vhere "d" {8 the particle diameter in aicrans and “t® is the time at wrick
it arrives in hours. In the ever’ thet partigles arrive from two heichts
as “indtcated for paint "PY in Pig, 1, one merely adds the two indices
arithmetically,. We have felt, in view of the erudeness of theese arsiments,
that very little wuld be achieved by keeping the power of "t* at «2.2 did
have used -2.0 instead.
One will note that in this form the dose index does act yet contain
Stoke's law but states meraly that pertieles of sise "<4" arrive at tine
"ee, The use of Stoke's Law and some of the other eseumptions permits
the dose index to be written in a wide variety of alternate forms, Stoke's
law states that the terminal rate of fall is proportional to the area of
the rerticle. In our case the terminal rate is reached so quickly that one
may write
are
(4)
shere "h* is the starting height, "t* is the time of fall, "4" is the
sarticle diameter and "K" is a constant of proportionslity sontaining
the density, the viecceity, and mmsrisa] fastors. Tae viseceity, in-
cidentally, is temperature dependent, but the variation is amall canpared
to the other uncertainties in this system and we have chosen to keep the
viscosity constant, Substitution of equation (4) permits ome to write
the dose index as
pees
(3a)
and further use of assumption (7) above permite the form
Se
+- .
(3)
.
whore "K'* is some new constant and “TI is the radial distance along «
bearing from ground sere.
Wamerical values of the dose index can be ccmputed from ery of the
forms of equation (3) vith the proper selection of write.
We defined the mmorical velue of the dose index as the ratio of the
square of the particle diameter in microns to the square of the tine of
fall in hours. In those units the dose index is cf the same order 4s
from a lOwmsgaton yield as determined by a roumh
tha dose
match wi
range is
ta. The adjustment to other ylolds in the meraton
ect proportionality es indicetod in assumption (4).
D8