279 



and c =: b. Their angle 2 F is 'snuxll or very small, soinetinies these 

 ainphiboles are nearly uniaxial and are connected with the distinctly 

 biaxial ones in zonal crystals. 



These aniphiboles sometimes are intergrown with biotite or aegi- 

 rine and also with a bluish green amphibole, in which the plane of 

 optic axes is also normal to the plane of symmetry, if they have 

 the same crystallographic orientation as the brownish green amphi- 

 boles. In sections parallel to (100) of the latter ones, the prism axis 

 is parallel to the fast ray in the bluish green amphiboles, whilst in 

 sections parallel to (010) it is nearly parallel to the slow ray. 



From the facts, which ha\e been mentioned above, it is evident, 

 that amphiboles, in which the plane of optic axes lies in the plane 

 of symmetry, very probably occur at the same locality. 



Astronomy. — "On canonical elements." By Prof. W. ue Sitter. 



In the developments of the planetary theory each of the three 

 anomalies has been used as independent variable : the mean anomaly 

 by Lagrange, the excentric anomaly by Hansen and the true anomaly 

 by Gylden. All systems of canonical elements, however, which have 

 been in use up to the presejit time, are only modifications of the 

 system of Delaunay, which is based on the use of the ??iea?i anomaly. 



Recently ^) Levi-Civita has proposed a new system of elements, in 

 which the excentric anomaly appears instead of the mean anomaly. 

 Almost simultaneously '*) Hill has called attention to another system 

 in which the true anomaly appears as one of the variables. The 

 method by which Hill arrived at his system is, however, very 

 different from that by which the systems of Delaunay and Levi-Civita 

 are developed. The object of the present paper is to show how these 

 three systems, as well as others, can be derived from the same 

 fundamental principle. 



Let ci'i be the co-ordinates of a body i\ and yi=: m — the com- 



dt 



ponents of its momentum (i = l, 2, 3). The equations of motion 

 are then 



dsBi dH dyi dH 



dt dyi dt dxi 



1) T. Levi-Civita. Nuovo sistema canonico di elemenli ellittici. Annali di Mate- 

 matica, Ser. Ill, Tom. XX, p. 153 (Aprile 1913). 



~\ G. W. Hill. Motion of a system of malerial points under the action of 

 gravitation. Astronomical Journal, Vol. XXVIl, Nr. 646-647, p. 171 (1918 April 28). 



