between Stars forming Binary or Multiple Groups. 411 



most probable result; and yet the improbability of that result 

 (though less improbable than any other given result) may 

 be very great. At the game of whist the most probable result 

 is, that each player should have as nearly as possible an equal 

 number of cards of each suit in his hand; and if the cards 

 admitted of equal subdivision, an exactly equal number: yet 

 such a result is manifestly most improbable. Its very occur- 

 rence in all the four hands would provoke the suspicion of an 

 interference with the common course of chance, at least as 

 much as (let us say) the total absence of one suit in one hand 

 would do. If we then were witnesses of only a single game, 

 how preposterous would be the idea of subtracting the num- 

 bers of any suit in any hand from the " most probable num- 

 bers," and declaring that the difference is a proof that the deal 

 has not been fair ! * 



24. I have thought it worth while to test a little by simple 

 experiment the differences to which " mere chance " gives 

 rise in the grouping of bodies dispersed over a surface, by a 

 method of " random scattering " which I conceive to be as 

 nearly as possible analogous to Mitchell's idea of chance as 

 affecting the placing of the stars. I had referred in my letter 

 in the Philosophical Magazine to the pretty fact noticed by 

 Mr. James Naysmith, that the sparkings of a brush loaded 

 with white paint produced a distribution of spots on a dark 

 ground which represented exceedingly well the general aspect 

 of the grouping of the stars, including many double and mul- 

 tiple specks ; and I quoted this partly as an illustration, and 

 partly as an argument against the assumed improbability of 

 producing such combinations by chance. The experiment 

 having been objected to as not free from causes of doubt, I 

 have made some trials in the following way. I placed a chess- 

 board, having, as usual, sixty-four squares, on the floor, and 

 I provided a large sieve into which I put a quantity of grains 

 of rice, which did not fall through the sieve until it was some- 

 what shaken. I then shook the sieve at a considerable height 

 above the chess-board until it was pretty well scattered over 

 with grains. And the "random scattering" of these grains 

 was much increased by the circumstance, that the board was 

 so elastic that every one of the grains rebounded from the 

 surface and fell once or oftener, so that their mutual posi- 

 tions were thus as much as possible interchanged. 



25. The following diagrams contain the results of five expe- 

 riments, the number of grains which fell on each of the sixty- 

 four squares being counted and registered. Only these five 

 experiments were made; none have been rejected. 



* Such an argument has actually been used to prove the physical con- 

 nexion of double stars. 



