212 Dr. Herschel on the Quantity 
inclination of 45 degrees. For in this case the chance of a 
greater or smaller deviation would be equal ; and when a 
number of stars are taken, the deviations either way might 
then be supposed to compensate each other ; but what is 
chiefly to our purpose, not only the angle of 45 degrees, but 
also any other, that might be fixed upon as a proper one to 
represent the mean quantity of sidereal motions, would lead 
exactly to the same result of the solar velocity to be investi- 
gated. For if the velocities of any two stars were equalized, 
when their motions are supposed to be perpendicular to the 
visual ray, they would be as much so when they make any 
other given angle with it ; and it is the equalization or ap- 
proach to equality and not the quantity of the velocities that 
is the spirit of this method. I have only to add, that an 
equalization of the solar motion with that of any star selected 
for the purpose may be had by a direct method of calculation, 
and will therefore be of great use in settling the rate of the 
motion to be determined. 
It must be evident from what has been said, that a certain 
mean rate, or middle rank, should be assigned to the motion 
of the sun, unless very sufficient reasons should induce us to 
depart from this condition. To obtain this end must conse- 
quently be our principal aim ; and if we can at the same time 
bring the sidereal motions to a greater equality among each 
other, it will certainly be a very proper secondary consi- 
deration. 
There are two ways of taking a mean of the sidereal 
motions, one of them may be called the rate and the other 
the rank. For instance, a number equal to the mean rate of 
the six numbers, 2, 6 , 13, 15, 17, 1 g, would be 12 ; but one 
