368 Prof. Draper on the Chmiic^l4-ction of Light. 



would be interrupted at some uioye, be;fore^ttie eild of .the- , game. 

 It would occupy too much sp£^ce to investigate (as we casdy 

 inight) tlie conncpon between i' j^nd /, It is enough to say that 



i' will be ^i^eatetthah"^,^ fcut iat lettst'itet' ^fdfeter' tha-^^'.' pH 



now the a priori probability that a given game would end with 

 the observed checkmate, and will generally (not necessarily) be 

 greater than the value of ;> in the former case. It must be small,^ 

 though it can never =0. If the arrangcnient be irregular, but 

 a commoH case of vheckmate, then, a being! always small, w«,h^ye 



-also small, and G very nearly =1. Tf the arrangcmeiTt be 



symmetrical, or remarkable in any way, and at the same tipeiaa; 



uncommon checkmate, then - is large and G is siuall. ~"^ )noq«}i 



24. We might pursue this problem much further into detstil; 

 but I hope it has sufficiently appeared that " the science of nura^" 

 bers-"' does not refuse "its aid to estimate the arithmetical force 

 of such arguments," if the assertion of such refusal be meant to 

 imply either an inaptitude in numbers to express the quantity of 

 our belief, or an inaptitude in symbolical forms to express the 

 laws according to which our belief is determined by phsenomena. 

 I must defer to a future occasion some further illustration of the 

 agreement between the mathematical theory of probabilities and 

 common sense, together with an examination of the mode of ap- 

 ])lying the precedmg principles to the question of the grouping 

 of stars ; to which I hope to add a brief inquiiy into the validity 

 of the method of least scpiares. At present I will only add in 

 conclusion, that the most important general result of the inves- 

 tigation, so far as it has been here carried, is this : that the pro- 

 babilities of causes, estimated a posteriori, will always depend, 

 not upon the absolute values of a priori jii'obabilities, but upon 

 their compjarative values, or the ratios whicli they bear to one 

 another; which ratios may be iinite and determinate, although 

 their terms, taken separately, may be intinitely small. 

 Oxford, Jan. 23, 1851. 



XLVIII. On tlte Chemical Action of Light. By John W. Draper, 

 M.D., Professor of Chemistry and Physiology in t/ie University 

 of New lor^*. j ■«!) oh vino Jen iKrlt ^§ri(jB->ibm ■iinxjloY 



THE general discussion'of 'die proMein'of 'tlie clietlifcarad'tion 

 of a ray of light involves the following considerations :— 

 1. In what manner does the ray act, and what are the changes' 

 it undergoes? ' , 



* Communicated bv the Author. ,,i 



