88 GROVE EARL GILBERT— DAVIS [MEMOIBS [voi T xxY; 



pressure exerted by a circular sheet will increase with its area, or with the square of its radius. 

 Part of the upward pressure may be given to lifting the weight of the cover, and in a cover of 

 constant thickness the weight will increase with the area of the sheet or the square of its radius, 

 and hence with the upward pressure; the remainder of the upward pressure may be given to 

 deforming the cover. Deformation by the formation of a vertical cylindrical fracture around 

 the margin of the sheet is first considered, and allowance is afterwards made for deformation 

 by flexure. The resistance to the making of a cylindrical fracture of the same diameter as 

 the intrusive sheet will increase with the area of the fracture surface; that is, with the circum- 

 ferential area of the cylinder; and this, in a cover of constant thickness, would increase only 

 with the first power of the cylinder or the sheet radius. Hence, while the resistance to cylin- 

 drical fracture will probably be greater than the available upward pressure of a small circular 

 sheet in the early stage of horizontal intrusion, equality of the two forces will be reached later 

 as the sheet increases in radius; and thereafter the direction of least resistance will be upward, 

 and the reservoir will increase in vertical thickness instead of in horizontal diameter. 



An important generalization follows: "The laccolite in its formation is constantly solving 

 the problem of 'least force,' and its form is the result" (91). " 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" (88). Therefore "when a lava forced upward through the strata reaches the level 

 at which under the law of hydrostatic equilibrium it must stop, we may conceive that it ex- 

 pands along some plane of bedding in a thin sheet, until its horizontal extent becomes so great 

 that it overcomes the resistance offered by the rigidity of its cover, and it begins to uplift it. 

 The direction of least resistance is now upward, and the reservoir of lava increases in depth 

 [thickness] instead of in width. The area of a laccohte thus tends to remain at its minimum 

 limit" (88, 89). But as the thickness of the laccolith increases, its .growing weight "is pro- 

 gressively subtracted from the pressure [exerted by the rising magma] against its top, and 

 this proceeds until the upward and lateral pressures become proportional to the resistances 

 which severally oppose them. Further expansion is then both upward and outward" until, 

 "when the sum of the weights of the cover and laccohte equals the total pressure of the in- 

 trusive lava, uplift ceases, and the maximum depth or thickness is attained" (90, 91). 



RELATION OF DIAMETER AND DEPTH 



A further consequence of this theoretical discussion is that the diameter of a Henry Moun- 

 tains laccohte "is proportioned to its depth beneath the surface"; and this is susceptible of 

 test by comparing the diameters of laccolites in the lower and upper zones of the Henry Moun- 

 tains strata. The test gives remarkable confirmation to the theory; for not only is the mean 

 diameter of 8 laccohths in the lower zone (2.6 miles) double the mean of 10 in the upper zone 

 (1.2 miles), but in the upper zone, where their stratigraphic position is best determined, the 

 highest laccolites are the smallest, and their size increases downward with some approach to 

 regularity. " There is no laccolith of the upper zone so large as the smallest in the lower zone; 

 and the mean diameter of those on the lower zone is double the mean of those on the upper. . . . 

 The confirmation of the conclusion is as nearly perfect as could have been anticipated. There 

 is no room to doubt that a relation exists between the diameters of laccolites and the depth of 

 their intrusion" (92, 93). 



A most ingenious extension of the theory is finally made in estimating the original thickness 

 of the covering strata: 



Having determined by observation the mean size of the laccolites in the upper and lower zones, as well as 

 the interval [3,300 feet] which separates the two zones, and knowing approximately the law which binds the size 

 of the laccolite to its depth of intrusion, we can compute the depth of intrusion of each zone. Our result will 

 doubtless have a large probable error, but it will not be entirely without value (94). 



