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 scientific purposes can not be executed in all weathers and at all hours.
Geodetical triangulation can be more successfully executed in mountainous regions, where the peaks act as natural observatories, and nothing interferes to prevent distant points being seen with the glass. Before 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 geodetical 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 lightning-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 geodetical or trigonometrical net of triangles. It is not an imaginary net, but
