474 THE LIFE OF JAMES D. FORBES. [CHAP. 



than they have at present. Hence, what we see of 

 double stars, and of groups of stars, suggests two ques- 

 tions, one purely geometrical (to which I alluded in 

 Section A), the other mechanical (which has only 

 occurred to me definitely since the meeting of the 

 Association). 



' 1. Are the stars of any individual group excessively 

 near one another as compared with their distances from 

 the earth ? 



' 2. Are the vis vivas of different stars of a group 

 estimated with reference to the centre of gravity of the 

 group, so small that they will always be excessively near 

 one another (unless disturbed by a body foreign to the 

 group) as compared with their distances from the earth ? 

 ' The first question gives rise to some very curious 

 geometrical considerations, which I think (so far as I 

 know of what has been written) have been overlooked 

 by those who have entered upon the probability calcu- 

 lations. Let us for a moment conceive that the 

 individuals of a double star subtend an infinitely small 

 angle when seen from the earth. Then, either the stars 

 must be close to one another, or they must be in a 

 line passing through the earth. Now, in general, any 

 arrangement that may be made of points in space of 

 three dimensions will be such that no two lines, each 

 joining two of them, will intersect. In a particular ci 

 two of these lines may intersect, but there may be no 

 other two which do so. It will be only in more and 

 more special cases that there are more intersections 

 than that of one pair of lines, or that there are three or 

 more of the lines which have a common intersection. 

 Question 1 then resolves itself into two : Is there any 

 position in the universe where n (the number of double 

 stars usually reckoned) lines joining pairs of stars (of 

 such and such brightness as seen from that position) 

 intersect, or so nearly intersect that they all pass through 

 a space of which the lineal dimensions are small com- 

 pared with the distances and the difference of the dis- 

 tances of the two individuals of each pair from that 



