44 C. E. VAN ORSTRAND 
and the corresponding equation to the isogeotherms, 
wz? Hd(i+ gA)\(z+ A+ 
Buse a gg RN ie Bi ED eee 6) 
2k 2?+ (2+ H+d)? 
As Eggs. (5) and (6) are cubics in z, it will be more convenient for purposes 
of calculation to put them in the respective forms: 

ea-f+Htd)[eteta+—| (7) 
iHd 
v= -b+H+a[e+n+q+— "| (8) 
in which the terms dependent on radioactivity have been neglected. 
Putting x =0 in (8), 
2+ (H+d—o)z—-(H+d)e+ «Hd =0 (9) 
and assigning particular values to ¢2, which according to Eq. (3) represents the 
depth beneath the plain at which a particular temperature v is reached, Eq. 
Taste I. Depth of tsogeotherms beneath level of plain and rise of tsogeotherms beneath apex of hill. 

Depth of Depth of 








Rise of : Rise of 
isogeotherms |. isogeotherms 
Isogeotherms| beneath level LeeeoE ee teoeeotueune beneath level Boost 
of plain ea ESI of plain a 
a apex of hill e apex of hill 
Sac °F | Meters | Feet |Meters} Feet | Cent. |Fahr.| Meters | Feet |Meters} Feet 
0.0 0 0.0 0} 89.2 | 293 | 38.9 70 | 1149.2 24.0] 79 
ileal 2 32.8 108 | 81.8 | 269 | 41.7 5 23a 22-351) a5 
De 4 65.7 215) 75.8 | 249 | 44.4 | 80 | 1313-3 JIEStiy ad 
3h 6 98.5 SYR | (Moth || PRY | 24/7 85 | 1395.4 20.9 | 68 
4.4 8 131735) 4345) (6653: |) 218) | 5020) |) 90) | 4147725 20.0 | 66 
5.6 10 164.2 S390 "6257 (e205 55.6 | 100 | 1641.6 18.5 61 
(cy) 12 197.0 646 | 59.1 | 194 61.1 | 110 | 1805.8 EUS 56 
7.8 14 229.8 754 | 56.1 | 184 66.7 | 120 | 1970.0 16.0 52 
8.9 16 262.7 862 | 53.5 | 175 12. 52)\ 1300) 213422 15.9 | 49 
10.0 18 295.5 969 | 51.1 |.167 77.8 | 140 | 2298.3 14.1 | 46 
lant 20 328.3 | 1077 | 48.9 | 160 | 83.3 | 150 | 2462.5 13.3 | 44 
13.9 25 410.4 | 1346 | 44.1 | 145 88.9 | 160 | 2626.6 12.6 41 
16.7 30 492.5 | 1616 | 40.3 | 132 94.4 | 170 | 2790.8 12.0 | 39 
19.4 35 574.6 | 1885 | 37.1 | 122 | 100.0 | 180 | 2955.0 11.4 38 
DDD 40 656.7 | 2154 | 34.4 | 113 | 105.6 | 190 | 3119.1 10.9 36 
25.0 45 Taf || AVA oN Os) abla sil |) Ba) |) BAIS} 10.5 34 
27.8 50 820.8 | 2693 | 30.0 98 | 116.7 | 210 | 3447.5 10.0 33 
30.6 55 902.9 | 2962 | 28.2 939) 12252592200 1"361126 9.6 32 
Jono 60 S85E0) |NS2320e2657 87 | 12758) | 230) WW siiees8 9.3 30 
36.1 65 LOGiet SSO E2522 83 | 133.3 | 240 3940 .0 8.9 29 
a=0.000 338 412°C per cm (=1°C in 29.55 meters=1°F in 53.86 feet). 
a’ =0.000 05°C per cm (=1°C in 200 meters=1°F in 364.5 feet).§ 
H = 360 feet =109.73 meters. 
6=3.85H =1385 feet =422.15 meters. 
d=1396.65 feet =425.70 meters. H/d=0.257 760. 
¢, =0.852 251 c=1641.654 cm per degree Fahrenheit. 
0. 
W. J. Humphreys, Physics of the Air. Sec. ed., p. 40 (1929). 
188 
