26 
ME. MACQIJOEN EANKDfE ON THE STABILITY OE LOOSE EAETH. 
In the case to which Problem III. refers, in which 
1 
(IB. 
COS^f 
equation (66.) becomes 
X < ./i + A cos^«p 1 
dti 
( 67 .) 
The most important apphcation of these principles relates to the power of a mass of 
earth whose upper smTace is horizontal, to sustain the weight of a building founded at 
a given depth. 
In this case, the condition of stability expressed by the equation (65.) becomes 
^ dx < 1 + sin (p 
dB ^ I + sin <p 
Now the horizontal pressm’e of the earth may be so mcreased by ramming, as to have 
the maximum amount consistent with the intrinsic vertical pressm’e due to the weight of 
the earth, in which case 
^ dx 1— sin(p 
'^H^=l + sin?5- 
(69.) 
And consequently, the extrinsic vertical pressure, due to the excess of the weight of a 
building above that of the earth which it displaces, is limited by the equation 
4 tan f 
y — dx 
4 sin <p 
(1— simp)^ 
(70.) 
and the ratio of the loeight of a building, to the weight of the earth displaced by its founda- 
tion, is limited by the equation 
Xh + X. / l + sin<p Y 
Xh ' 
(71.) 
When the angle of repose, for example, is 30°, the limit of that ratio is 9. 
§ 21. Negative Extrinsic Pressure. Resistance of Screw Piles to Extraction. 
When the mtrinsic vertical pressure exceeds the lower limit given by the equation (65.), 
the earth will resist a Negative Extrinsic Pressure, or upward tension, not exceeding such 
excess. To avoid the use of negative signs, let 
then 
-X,=T,; 
T,<Xh- 
dx 
cos® <p 
\ V COS® 6 / 
(72.) 
