1814.] Imperial Academy of Pelershirgh. ^97 



express the square Roots of whole Numbers; and on their use in 

 researches imo the Factors of Numbers. By C. F. Kausler. P. 95. 



10. Demon.-tration of an Algebraic Theorem. By F. T. Schu- 

 bert. P. 124 This is a theorem given by Newton in his Uni- 

 versal Arithmetic, without deu)onstration, under the article Trans- 

 mutation of Equations. It is as follows : — Suppose an equation of 

 the nth degree oi this form (A) o = x' — «, jc""' — a, x""* — 



.... — c„ x""" — .... — G, x"""' — — o,_, X — a„; the 



roots of which are a, 0, c, . . . . w, n ; and let the sum of all the 

 nth roots a + d + c + . . . . + m + n = R, and the sum of all 

 their squares a- + b^ + . . . + «^ = R, ; in like manner let the 

 sum of the rth power of all these roots a'' + b'' + ....«" = R , 

 then (B) R, = o, Rv .. , + «» Rj _ , + . . . . + a„ R^ _ „ + .... 



+ a, .. , R, + r. o,. 



11. Determination of the Radius of Osculation in Lines of 

 Double Curvature. By S. Gouriev. P. l.?0. 



12. A Dissertation on the progressive Motion of Bodies, both 

 free through an indeterminate Space, and not free but confined to 

 the Surface of Curves. By S. Gouriev. P. 138. 



13. Remarks on some Equations of the Moon. By F. T. Schu- 

 bert. P. i7J. 



14. Calculus of the Oppositions of Uranus and Saturn, observed 

 at St. Petersburgh in 1808. By F. T. Schubert. P. 18/. 



15. Calculus of the Observations of the great Comet of 180/, 

 made at the Observatory of St. Petersburgh. By F. T. Schubert. 

 P. 213. 



16". Meteorological Observations made at St. Petersburgh during 

 the Years 1801 and 1802, by the late Mr. Inochodzovv. Arranged 

 by Basil Petrow. P. 224. 



17. Astronomical Observations, made at the Observatory of 

 Mitau, in the Government of Courland. By Guill. Theoph. Fred. 

 Beitler. P. 248. 



18. On the Genus Musc'icapa, in the order of Passeres. By N. 

 Ozeretskovsky. P. '2'J*J. This is a general paper, in which the 

 author points out various defects in the arrangement of this genus, 

 and that several birds are placed in it that do not possess the charac- 

 ters by which it is distinguished. 



19. A Description of twenty Species of Grasses not generally 

 known. By M. Sprongcl. P. 287. The grasses described, and 

 many of them figured, in this paper, are the following: — 



Muhlenbergia crccla, 

 Muhlenbergia diffusa, 

 Digitoria pilsosa, 

 Panicum dichotomum, 

 Panicum laxiflorum, 

 Panicum virgatuni, 

 Panicum clandcstinura, 

 Aristida dichotoma, 



Agrostis tremula, 

 Agrostis cinna, 

 Limnetis cynosuroides, 

 Aira pensylvanica, 

 Aruiido pygmsea, 

 Rottbilllia muricata, 

 Poa racemosa, 

 Poa sudctica, 



