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tion of the solar motion : he now proceeds to consider the quantity 

 and velocity of that motion ; and as, in the former paper, the proper 

 motions, when reduced to one direction, were called quantities, to 

 distinguish them from the velocities required in the moving stars to 

 produce those motions, so also in the present inquiry, it will, the 

 author says, be necessary to keep up the same distinction with re- 

 spect to the velocity of the solar motion. To determine this, we 

 ought to have in view the real motion of every star whose apparent 

 motion we know ; but as trials with a number of stars would be very 

 inconvenient, Dr. Herschel makes use only of the six stars mentioned 

 in his former paper, in laying down the method followed with all the 

 rest. 



He first considers the proportional distance of the stars ; for till 

 this is fixed upon, neither the parallactic nor the real motion of a star 

 can, he says, be ascertained. And as it is not sufficiently satisfactory 

 to divide the stars into a few magnitudes, and suppose these to re- 

 present their relative distances, he expresses the relative brightness 

 of the six stars already alluded to, according to the notation formerly 

 used by him for that purpose ; and from that introduces, by using 

 fractional distinctions, a more minute subdivision than has been com- 

 monly admitted. He then proposes , the following arrangement, as 

 expressing their proportional distance : Sirius I'OO, Arcturus 1'20, 

 Capella 1'25, Lyra 1'30, Aldebaran 1*40, Procyon 1-40. 



Our author next considers the effect of the increase and decrease 

 of the solar motion, and the conditions to be observed in the investi- 

 gation of its quantity. He gives a table, calculated with a view to 

 show that an increase or decrease of the solar motion will have a 

 contrary effect upon the required real motion of different stars : and 

 deduces from it, that a certain equalization, or approach to equality, 

 may be obtained between the motion of the stars, or between that 

 of the sun and any one of them selected for that purpose. These 

 calculated velocities, he says, are such as would be true, if the stars 

 were at the assumed distances, and if their real motions were per- 

 formed in lines at right angles to the visual ray ; but if the stars do 

 not move in that direction, we should still certainly have the mini- 

 mum of their velocities : and it must be allowed to be a considerable 

 point gained if we could show what is likely to be the least velocity 

 of the solar motion. Besides, if the velocities of any two stars are 

 equalized when their motions are supposed to be perpendicular to the 

 visual ray, they will be as much so when they make any other given 

 angle with it ; and it is the equalization, not the quantity of the ve- 

 locities, that is required. 



It is, Dr. Herschel says, evident, that either a certain mean rate, 

 or a middle rank, should be assigned to the motion of the sun, unless 

 very sufficient reasons should induce us to depart from this condition ; 

 and he thinks it most eligible to prefer the latter ; but says, that 

 nearly the same result will be obtained from either of the methods. 

 He adds, that if we can at the same time bring the sidereal motions 

 Q2 



