252 THE POPULAR SCIENCE MONTHLY. 



made, another set of observations is begun with the field-glass inverted. 

 The observer places the larger end of the glass toward him, and turns 

 the glass upside down around the axis, so that by this movement the 

 smaller end of the glass comes to stay near the observer. "With the 

 glass thus inverted observations are repeated. The moving around of 

 the circle and inverting of the glass are intended to avoid any errors 

 which might be caused by faulty construction of the instrument, as, 

 however costly and delicate the instrument may be, human skill can 

 not make it mathematically precise. 



When the angles have been measured, all the calculations have to 

 be made for each triangle and for each polygon separately. Neither 

 the work of mensuration in the field nor the calculations are what 

 would be called work done by steam or by electricity. The season 

 for the field observations being necessarily limited, each observer can 

 not cover more than two or three first-class stations each year, as 

 much as two months being often spent for one station alone when 

 the climatic conditions are unfavorable. Angular observations for sci- 

 entific purposes can not be executed in all weathers and at all hours. 



Geodetical triangulation can be more successfully executed in mount- 

 ainous regions, where the peaks act as natural observatories, and noth- 

 ing interferes to prevent distant points being seen with the glass. Be- 

 fore the measuring of the angles actually begins, the net has to be laid 

 out, the stations have to be visited, the most suitable point to be chosen 

 and marked with some permanent sign. Stone blocks are used for this 

 purpose, in the center of which a square metallic tablet is laid. The 

 intersection of the two diagonals of the metallic tablet is the geodet- 

 ical point. A small pyramid is sometimes placed in lieu of the tablet. 

 In order to see the exact spot at a distance, a pyramid of wood or other 

 material is built over the same, and a metallic rod, similar to a light- 

 ning-rod, situated in an exact perpendicular to the " point," is placed 

 on top of the pyramid. This rod acts for all practical purposes as the 

 real spot when the observer is at a distance. For stations situated in 

 the plains, church-steeples, towers, or the tops of high buildings are 

 used, and a given spot on these is chosen as the geodetical point, care 

 being taken to choose only such points as are likely to be permanent 

 for future reference, and are not liable to get out of the perpendicular. 



The carefully executed observations described in the foregoing 

 have to be made so accurate in order to avoid errors, which, although 

 they may be allowed up to a certain limit when a topographical survey 

 is alone being made, can not be allowed when the triangulation has to 

 be made use of for purposes of getting at the real dimensions of the 

 globe. An error which may be neglected on an area of a few hundred 

 square miles is not permissible, and would be too large if multiplied to 

 the whole length of the earth's meridian. 



The accompanying illustration will serve to show what is a geodet- 

 ical or trigonometrical net of triangles. It is not an imaginary net, but 



