A. MATHEMATICS AND ASTRONOMY. 35 



then (March, 1875) hoped would be completed by the end 

 of July, 1875. The greatest hinderance to the prosecution 

 of this undertaking consists in the difficulty of securing the 

 services of an adequate number of trained astronomical com- 

 puters. 



Of the large number of stars observed in these zones, a 

 small portion have been selected as fit to form a special 

 catalogue of brighter stars. This catalogue includes nearly 

 5000 stars, and some 12,400 observations upon these were 

 made during the year. Dr. Gould adds that not one hour 

 of unclouded sky between sunset and midnight was lost by 

 his assistants during the whole time of his recent visit to the 

 United States, notwithstanding that other observations were 

 also going on by night, and continual computations by day. 

 The equatorial telescope has been as busily employed as the 

 meridian circle. Coggia's comet was observed from the 27th 

 of July to the 18th of October. Standard Cordoba time has 

 been given regularly from the observatory without a single 



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case of failure; and latterly the exact Buenos Ayres time 

 has been telegraphically transmitted to that city for the 

 convenience of the shipping. Meteorological observations 

 have been conducted and reported regularly to the Mete- 

 orological Office. Dr. Gould's corps of assistants has con- 

 sisted of four persons, with occasional aid from others com- 

 petent to act as copyists and computers. The assiduity of 

 the labors of all concerned is abundantly testified to by the 

 record of their results. Annual Report, March, 1875. 



PEOPEETIES OF THE TETE^EDEOX. 



In an exhaustive memoir by Dostor on the application of 

 determinants to certain problems in solid geometry, we find 

 the following theorems relating to tetraedrons: The sine of 



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a triedral angle is equal to the product of the sines of two 

 of its faces, multiplied by the sine of the inclosed diedral 

 angle. Again, in every tetraedron each face is equal to the 

 sum of the products which we obtain by multiplying each 

 of the three other faces by the cosine of its inclination to 

 the first face. And, again, in every tetraedron the faces are 

 to each other in the same proportion as the sines of the 

 supplements of the opposite triedral angles. The volume 

 of the tetraedron is equal to one sixth of the product of three 



