278 BECKER 



mountain and have more than once been known to reach the sea. 

 The last eruption in which this happened was in March, 1900, 

 and the account of it given by Colonel. Waher Howe appears in 

 the Census of the Philippine Islands, Vol. i, p. 223, 1905. 

 Besides the fairl}^ solid rock masses represented by lava flows, 

 it may be considered tolerably certain that, as elsewhere, vol- 

 canic ash, wet by the showers accompanying eruptions, cements 

 into a firm tuff. In all probability, how^ever, the actual smooth- 

 ness of external form of the volcano is due to a mantle of ash 

 which dresses up the surface, filling out inequalities, increasing 

 the steepness wherever possible, and producing a conical figure 

 very characteristic of a large class of volcanic cones. This 

 shape is still recognizable and fairly well preserved in moun- 

 tains like Shasta and Ranier. One of the most perfect ex- 

 amples in the w^orld is the famous Fujisan of Japan, which, 

 however, has had no eruption since 1707. Evidently, had 

 Fujisan been entirely loose ash, the erosion and gales of 2 cen- 

 turies w^ould have seriously impaired its beaut}-, and since it is 

 still so perfect, the material must offer considerable resistance 

 to the forces of degradation. Mayon is even more perfect than 

 Fujisan, because of its frequent eruptions. 



This characteristic form of volcanic cone is rarely associated 

 with rocks of an exclusively basaltic character. The Hawaiian 

 volcanoes emit basalts which flow for immense distances before 

 final solidification, and as a consequence, the accumulations of 

 lava aggregate to dome-like shapes the height of which is small 

 as compared with the mass and with the diameter. Small 

 cinder-cones of basaltic ash, however, sometimes occur which 

 are recognizably of the same geometrical type as Fuji. 



Mere inspection shows that these beautiful cones have un- 

 broken outlines, and observation indicates that the characteristic 

 form is due to ash. Hence the mathematical problem of the 

 figure appears to be this : To find the loftiest figure of given 

 volume and continuous curvature which can be built up of suc- 

 cessive showers of ash, each ash layer being supposed to be- 

 come indurated after its deposition. In dealing with this prob- 

 lem, the crater may be supposed of inlinitesinial size. 



In 1885, I published a theory of volcanic cones, and in 1898 



