Page 269 - Introduction to Mineral Exploration

252 M.K.G. WHATELEY & B. SCOTT

95% probability. The sphalerite is liberated This is the sample weight to constrain the
from its gangue at a particle size of 150 µm: the fundamental variance. For the total variance
−3
gangue density is 2.7 kg m . Sampling is under- a sample weight of twice this quantity is
2
2
taken during crushing when the top particle required [i.e. S (TE) ≤ 2S (FE)], or 51 kg.
size (d) is 25 mm. To illustrate the benefits of sampling
Critical content (a t ) = 7% zinc = 10.5% sphal- material when it is in its most finely divided
erite = 0.105 as a fraction. state, assume that the same limit (±0.2% zinc)
Constitution factor (c) as in previous example is required when sampling aftergrinding to
= 33. its liberation size when d is 0.015 cm and β
Liberation factor (β) = (0.015/2.5)0.5 = equals 1.0:
(0.006)0.5 = 0.077.
Heterogeneity constant (C) = cβfg = 33 × 0.077 × C = 33 × 1 × 0.5 × 0.25 = 4.13
0.5 × 0.25 = 0.32. 3 3 −6
3
Top size (d) = (2.5) =15.62. d = (0.015) = 3.3 × 10
3
3
−6
Cd = 0.32 × 15.62 = 5.0. Cd = 13.63 × 10 and
Fundamental variance (FE).
02.% M == == = 6.9 grams, say 7 g
Relative standard deviation 2S = . There-
7
fore S = 0.014.
.
Cd 3 50
Mass of sample = = = 25.5 kg.
0 014)
(
2
SFE) (. 2