. 
7. Exponential Decay: F 
ae F(t) = Fe7t/? H(t) _N¥/e 
(0) 6 —— >t 
Substituting into Eq. (I-5): 
-t/8 
D2 + w M (Dy + 40) (Dy - 4) (Dy + =) ™ 
P - * 
(D, + 1a) (~210) (L -io) (D,- 1) (240) (2 + io) 
(D, + 3) (lo - rs oo. io) 
er iot E * to | iat 2 3 10 | .-t/0 
8 (°) 
pe ts = H(t) 
1 2 ‘i 1 2 ; 1 2 ; 
Foss hese epee | (oe) Ente 
M F aes (cit _ griot) _ - (eiwt 4 g-iot) 4 | H(t) 
ule 4 =| 2109 
-102- 
