THE ISOPIESTIC LEVEL 403 



at this level the irregularities in pressure due to local topography flatten 

 out and the pressure of the superincumbent crust is everywhere the same. 



The depth of this isopiestic level has been computed by several geode- 

 sists by different methods, but always on the assumption that there is 

 equal vertical distribution of density in the column. The results vary 

 within rather wide limits, which is not surprising when the somewhat 

 uncertain character of the data used is considered, but they are all of the 

 same order of magnitude, varying only from about 40 to 122 kilometers. 

 Many years ago 0. Fisher 23 estimated the depth at about 25 miles, arriv- 

 ing at this along two lines of reasoning. An early computation by Hay- 

 ford 24 gives 113 kilometers, and a little later he arrives at the value 122 

 kilometers. 25 The latest estimate is that of Bowie, 26 who gives the value 

 60 kilometers (37.28 miles), derived from 216 stations distributed over 

 the United States, as well as the value 96 kilometers (59.65 miles), de- 

 rived from observations at the stations in mountainous regions of the 

 United States. He accepts the latter (96 kilometers) as the best, for the 

 reason that the values of gravity are more sensitive to change in depth at 

 such elevated stations than at those situated on coastal plains or plateaus. 



The depth of the isopiestic level has been calculated from the data 

 arrived at by the normative method and given in Table III. The height 

 of any column of density, 8, is considered to be made up of two portions, 

 the altitude above sealevel, h, and the depth from sealevel to the isopiestic 

 level = M (h and 8 being the variables). As the columns are all of equal 

 weight and as M is a constant, we have the general relation: (M -f- h) 

 8 = A, A being a constant. From this we have : 



8 — : ^r~ l — 7~; an d 8 = ^r-, 

 M + h M ' 



8 being the theoretical density of a column whose height is M, or that 

 of an area at sealevel. The process of calculation was the ordinary 

 method of least squares, the equations used being given below. 27 It is to 

 be noted that the equation A= (M + h) 8, although linear with respect 

 to h8 (considered as a single variable) and to 8 (the other variable), is, 

 of course, not linear with respect to h and 8 as the variables. 



23 O. Fisher: The physics of the earth's crust, second edition, 1889, p. 217. 

 -*J. F. Hayford : The figure of the earth. U. S. Coast and Geodetic Survey, 1900, p 

 175. 



25 J. F. Hayford : Supplementary investigation, r. S. Coast and Geodetic Survey. 

 1010, p. 77. 



26 W. Bowie : Investigation of gravity and isostasy. TJ. S. Coast and Geodetic Survey. 

 Special Publication no. 40, 1917, p. 133 ; and Amer. Jour. Sci., vol. ii, 1921, p. a. 



27 A _ 2 5 2 2 h8 — 2 5 2 hS 2 ; _ 2 52 h8 — it 2 Ji8- 



— h2 5 2 — (2 5)- ' ~~ J/2 5-— (2 5) 2 ' 



in which n = the number of observations. 



