10 



NOTES AND QUERIES. 



[2°<« S. IX. Jan. 7. '60. 



celebrated Berkleian controversy about the prin- 

 ciples of fluxions : — 



"An introduction to the Doctrine of Fluxions, and de- 

 fence of the mathematicians against the objections of the 

 author of the Analyst, so far as they are designed to 

 affect their general methods of reasoning. London : 

 Printed for J. Noon .... 17S6, 8vo." 



This very acute tract is anonymous, but it was 

 always attributed to Bayes by the contemporaries 

 who write in the names of authors ; as I have 

 seen in various copies : and it bears his name in 

 other places. 



Winston, in his Autobiography (p. 425., 2nd 

 ed.), mentions a conversation he had at Tunbridge 

 Wells with Bayes in 1746. He calls Bayes the 

 successor of Humphrey Ditton, who it thus ap- 

 pears was also Unitarian. 



But the work on which the fame of Bayes will 

 rest is his paper in the Philosophical Transactions 

 for 1763, and the supplement in the volume for 

 1764. These papers were communicated after 

 Bayes's death by Mr. Richard (afterwards Dr.) 

 Price. They are the mathematical foundation of 

 that branch of the theory of probabilities in which 

 the probabilities of the future are matter of cal- 

 culation from the events of the past. Bayes 

 shows a very superior mathematical power : and 

 Laplace, who makes but slight mention of him, is 

 very much indebted to him. More justice has 

 been done by Dr. C. Gouraud, in his short His- 

 toire du Calcul des Probability, Paris, 1848, 8vo. 



"Bayes, geometre anglais, d'une grandc penetration 

 d'esprit, de'termina directement la probabilite que les pos- 

 sibilites indiquees par les experiences deia faites sont 

 comprises dans des limites donuees, et fou'rnit ainsi la 

 premiere ide'e d'une theorie encore inconnue, la the'orie 

 de la probabilite des causes et de leur action future 

 conclue de la simple observation des evenements pas- 

 se'es." 



Bayes gave more than the premiere idee : he 

 worked out a method for solving problems involv- 

 ing large numbers of cases : not so easily used as 

 Laplace's method helped by tables, but far more 

 easy than could have been expected. Accord- 

 ingly, Bayes is one of the chief leaders in the ma- 

 thematical theory of probabilities. What he did 

 was of small extent, judged by paper and print, 

 but of fundamental importance and wide conse- 

 quence : he is of the calibre of De Moivre and 

 Laplace in his power over the subject. He chose 

 to keep his researches to himself, and they would 

 probably have been lost but for Dr. Price : if 

 whom I may add that he appears as a far more 

 powerful mathematician in his explanations and 

 comments upon Bayes than in any part of his 

 own writings on his own subjects. 



I have ascertained that there is no chance of 

 any of Dr. Price's papers being in existence, at 

 least of those which have any reference to the 

 time at which Bayes was alive. A. De Morgan. 



THE THROW FOE LIFE OR DEATH. 



I want an authority for the following, recorded 

 in the Familie Magazijn for 1859, p. 271. : — 



"As King William III. of England, the Stadtholder 

 of the Netherlands, was besieging Namur in 1695, sundry 

 soldiers from his army suffered themselves to be seduced 

 by the want which reigned in the camp to go a maraud- 

 ing, though such a transgression of the martial law had 

 been forbidden on pain of death. Most of these ma- 

 rauders were caught by the country people and killed: 

 only two of them were able again to reach the camp un- 

 scathed. In the mean while, however, their absence had 

 been noticed, and without delay they were sentenced to 

 death. Already the following morning it had to be exe- 

 cuted by hanging. 



"The" morning had dawned, and the necessary prepa- 

 rations were being made to follow up the verdict. The 

 general-in-chief, however, to whom both the condemned 

 were known as brave soldiers, wanted to save one of 

 them, and thus commuted their yesterday's judgment in 

 so far, that they should have to throw at dice for their 

 life. 



" In former times it often was the custom, in the appli- 

 cation of military punishments, when the judge did not 

 desire to bring the law home upon all the delinquents, to 

 let it be decided by lot, who should be free and who 

 should suffer. And so it also happened in this case, that 

 both the marauders were led to a drum, in order there- 

 upon to cast the decisive throw. A few hundred paces 

 farther the fatal pole already stood erect, and its aspect 

 rendered the scene, so awful in itself, still more impres- 

 sive. Full of anxious expectation, a group of officers, the 

 regimental chaplain, and the executioner, silently and 

 with an earnest mien surrounded the poor fellows. With 

 a shaking hand one of the condemned now took up the 

 dice, which were offered to him. He threw . . . two 

 sixes ! But, as soon as he noticed what he had cast, he 

 wrung his hands in despair and gave himself up as lost. 

 Who, however, will picture his delight, when, in the next 

 moment, he saw that his fellow also had thrown . . . two 

 sixes! 



" The commanding officers were not a little stricken with 

 this strange occurrence, and stared at each other in mute 

 astonishment. They were nearly at a loss how to act. 

 But the orders which had been given to them were too 

 precise, that they should have dared to deviate from them : 

 so they commanded both the men to throw again. This 

 was done : the dice were cast, and indescribable was the 

 universal amazement, when in the throws of both there 

 upturned . . . two fives ! Loudly the spectators now 

 called out, that both should be pardoned. The case, in- 

 deed, was extraordinary, and the officers thus resolved to 

 ask for new directions in such an out-of-the-way predi- 

 cament, and momentarily to put off the execution. 



"To get further orders, they accordingly applied to the 

 court martial, which they still found assembled. Long 

 was the discussion, but at last the disheartening reply 

 was given, that new dice had to be tendered to the delin- 

 quents, and that again they had to try their lot. Once 

 more both of them cast, and, lo . . . each had thrown 

 two fours ! 



" ' This is the finger of God ! ' said all present. 



"The officers, now quite upset, again laid down the 

 strangeness of the case before the still deliberating court 

 martial. This time, even over the members of that court, 

 there crept a shudder. They began to distrust the justice 

 of their sentence, and resolved to make the decision of the 

 dilemma, whether or not the judgment should bo executed, 

 depend on the general-in-chief, whose arrival they every 

 moment expected. 



