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Two similar, elongated revolution-ellipsoids move about their common 

 centre of gravity in elliptic orbits. We assume that the major axes 

 of the ellipsoids are continually in each other's prolongation while 

 their centres move about their common centre of gravity in obedience 

 to the laws of Kepler. Required the intensity of the light as it 

 appears to our eye, if we assume that the ellipsoids may be exchanged 

 for their uniformly illuminated projections on the sphere. 



As unit of length we take the semi major axis of the larger 

 ellipsoid (E^); as unit of brightness the maximum of /?-Lyrae. 



Further let be : 



X the semi major axis of the smaller body: 



q the proportion of the major axis to the diameter of the equator; 



ƒ the proportion of the major axis of the ellipse, which is the 

 projection of one of the ellipsoids on the sphere, to the major axis 

 of that same ellipsoid ; 



a the semi major axis of the relative orbit of the smaller body 

 (E^), e the excentiicity, v the true anomaly, /• the radius vector in 

 the true relative orbit. 



/3 the angle formed by the radius vector in the true orbit with 

 the projection of the visual line on the plane of the orbit (on the 

 further side of the sphere); this angle increases with the motion in 

 the orbit; 



(o the longitude of the periastron, counted in the same way as /?; 



i the angle between the plane of the orbit and a plane tangent 

 to the sphere; 



Q the projection of r on the sphere ; 



M the common part of two circles the radii of which are resp. 



o 



= 1 and = >c, having their centres at a distance of 9' = — ; 



). the proportion of the brightness (per unit of surface) of the 

 larger of the elliptic projections to the smaller one; 



J the apparent total light-intensity at the time t, (as seen from 

 the earth). 



As long as E^ and E^ do not cover each other, we have: 



When E^ is covered by E^ 



j=f(i ""—). 



When ^1 is covered by E, 



f XM \ 

 J—f\\ . 



