290 Becker — Geometrical Form of Volcanic Cones 



the center. On recomputing it however for the slight discrep- 

 ancy mentioned, I find that the difference in the cross section 

 of the mountain would be imperceptible on the scale of the 

 figure, and I therefore prefer to present it exactly as it results 

 from Professor Milne's measurements. A small part of the 

 lower portions of the left sides of the mountains as given by 

 Professor Milne are omitted because they could not be included 

 without unduly reducing the scale of the cut. These portions 

 correspond as well as the remainder with the theoretical form. 

 Professor Milne gives no more of the right side of Kumagatake 

 than the cut shows. 



In computing the value of the natural unit I rejected the 

 two measurements nearest the peak because the summit is not 

 only most subject to erosion when not snow-capped but should 

 not theoretically coincide with the figure of least variable 

 resistance ; for such a coincidence would imply an infinitesi- 

 mal crater while the existence of an actual crater implies the 

 presence of less matter, or a smaller load, close to the summit 

 and consequently a more rapid convergence of the sides. 

 Strictly speaking, the presence of a crater would affect the 

 whole figure, but the influence of this diminution of the load 

 will manifestly be extremely slight excepting near the crater 

 itself whenever the crater is small compared with the volume 

 of the cone. 



For the sake of comparison with these very perfect examples 

 I have introduced outlines of Mt. Shasta, Mt. Hood and 

 Popocatapet'l carefully reduced to appropriate scales from pho- 

 tographs. These mountains are all rather irregular but will 

 serve at least to show a striking similarity in the curvature of 

 volcanic cones, and a pretty close agreement with the theo- 

 retical form. This likeness can best be judged of by making 

 a tracing of the theoretical cone and placing it upon the out- 

 lines of the mountains. Professor George Davidson has kindly 

 lent me a sketch of Mt. Eenier, which he made for the special 

 purpose of recording its slopes. Long practice in this kind of 

 work makes him confident that this sketch is correct as to 

 angles to something like one degree. The sketch coincides 

 most remarkably with the theoretical form but is not added to 

 the diagram because its evidence is scarcely comparable with 

 that obtained mechanically by photography. In the case of a 

 very large and deep crater it might be interesting to compare 

 the form of greatest stability with that of the wall of the crater. 

 If E were the radius of the outer surface of this wall at any 

 level and r the radius of the inner surface the area of the ring 

 would be 7r(R 2 — r 2 ) and (R 2 — r 2 )^ would have the same value 

 as y in the equation given for a pointed cone. 



Professor Milne states that the highest slope he has observed 



