114 GROVE KAEL GILBERT— DAVIS [Memoies [V N o A l!xx£ 



Gilbert himself recorded many barometer readings in connection with his notes on struc- 

 ture and topography in the Henry Mountains and elsewhere, and it is to be presumed that they 

 were utilized in calculating the thickness of stratified formations as well as in determining alti- 

 tudes and constructing topographic maps. But he appears, judging from a passage on "Office 

 work" in Powell's report for 1876-77, to have been troubled by errors in readings recorded at 

 base stations by his assistants. The report states that — 



Mr. Gilbert has made a critical examination and discussion of the barometric observations extending through 

 the previous years of the work, for the purpose of determining the range of error, and of detecting as far as possi- 

 ble the source thereof. The result of this examination tended to show that one of the principal sources of error 

 was inaccuracy in reading and recording, and for the purpose of eliminating these, [he] suggested a number of 

 checks, of which the most important was the reading and recording of the two verniers of the Green barometer 

 instead of a single one. The interval between the tyvo verniers is of such length that their fractional readings 

 are always different, and it is practically impossible to repeat the same, error. 



The chief outcome of Gilbert's attention to this subject is a remarkable essay, "A new 

 method of measuring heights by means of the barometer," the preparation of which must have 

 demanded much thought and labor during the later years of his connection with the Powell 

 survey; it is published in the first annual report of the national survey (the second of the series) 

 after Powell became its director. It made what musicians might call a prompt "attack" by 

 the immediate announcement of the essence of the plan in the very first paragraph : 



The change proposed in this paper is of a radical nature. Since the time of Laplace the formula he 

 developed has formed the groundwork of all investigation and practice. ... It is here proposed to abandon 

 it entirely for the greater part of hypsometric work and to substitute a new formula involving none of his con- 

 stants and having but a single element in common. The new element abandons both psychrometer and ther- 

 mometer and employs the barometer alone (405). 



The novelty of the method consisted, first, in the use of three barometers, two at stations 

 of known altitude, as near to each other horizontally and as far separated vertically as possible, 

 and the third at a point the altitude of which is to be determined; and, second, in the omission, 

 as above noted, of all factors dependent on air temperature and moisture. 



The essay as a whole is very carefully prepared. After the many complicating factors of 

 the general problem are set forth, the new solution is first briefly stated with gratifying direct- 

 ness and then demonstrated with mathematical elaboration. The solution is in essence as 

 follows: Given two stations, A and B, the altitudes of which are known, and a third station, C, 

 the altitude of which is to be determined. Assume the air to be dry and of uniform temperature 

 at 32°, and compute the altitudes B-A and C-A by the usual formula, thus gaining approximate 

 results. Then solve the proportion in which the first three terms are known: 

 Approximate B-A : true B-A :: approximate C-A : true C-A 



The value of the new solution was tested by comparing its results with those obtained by 

 other methods at various places where the necessary observations were available; a series of 

 tables is added to facilitate the calculations necessary in practical work. 



The whole essay shows an immense amount of conscientious labor. It closes with a beau- 

 tiful "graphic table" for the ready determination of a small correction dependent on two 

 "arguments," which serve as abscissas and ordinates for the correction values represented by 

 a series of curves. Gilbert's comment on this handy device shows the exceptional breadth of 

 his treatment: 



The graphic table is in some sense an experiment. The idea, indeed, is not novel, but it has not been 

 widely applied. It appears to the writer that a similar plan might advantageously be adopted for the tabula- 

 tion of factors dependent on two arguments, whenever the arguments are large as compared with the tabulated 

 factor; or rather, whenever the number of digits used to express each argument is large as compared with the 

 number of digits used to express the dependent factor. 



Two comments of a rather mournful turn must be made on this exceptionally ingenious 

 essay. First, it appears from a chapter on the work of other hypsometricians near the close of 

 the essay, in which Gilbert refers to himself only in the third person, as if to make the statement 

 more impersonal, that his method was not so novel as he had at first supposed. The new 

 solution "was first advanced by the writer at a meeting of the Philosophical Society of Wash- 



