404 Prof. Forbes on the evidence for a Physical Connexion 



leisure, and studied Mitchell's arguments, I am confirmed in 

 my conviction of the fallacy of the numerical estimates of the 

 so-called proof of the physical connexion of double stars. I 

 also believe that the refutation of the fallacy (if such it be) is 

 of great importance; first, because any abuse of the mathe- 

 matical sciences, such as to give definite demonstrations and 

 results where no such demonstrations and results can, in the 

 nature of things, be legitimately attained, tends to weaken our 

 confidence in mathematical conclusions generally; and se- 

 condly, and still more strongly, because the evidence for final 

 causes is so peculiar, and its discussion so confessedly difficult 

 and delicate, that all attempts to base the proof of design on 

 strictly a priori and geometrical grounds, and to estimate it 

 numerically, should be received with scrupulous caution. 

 These are questions in regard to which our suspicions cannot 

 be too sensitively awake. The natural philosopher, in par- 

 ticular, who must rely at every instant on the certainty of 

 mathematical proof, must not harbour even a doubt of its 

 accuracy without probing the matter to the bottom. After 

 doing so, should he remain unsatisfied, he must feel it a duty 

 to communicate to others the result at which he has arrived, 

 for correction, if need be, but in any case regardless of the 

 authority of names which may be arrayed on the other side. 

 [8.] Mitchell's argument, .stated in the Philosophical Trans- 

 actions for 1767, to prove the proposition that when two or 

 more stars appear very near one another in position they are 

 not merely apparently but really so, "either by an original act 

 of the Creator, or in consequence of some general law, such 

 perhaps as gravity," is to the following effect. Let a star be 

 given in (apparent) position, and call it A. Let other similar 

 stars, B, C, D, &c, be "scattered by mere chance as it might 

 happen " over the heavens. ct Now it is manifest," says Mit- 

 chell, " upon this supposition, that every star being as likely 

 to be in any one situation as another, the probabilit}' that any 

 one particular star should happen to be within a certain di- 

 stance (as, for example, one degree) of any other star would 

 be represented by a fraction whose numerator would be to its 

 denominator as a circle of one degree radius to a circle whose 

 radius is the diameter of a great circle (this last quantity being 

 equal to the whole surface of the sphere), that is, about I in 

 13131." This ratio expresses the probability (according to 

 Mitchell), that if there were but two stars in the heavens, they 

 should be found (supposing them placed " at random ") within 



1 Q I n A 



1° of one another, and will express the probability that 



they shall not be so near. 



