248 Dr. Herschel on the Direction of the 
to deprive Arcturus and Sirius of real motions, in order to give 
one of the same nature to our third star : and indeed to every 
star that has a proper motion which does not tend to the same 
parallactic center as the motions of Arcturus and Sirius. 
This objection is perfectly well founded, and I have given 
the above calculation on purpose to show that, when we are in 
search of an apex for the solar motion, it ought to be so fixed 
upon as to be equally favourable to every star which is proper 
for directing our choice. Hence a problem will arise, in our 
present case, how to find a point whose situation among three 
given apices shall be so that, if the sun's motion be directed 
towards it, there may be taken away the greatest quantity of 
proper motion possible from the given three stars. The intri- 
cacy of the problem is greater than at first it may appear, 
because by a change of the distance of the apex from any one 
of the stars, its parallactic motion, which is as the sine of that 
distance, will be afieeted ; so that it is not the mere alteration 
of the angle of direction, which is concerned. However, it 
will not be necessary to enter into a solution of the problem ; 
for it must be very evident that a much more complex one 
would immediately succeed it, since three stars would cer- 
tainly not be sufficient to direct us in our present endeavour to 
find the best situation cf an apex for the solar motion ; I shall 
therefore now leave these stars, and the apices pointed out 
by them, in order to proceed to a more general view of the 
subject. 
We have already seen that the brightest stars are most 
proper for showing the effect of parallax, and that in our 
search after the direction of the solar motion, our aim must be 
to reduce the proper motions of the stars to their lowest 
