A FEATURE OF MAYON VOLCANO 279 



o-ave a fresh demonstration of the formuhi deduced.^ Accord- 

 ingto this theory, the outHne of a volcano should be represented 

 by the hyperbolic sine curve, or 



z = 



c 



e'-'- — c-''" 



where .v is the distance below the summit, y the radius of the 

 horizontal cross-section and c a unit of measurement which is 

 in fact twice the height of a column of the lava which would 

 just support its own weight. 



Mr. Gannett's photograph, together with the elevation of the 

 mountain given by the Coast Survey, enables me to compute 

 the particular value of c for this volcano. If the outline of the 

 mountain were perfectly smooth, the value of c could be deter- 

 mined for any point upon the slope. -^ The actual outline in the 

 photograph, although remarkably regular, is not absolutely 

 smooth, and therefore this means of ascertaining c affords only 

 an approximation. I thus found that c must be between 8 and 

 9 mm. On plotting the hyperbolic sine curve for c = 8.8 mm., 

 it appeared that this value was decidedly too large, while a 

 similar trial showed that 8.3 was decidedl}^ too small. The 

 third trial, taking c = 8.6 mm., gave a curve almost indis- 

 tinguishable from the natural outline. Both the photograph 



1 Amer. Journ. Sci., vol. 30, 1SS5, p. 283. U. S. Geol. Survey, iSth Ann. 

 Rep., Pt. Ill, 1S9S, p. 20. 



2 If 1? is the angle which the curve makes with the axis, 



l/tan^i? — I 



The angle at the summit when the crater is infinitesimal, or 45°, is the maxi- 

 mum possible angle of rest. If IV is the resistance due to friction and IV the 

 normal pressure, while p is the angle of rest, 



tan p = WIN. 



Now the resistance, IV, cannot possibly exceed the normal pressure which 

 excites it, so that the limiting value of WIN is 1 or 10 = 45°. 



The meaning of the constant c is readily grasped by considering that at a 

 great distance from the summit the theoretical volcanic cone sensibly coincides 

 with the logarithmic column 



and here the maximum possible value of c is twice the height of a prismatic 

 column of the material which will just support its own weight. 



