Exploration of the Colorado, pp. 182–184. Explorations West of the 100th Meridian, Vol. III, p. 48. American Journal of Science, July, 1876, p. 21. It is possible to give a mathematical expression to the force necessary to produce such a circular fault. Disregarding lithologic differences, the resistance to the rupture is measured by the area of the faulted surface, or what is the same thing, the area of the convex surface of the cylinder. Representing the resistance to be overcome by _r_, the height of the cylinder (equal to the depth of the cover of the laccolite) by _d_, and its circumference by _c_, we have _r_ = _dcC_ (1), in which _C_ is a function of the cohesion of the material and is constant. The force by which the cylinder is lifted and by which it is assumed that the faulting is accomplished, is communicated through the molten lava of the forming laccolite. Being thus communicated it is applied equally to all parts of the base of the cylinder, and its efficient total is measured by the area of that base. A part of it is devoted to lifting the weight of the cylinder, and the remainder is devoted to the making of the fault. Each of these parts is proportioned, like the whole, to the area of the base of the cylinder, or to the area of the laccolite. Representing the portion applied to the faulting by _f_, and the area of the laccolite by _a_, we have _f_ = _a C_{l}_ in which _C_{l}_, is a constant, and a function of the pressure under which the lava is injected. Substituting for _a_ its equivalent, _c_^²⁄₄π _f_ = _c^2 C_{l}_/4π and substituting _C_{ll}_ for the constant term _C_{l}_/4π _f_ = _c^2 C_{ll}_ (2) Equation 1 gives an expression for the resistance which cohesion can oppose to the uplift of the cylinder. Equation 2 gives an expression for the force exerted by the fluid laccolite toward overcoming the resistance of cohesion. It is evident that for a given value of _d_ it is possible to assign a value of _C_ so large that _f_ will be greater than _r_, or so small that _f_ will be less than _r_. That is to say, at a given depth beneath the surface a laccolite of a certain circumference will be able to force upward the superjacent cylinder of rock, while a laccolite of a certain smaller circumference will be unable to lift its cover. Or in other words, there is a limit in size beneath which a laccolite cannot be formed.