132 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
From this equation we soon find by familiar processes the 
lengths and directions of the principal axes. 
As to the question, Which of the alignment curves should be 
used in geodesy? I observe that between two intervisible points on 
the terrestrial spheroid the difference between the course of these 
curves is so extremely minute that they are practically identical ; 
we can use then that method of tracing which is most convenient. 
For the distance of non-intervisible stations I consider the brachis- 
thode the geodetic line as heretofore, because 1st, the diorthode be- 
comes impracticable; and 2d, it cannot be divided into portions 
which are themselves diorthodes. As Assistant Wm. Eimbeck, of 
the United States Coast and Geodetic Survey, suggested to me, the 
diorthode proper cannot even be traced between very distant 
stations, which are intervisible only from very elevated positions, 
such as high peaks or the usual wooden structures. Thisled me to 
consider a new class of alignment curves—the apparent horizon 
alignment curves. The a. h. pro-orthode would be the locus of all 
points for which the tangent cuts the normal at the forward end; 
while the a. h. diorthode is a curve, at any point of which a tangent 
to the surface, which passes through the normal at one end, also 
passes through that at the other end. The equation (3) being 
adapted to these changed conditions will furnish also the equations 
of these curves; and I have thus found that the a. h. diorthode on 
an ellipsoid has an intersecting surface of the fourth order. 
Messrs. HARKNEsS and DooLirrLE made remarks on this paper. 
Mr. Asapu HAtt then made a communication on 
THE DETERMINATION OF THE MASS OF A PLANET FROM OBSERVA- 
TIONS OF TWO SATELLITES. 
[ Abstract. ] 
M. Struve recommends that the position angle and distance of one 
satellite from another satellite be measured, instead of referring the 
place of each to the center of the primary planet; and a series of 
such measurements on satellites of Jupiter has been begun under 
his direction at Pulkowa. ‘These observations are found to occupy 
one-third the time, and are considered two or three timés as accurate 
as those where the planet is used. The most important advantage 
of the new method is its freedom from the unknown constant errors 
attending the old, due to the great difference in size and bright- 
