V. MAPS, ETC. 663 



The system of lines is so disposed that it offers numerous polygons in order- 

 to establish conditions which may give greater precision to the results. 



In conformity with the instructions of the Commission appointed to carry 

 out this map, the levelling of precision will follow in general the roads of 

 communication, as railroads and bye-roads of every description. The level- 

 ling will be from the centre and double, carried out by different observers, 

 and with different instruments. The calculations will be taken from Madrid. 

 The greatest error admissible, deduced from a double levelling, is not to exceed 

 4 millimeters per kilometer, and in general will be less than 5 mm //R, R being 

 the number of kilometers. 



The general lines must be divided into independent sections, and these into 

 portions of a kilometer, with benchmarks at the extremities of the section, 

 important towns, &c. 



In August 1871, the levelling of the line between Alicante and Madrid was 

 begun ; touching Madridejos at its base, 540 kilometers were levelled in 916 

 days, of which only 451 were useful. The number of stations verified was 

 11,782. 



The line from Santander to Madrid was levelled in 1873 in the same 

 manner, and this will determine the difference of level between the ocean 

 and Mediterranean. 



Without taking into account the datum points of the seaport towns, a 

 standard datum has been established irrespective of mean sea level. This 

 point is situated at the observatory of Madrid, although, considering its 

 geological conditions, the hill upon which it is placed does not offer the 

 securities which might be desired. Four others have been placed in different 

 parts of Madrid. 



(11.) Experiments made with the Apparatus for Measuring 

 Bases, belonging to the Commission of the Map of Spain. Madrid, 

 1859. 



The authors, Don Carlos Ibaner and Don Frutos Saavedra Meneses, were 

 appointed in 1853 to propose the system of microscopes and bars with which 

 the base of the geodesical net of the Peninsula was to be measured. They 

 went to Paris to superintend the construction of an apparatus of their inven- 

 tion, intrusted to M. Brunner. 



This apparatus principally consists of a platinum bar, which forms a 

 metallic thermometer with another of latteen ; they both rest on an iron bench 

 placed upon movable supports resting upon wooden tripods. Various micro- 

 metric microscopes are placed in the centres of graduated circles fixed in 

 other tripods, and these divide the geodesian base which is to be measured 

 into small intervals, the length of which is determined by placing the bar 

 between every two microscopes, and observing the divisions of the platinum 

 and latteen. An eye-glass and two lenses are used to establish the tripods of 

 the microscopes in the line of the base, and another glass settles the beginning 

 and end of the day's work. 



This delicate apparatus cannot be sent out of the country!; it is preserved at 

 the Geographical Institute of Madrid, as the type of all lineal metrological 

 and geodesical studies. 



After this study was made, the expansion of the bars was investigated and 

 compared with that of Borda, at the Paris Observatory, which has served as 

 the metric type of all the geodesian bases measured in France since 1798. 



The result of the studies is given in this work, and the manner of using this 

 apparatus and carrying out the calculations. 



These plates represent 



(a.) Two of the projections of the bar and level mounted upon its supports 



