USED POR INDICATING ALTITUDES. 



Comparisons of the American standards with new French standards, recently pre- 

 sented to the United States by the French government, are still in progress. 



For the present, however, it seems best to adhere to the value of the metre, ex- 

 pressed in American standard inches, adopted by the Coast Survey as given above. 

 From this value the separate tables, which will be found below, for the reduction of 

 the American yard and foot, were computed. 



5. The Klafter of Vienna is a silver line let into a prismatic bar of iron, on which 

 the length of the klafter was engraved by Voigtlander. It has its normal length at 

 13 Reaumur, and was declared by law, in 1816, the standard Klafter of Vienna. 

 On the same silver line the French toise is marked, from the standard toise sent, in 

 1760, by La Caille and La Condamine to the Observatory of Vienna. According to 

 a recent and very careful comparison by Struve (Mem. of the Austrian Acad., Vol. 

 V., I. p. 117), the value of the klafter of Vienna is 0.9730317 toise du Perou. 



6. The Prussian Foot is marked on a standard iron bar, 3 feet long, made by Pistor 

 in Berlin ; it is a standard at the temperature of 13 Reaumur. The length of the 

 Prussian foot was declared by law to be = 139.13 lines of the toise du Perou. 



7. A Mexican Vara, the standard length, brought from Mexico at the close of the 

 war, by Major Turnbull of the Topographical Engineers, was presented to the Office 

 of Weights and Measures. This standard was made by soldering sheet-brass upon 

 the tinned surface of an iron bar. A careful comparison of its length with the Amer- 

 ican standard was made under the direction of Prof. Bache, which gave its length 

 to be = 32.9682 inches at 58.7 Fahrenheit, or 32.9680 when reduced to 62 Fah- 

 renheit. 



The relation of that particular Mexican standard to the Spanish standard not being 

 known, it was thought better to adopt, for the present, the value of the Spanish Vara, 

 and of its third part, the Castilian foot, found in Thionville, Traite des Poids et 

 Mesures, &c., in Balbi's Abrege de Geographie, viz. 1 vara = 0.847965 metre. 



From the fundamental equations indicated above have been derived all those which 

 have been used for computing the reduction tables given in the Appendix. At the 

 head of each table will be found the value from which it was computed. 



The tables are so arranged as to give directly the reduction of any whole number 

 not exceeding three or four figures, and larger numbers within the limits needed for 

 altitudes, by means of a single addition. 



Example. 



Reduce 25,351 English feet into metres. 



In Table XVI., on the line beginning with 25,000 and in the column headed 300, 

 take for 25,300 = 7711.30 metres. 



In the second part of the table, on the line beginning 

 with 50, and in column headed 1, take for 51 = 15.54 " 



English feet 25,351 = 7726.84 " 



The fractions, which seldom occur, are treated as whole numbers, taking care only 

 properly to move the decimal point. 



Tables XL. to XLIV. will be found convenient for converting fractional parts of a 

 toise or of a foot into each other. 



D 113 



