and the Elastic Limit of Lava. 287 



and this is the equation of the curve which by its revolution 

 about the a>axis will generate the finite unloaded column of 

 " least variable resistance."* 



This is the same curve barring the value of constants which 

 I have shown twice elsewhere,f characterizes step faults. It 

 might have been deduced directly from the discussion pre- 

 sented in the latter paper on the distribution of energy in 

 compressible masses under the action of a constant force, or 

 that discussion might have been evolved from this. The 

 arrangement of sheets of rock in a complex fault, the distribu- 

 tion of pressure in the atmospheric column, the form assumed 

 by a cold rivet, and the shape of a volcanic cone, as well as 

 some other important cases, and possibly some vegetable forms:}: 

 are mere variations of a single problem and find their solution 

 in different readings of the equation 



w=As~ x/c +Bs x/c 

 where w is the energy potentialized per unit volume. 



The quantity is the natural unit of the volcanic curve 



. - P 



corresponding to the constant sub-tangent of the infinite form 



and to the constant of the catenary curve. It is of course con- 

 stant for any given homogeneous material and different for 

 different materials. Consequently solids of different materials 



* Whether this proposition is new or not my reading is insufficient to deter- 

 mine. I can only say that I have looked for it in vain in a number of treatises in 

 which it might have been expected to be mentioned if known. 



f Geology of the Comstock Lode, chap, iv ; Impact Friction and Faulting, this 

 Journal, vol. xxx, p. 116. 



% The case of a loaded column of uniform strength seems unlikely to be met 

 with in inorganic nature for it appears to imply an adjustment of the column 

 after the imposition of the load. 1 strongly suspect however that the simple 

 logarithmic column is the form to which tree trunks tend in forests where the 

 influence of winds is but little felt. Where such trees reach a large size and 

 especially where the wood is soft, the increase in diameter near the ground is 

 very marked. Thus in the red-wood forests of California the largest trees are 

 generally cut some ten or more feet above the ground to save the inconvenience 

 of handling a trumpet shaped log. This increase of diameter is less marked in 

 trees of moderate size than in very large ones and less among hard wood trees 

 than in species the wood of which is soft. Forest trees of course seek the light, 

 and one can scarcely doubt that they reach it as rapidly as it is possible to do so 

 consistently with stability. If so the load at any section below the branches per 

 unit of area of this section will be a maximum and will be the same at all sections, 

 and if this is true the form is the simple logarithmic column. For if F is the 

 area of the section or Try' 2 , and if F is the value of F for the datum plane, the 

 equation may also be written 



F = F e- x P/ K . 



This would lead to a simple means of testing the question under favorable cir- 

 cumstances. If one were to cut a well developed forest tree just below the 

 branches and divide the trunk into two or more portions, weigh the branches 

 and each log, and measure each cross-section, it could of course be determined in 

 a moment whether the load per square inch of all sections were uniform or not. 



