34 ANNUAL RECORD OF SCIENCE AND INDUSTRY. 



necessities of the arts. In order to represent as closely as 

 possible a curved figure by a series of polygons, Tchebit- 

 cheff takes six terms of the integral formula corresponding 

 to six ordinates selected in the following manner: Let the 

 surface be inclosed by the curved line A B C D, and the 

 straight line A D: subdivide A D at E. The one half of 

 A E, multiplied by the measured values of its ordinate, is 

 then to be set off on either side of E, thus marking the places 

 where new ordinates are to be measured, which are them- 

 selves to be multiplied by one half of A E; the products 

 again set off on either side of E, and then a third pair of or- 

 dinates measured. In this way three pairs, or six ordinates, 

 are obtained, whose values have a certain relation to each 

 other and to the given curved line. The desired area is found 

 by multiplying one sixth of the sum of these ordinates by the 

 length of the line A E D. Other methods generally give 

 results somewhat less than the truth. The method of Tche- 

 bitcheff generally gives larger results than the others. 

 " Mittheilungen" Austrian Itydrogr. Office, 1874, p. 530. 



ASTROXOMICAL WORK AT CORDOBA. 



In his annual report, as Director of the National Observa- 

 tory of the Argentine Republic, for the year 1874, Dr. Gould 

 states that the three principal undertakings of that observ- 

 atory, viz., the uranometry, the zones, and the smaller cata- 

 logue of stars, have satisfactorily advanced toward their 

 completion. An inevitable delay having occurred in the 

 publication of the first mentioned of these works, the op- 

 portunity was seized to revise some portions of it a revision 

 which indicates that the accuracy attained is quite commen- 

 surable with Gould's original hopes and expectations. Hav- 

 ing secured the necessary funds, it is now expected that in 

 the course of the present year the publication of the charts 

 will be completed. These will be thirteen in number, compris- 

 ing the whole of the southern heavens. The total number of 

 stars whose positions and magnitudes will be given will be 

 not far from 8500. With reference to the zones of stars, he 

 reports that some 12,500 additional observations have been 

 made, bringing the total number up to 82,537. It is not 

 improbable that the number of observations yet to be made 

 will swell the total to more than 100,000; which work he 



