May 21, 1886.] 



SCIENCE. 



461 



It is therefore only necessary to measure the angles 

 with the same precision as the base, to insure equally 

 precise results. This is so far attainable, that the 

 latest great primary triangulation of the coast and 

 geodetic survey, enclosed between two measured bases 

 six hundred miles apart, met nearly midway, at a 

 line about twenty-nine miles and a half long. The 

 computed lengths of the line, from measured bases 

 distant about three hundred miles from either of 

 them, agreed within about five-eighths of an inch. 



It follows from the above, that, in any system of 

 triangulation carefully conducted, the relation of 

 every point in the system to every other point may 

 be determined with a degree of precision almost 

 absolute. It renders the position of each apex of a 

 triangle infallible ; since its error, if any, can only 

 be detected by application of similar methods of pre- 

 cision, which will themselves be liable to the same 

 sources of error. 



Referring to what has been written as to cumula- 

 tive errors belonging to all ordinary local topographi- 

 cal or other surveys, it is evident, that, if these sur- 

 veys include two or more trigonometrical points 

 within their limits, the inevitable error involved in 

 their methods is checked and corrected as each such 

 point is successively reached. If it is not exactly 

 hit, the local survey is wrong, and must be corrected 

 to meet the triangulation-point, which stands as in- 

 fallible in its assigned position as the pope claims to 

 be in his. 



The triangulation gives the relation of every point 

 in the system to every other point. To apply the 

 data thus obtained to its chief use in the construction 

 of accurate maps, from the local surveys thus 

 checked and corrected, another class of observations 

 and reductions becomes necessary to fit the frame- 

 work which has been constructed to its proper place 

 upon the surface of the earth. This, with the tri- 

 angulation, constitutes what may properly be called 

 geodesy. No better definition of this term can be 

 given than that by the late Gen. E. D. Cutts : 

 ''Geodesy, in practice, may be described as a sys- 

 tem of the most exact land-measurements, extended 

 in the form of a triangulation over a large area ; con- 

 trolled, in its relation to the meridian, by astronom- 

 ical azimuths ; computed by formulae based on the 

 dimensions of the [adopted] spheroid ; and placed in 

 its true position on the surface of the earth by as- 

 tronomical latitudes and differences of longitude 

 from an established meridian." 



The whole system of triangulation thus combined 

 and co-ordinated, and made to occupy its true posi- 

 tion upon the earth's surface, may be compared to a 

 human skeleton. As the skeleton is the framework 

 on which is built and sustained the varied elements 

 of the human body, each fitted to and held in its 

 place by the unyielding structure sustaining it, so the 

 triangulation is the framework on which each varied 

 portion of the earth's surface within its range is also 

 fitted to and held in its true position, and the result- 

 ing map becomes an absolutely true topographical 

 picture of the country it purports to represent. 



But this is only one, and not the greatest, good 

 represented by a well executed and complete geodetic 

 survey. Every point of the triangulation is care- 

 fully marked above and beneath the surface for 

 reference in future ages. Every recorded distance 

 between any two points thus marked becomes a base- 

 line, whose length is known with a degree of pre- 

 cision unattainable by ordinary methods. So, also, 



is the azimuth or angle with the true meridian made 

 by every such line, thus affording means for ascer 

 taining the local magnetic variation and its yearly 

 change. The recorded and published latitude and 

 longitude of any station will enable future astrono- 

 mers to find close at hand the means of fixing their 

 precise relations to other and distant observatories. 

 As the country increases in population and wealth, 

 its topographical features change. New towns are 

 built, and new roads and new railroads laid out. 

 New maps will be called for, and easily supplied, 

 since the framework of the triangulation. executed 

 half a century before, perhaps, is there, always cor- 

 rect and reliable. As the elevations of all the sta- 

 tions above the mean level of the sea have been de- 

 termined in the original survey, so, if schemes of 

 drainage are planned to bring: swamp lands into use 

 for arable purposes, these differences of level will 

 afford data for obtaining the amount of fall and 

 its proper direction. And so long as the earth and 

 sea maintain their relative positions, so long the 

 beneficent effect of early and exact triangulation 

 will continue to be felt. 



This is essentially a national work. It cannot be 

 defined by, or confined within, state boundaries. 

 Whatever views may be held as to local topographi- 

 cal surveys, and who shall execute them, it is evident 

 that the framework on which they are to be built 

 must be independent of political boundaries. The 

 triangle sides leap across bays and lakes, or from 

 mountain to mountain and hill to hill, or they travel 

 ' upon stilts ' across the level swamps and prairies. 

 Nature only fixes its limits. It is homogeneous and 

 universal by its own conditions of existence. The 

 geodetic survey of all our country is therefore a work 

 eminently proper for the national government to 

 carry on, leaving the other questions of local topo- 

 graphical surveys for national or state action, or for 

 both combined, as in Massachusetts. 



The National academy of sciences, which is, by 

 law, the adviser of congress and the executive upon 

 scientific matters, has twice, at the call of congress, 

 advised the early execution of this great work, and 

 that its execution should be intrusted to the coast 

 and geodetic survey as best fitted, in men, means, 

 and training, to carry it on. Lately the need of 

 prompt action in the same direction has been well 

 and strongly set forth by Prof. W. P. Trowbridge of 

 Columbia college, whose large experience gives 

 weight to his words. 



If states whose interests require good maps will 

 join with commercial bodies and scientific men in 

 urging legislation, the plan proposed by the national 

 academy in 1878, and again in 1884, may be carried 

 out with no duplication of other work, but, on the 

 contrary, with cordial and complete co-ordination 

 with other surveys. The whole country would be 

 benefited thereby to an amount far exceeding the 

 outlay. CO. Boutelle. 



"Washington, May 11. 



Double vision. 



Your correspondent, Dr. George Keller, will find 

 the phenomena of double vision discussed in Helm- 

 holtz's ' Physiological optics,' and in LeConte's book 

 on sight. The latter is a small volume published by 

 D. Appleton & Co., New York. The production of 

 binocular images, apparently suspended in mid-air, 

 on regarding a tessellated pavement or papered wall 



