826 
ME. W. HOPKINS’S EXPEEI^IENTAL EESEAECHES 
we have 
V ^ 
(2.) 
which gives the rate at which the temperature in the (/4-l)th stratum decreases in 
ascending. Comparing this -with the rate in the former system, we have 
dK 
1 + 
( 3 .) 
d^ _p_ ^ 
/k,\ 
dz' ^ q 
To form a general estimate of the numerical values of 2 ^ and 2 let us suppose 
k 
the value of - for each of the strata to equal -5, which is nearly a mean value of 
k * • P 
as above determined, one foot being the unit of length. Then will ^ = 2, and 
.ph_p 
~k' 
=2H, 
when H is the aggregate thickness of the system of strata. Again the number of dis- 
continuities in the w+1 strata will =n\ so that if we take a mean value of we shall 
have 
2? 1 • H 
and if we take Jq’ which is greater than the mean of the values given above (art. 7), 
q q 
we have 
yP—JL 
^ g~10' 
Hence if twice the aggregate thickness of the strata, expressed in feet, be much greater 
than one-tenth of the number of strata, and also much greater than unity, the denomi- 
2)/i 
nator of the expression in equation (3.) will reduce itself nearly to 2^^; and in like 
manner, under similar conditions, the numerator will be reduced nearly to 2 ^ • Con- 
sequently, we shall thus have 
y p'h' 
~dz p If 
d^~ p''X 
d^ k 
nearly, 
(^•) 
15. There are two particular cases which it is important to notice : fii'st, that in which 
the strata particularized by the conductive powers and each of large thickness 
compared with the aggregate thickness of the remaining strata ; and, secondly, that in 
which these two strata are of very small thickness compared udth the aggregate thick- 
7)1h 7)^ Jl! 
ness of the whole mass. Writing 2y and 2^- at full length, we obtain 
