A. MATHEMATICS AND ASTKOXOMY. 33 



of stars, at equal zenith distances, was proposed and applied 

 by him in 1848, at the Naval Observatory in Venice, but has 

 in later times been widely adopted, and is known in America 

 as Talcott's method. Admiral Von Wullerstorff-Urbair shows 

 that the same system may be applied with accuracy to the 

 determination of time; and quotes a note from Palissa, at the 

 Naval Observatory at Pola, who says that this method was 

 applied by him in December, 1873, and gives results whose 

 value is equal to those deduced from the transit instruments. 

 The method is specially to be recommended to travelers, 

 since by means of the same theodolite both time and latitude 

 may be accurately determined. The formulae given by Von 

 Wullerstorff-Urbair seem scarcely so convenient in practice as 

 those taught for many years past by Dollen and the Russian 

 geographers, and which were published in full some years 

 ago by Smysloff. "Mitth." Austrian Hydrogr.Off^W.^ 129. 



THE COMPUTATION OF THE AREAS OF IRREGULAR FIGURES. 



There often occurs a necessity for determining from a 

 drawing the superficial contents of planes bounded by curved 

 lines. This is the case, for instance, in the determination of 

 the superficial contents of the water-lines of vessels. In such 

 computations, ordinarily, we employ somewhat rude approx- 

 imations, as in Simpson's or Stirling's methods. The latter 

 author has given two methods: the first depending upon the 

 principle that the portion of a curved line, between any two 

 ordinates, may be considered as a portion of a parabola of 

 the second degree. In the second method, given by the 

 same author, the curve is considered as a portion of a para- 

 bola of the third degree. These three methods may be sup- 

 plemented by other methods depending upon formulae devel- 

 oped by Gauss, Cotes, and others. But in general all these 

 methods are somewhat more difficult of application than that 

 known as Simpson's, which is for more frequently employed 

 than any other. A very decidedly better way has been pro- 

 posed by the Russian mathematician, Tchebitcheff, whose 

 method is simpler than either of those just mentioned, and, 

 although less accurate than that of Gauss, is more accurate 

 than those of Cotes, Stirling, and others. Indeed, a greater 

 simplicity of application than this method offers is scarcely 

 to be demanded, and its accuracy surpasses the ordinary 



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