DIRECT INVESTIGATIONS OF ISOSTASY 179 



Geodesists, I have been tokl, were well aware for many years that with 

 sufficient labor it would be possible to test Pratt's theory, to which C. E. 

 Button gave the name isostasy.-- They recognized, however, that the 

 task would be a very formidable one. As we all know, it was at last 

 undertaken by Mr. John F. Hayford,"^ in what Mr. Helmert character- 

 izes as a "truly magnificent investigation.'' The same veteran geodesist 

 renamed the underlying idea "the Pratt-Hayford hypothesis" in recog- 

 nition of the importance of Hayford's work in establishing the actuality 

 of isostasy. 



Mr. Hayford's second memoir-'* is a supplement to the first and the two 

 should be considered together. In all they embrace and discuss 765 de- 

 flections of the vertical in the United States. In the nature of the case, 

 isostasy can be investigated only by trial and error. Among many hy- 

 potheses, reasonable or unreasonable, as to the distribution of isostatic 

 compensation, one is selected and all of the deflections are computed as 

 if it were true. The results of such a discussion are called by Mr. Hay- 

 ford a "solution." Those portions of the deflections which remain unex- 

 plained after each solution are known as residuals. Pretty nearly, but not 

 exactly, a residual is the difference between the observed deflection and 

 the computed deflection.-^ This is not an exact definition because the 

 observed deflection involves errors of observation and instrumental errors, 

 while the computed deflection may be inaccurate from many causes; thus 

 the maps from which the volume of topographic features is derived are 

 not perfectly accurate, nor is the density of the rocks accurately known, 

 while the determination of the latitude, longitude, azimut]i, zenith, etcet- 

 era, are all to some extent imperfect. The residuals include errors of all 

 descriptions, and would reduce to zero only if ideal conditions were dealt 

 with by infallible observers and computers. Among trial hypotheses that 

 is the best in which the sum of the squares of the residuals is smallest. 



For each observed deflection Mr. Hayford computes the deflection 

 which would be produced by all the topography within 2,564 miles or 

 4,126 kilometers.-^ This so-called topographic deflection (or perhaps 

 better orographic deflection) always differs from the observed deflection 

 in the sense to be expected on the hypothesis of isostatic compensation — 



-" Phil. Soc. Washington, vol. ii, 1889, p. 51. 



'■a The flgure of the earth and Isostasy from mcasiirt'iiifuts iu the U. S. Coast and 

 Geod. Surv., 1000. 



-* SuppU'iiieiilary iiivesi in;! I ion in I'.Kiil of the ligiire of the earth ;in(l isostasy. t'oast 

 and Ceod. Surv., 1010. 



-'^ C"f. Hayford's first moiioKra|)h, p. lOO, and his second nionosi'aph, p. tiO, footnote. 



=» Helmert considers 1,000 kilometers a sufficient radius, and disagrees witli Hayford's 

 method of dealing with the more distant masses. Sitzungsber. k. I'reuss. Akad. der Wlss., 

 1914, p. 440. 



