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The National Geographic Magazine 



characteristic of the triangulation is its 

 rigidity imparted to it by quadrilaterals 

 and other polygons. In crossing the 

 Rocky Mountains many of its sides ex- 

 ceed one hundred miles in length, and 

 there is one side reaching to a length of 

 294 km,, or 183 St. miles; the altitude 

 of many of the stations is also consider- 

 able, reaching to 4,300 metres, or 14,108 

 feet, in the case of Pike's Peak, and to 

 14,421 feet at Mount Elbert. All geomet- 

 rical conditions subsisting in the triangu- 

 lation are satisfied by adjustment, inclu- 

 sive of the required accord of the base 

 lines, so that the same length for any given 

 line is found no matter from what line 

 one may start. This involved much heavy 

 work ; for instance, the triangulation ad- 

 justment between the Salina and the El 

 Paso base demanded the simultaneous 

 solution of ninety-nine normal equations 

 (with as many unknowns). In addition 

 the figures required the evolution of a 

 correction to each of the two hundred and 

 twenty-five observed directions. 



Coming to the astronomical measures, 

 we have distributed over or near the arc 

 one hundred and nine latitude stations, oc- 

 cupied almost exclusively with zenith tele- 

 scopes ; there are, also, seventy-three 

 azimuth stations, various methods having 

 been used, and lastly we have twenty-nine 

 telegraphically determined longitudes. 

 These, of course, are of paramount im- 

 portance for an arc of the parallel. There 

 cannot be too many longitude stations in 



consequence of that great stumbling-block 

 in geodesy, the local deflections of the ver- 

 tical or plumb-line. These deflections of 

 the zenith from a normal direction have 

 been divided into two groups: Those 

 which are regional or manifest themselves 

 with marked common features over thou- 

 sands of square miles, and those which are 

 quite local and greatly depend upon the 

 surface features immediately surrounding 

 them. 



These deflections, even in level coun- 

 tries, average about 2.5"; but in moun- 

 tainous regions this deflection is greatly 

 surpassed. Thus we find for deviation of 

 the plumb-line at Patmos Head station 

 12" to the north, at Colorado Springs 25" 

 to the west, at Salt Lake City about 17", 

 and at Ogden about 15" to the east, at 

 Genoa Station, Nev., nearly 29" to the 

 west, the quantities depending to some 

 extent on the spheroid of reference; but 

 their amount and direction are obviously 

 well accounted for by the position of the 

 known attracting masses. In connection 

 with this, continental attraction may man- 

 ifest, itself and be recognized by the as- 

 tronomic amplitude of the longitudes of 

 extreme stations of a long arc being in 

 excess of the corresponding geodetic 

 amplitude. The matter cannot be further 

 pursued here in detail, but it may suffice 

 to state that the average curvature of the 

 equipotential surface of the geoid along 

 the parallel of 39° approaches for about 

 four-sevenths of the arc from its eastern 



A NOTE CONCERNING THE CHART ON THE 

 OPPOSITE PAGE 



The value of the Chart of the World, shown on the opposite page, is that the areas of all 

 parts of the world appear in true proportion. 

 The projection is the invention of Professor C. B. Mollweide, in 1805 ; numerous 

 applications of it were made by Babinet in 1857, which gave rise to his name being attached to it 

 under the designation Babinet's homolographic projection. It is an equal surface projection in 

 which the entire surface of the earth is represented enclosed within an elliptic outline, whose major 

 and minor axes represent the equator and central meridian respectively, with a ratio of 2 to i. 

 The parallels are straight lines, and the meridian, ellipses, and each zone or subdivision of the pro- 

 jection is in due proportion to the corresponding area on the sphere. The distances of the parallels 

 from the equator-line are computed from the formula characteristic of the projection. C. A. S. , 



