F. GEOGRAPHY. 251 



the relief of the soil. The probable error of the angles ob- 

 served by himself is 3 J seconds, while the error of the trian- 

 gles observed by Tranchot is 10 seconds. The primary trian- 

 gulation conducted by Perrier includes G7 stations, extending 

 over an arc of 5 in latitude. Levelings have been con- 

 ducted throughout the whole island. The discordances be- 

 tween the levelings that have been independently conducted 

 up to the principal points are generally small, and never ex- 

 ceed 10 feet, even for differences of level as great as 8000 

 feet. G B, LXXVIIL, 1570. 



ERRORS IX TRIGONOMETRICAL LEVELINGS. 



Baeyer has published a thorough investigation into the 

 question of the influence of local deviations of the plumb-line 

 upon the accuracy of leveling operations. These local de- 

 viations, as is well known, exist in all parts of the earth, and 

 are generally specially notable in mountainous countries 

 at times amounting to a large angle, so that the plumb-line 

 can no longer be considered as truly vertical ; and their or- 

 igin, although not always definitely known, is yet probably 

 always to be attributed to the attraction of mountains, the 

 absence of attraction in the case of cavities within the earth, 

 and to the sometimes greater density of the strata under- 

 neath the ocean. Having deduced a general mathematical 



CD CD 



formula applicable to all cases, Baeyer concludes that a level- 

 ing is not strictly reliable unless it has been proved either 

 that no local deviations of the plumb-line exist, or unless the 

 existing deviations have been properly allowed for by the 

 formula given by him. In applying this formula to a special 

 case of accurate measurements in Germany, Baeyer shows 

 that, in a horizontal distance of about eight miles, and a ver- 

 tical altitude of one thousand feet, an error of half a foot is 

 involved ; and that again, in another instance, in a distance 

 of nine miles, and a vertical altitude of fifteen hundred feet, 

 an error of eight tenths of a foot is to be attributed to the 

 effects of local deviations. The result of this investigation 

 will be to fix more definitely the standard sea level to be 

 adopted by all nations as the reference plane to which to re- 

 fer their geodetic measurements. Applying Baeyer's formula 

 approximately to what may be assumed to be the deviations 

 of the plumb-line in the interior of the American continent, 



