( 464 ) 



Let 2 ^' and 2 </; be the angles formed by the common chord 

 of the circles, which define M, as seen from their respective centres, 

 then 



M=\ \{2tp' - sin 2<f') 4- a' {2(p — sin 2(f)\ 



fj" -\- y,^ — I 



sin (f ■= a sin (p ; cos (p 



2xo' 



üt 



tp' is always <^ - ; ^ may become = üt, in the case that the smaller 



Li 



disc is seen projected whollj' within tiie larger one. 

 Furthermore : 



^"^ z=. r"^ {V — cos"^ ^shi^ i) ; (i z=i to -\- v . 



These formulae agree with those of Dr. Myers. 



Computation of f. 



x^ y^ z^ 

 The equation of the cylindre, enveloping the ellipsoid 1 1 = 1 



the axis of which makes the angles y', /, i|' with the A-, 1^- and 



.^-axis, is : 



fcos^w cos^ 1 cos ^ tiA /a-^ y'^ z^ \ 



V a' ' b' ^ c' J ya' ^ b' ^ c' J 



X cos (p , y cos / z cox \p 

 ~~a^ ^ b-" ^ 



The surface of an orthogonal section of this cylindre is : 



Si =: rr [/a^ b^ cos^ if? -j- 6" c^ cos^ (p -\- c^ a' cos'' •/• 



or, putting 



_ _ 1 _ 



Q ' 



jr , q' — 1 



£i = ~ [/I — 8' cos'' If; , £' = . 



q q' 



1 



The semi minor axis of the section is — , therefore the semi major 



9 

 axis 



ƒ = 1/ 1 — s^ cos^ tfj ; cos^ xp = cos^ [i sin'' i ; 



because ifj is the angle between the major axis of the ellipsoid and 

 the visual line. 



In the computation of ƒ Dr. Myers, instead of taking the instan- 

 taneous projection of the ellipsoid on the sphere, takes the intersection 

 of the ellipsoid with a plane through the centre, at right angles to 

 the visual line. In his opinion this is allowable "wenn die Abplattung 



