107 



that exactly 50 of each kind will be drawn, and an even chance that 

 there will not be more than 53 of either ; and that it is barely pos- 

 sible that 100 black, or 100 white, should be drawn in succession. 



From calculations contained in this paper, Dr. Young infers that 

 the original conditions of the probability of different errors do not 

 considerably modify the conclusions respecting the accuracy of the 

 mean result, because their effect is comprehended in the magnitude 

 of the mean error from which these conclusions are deduced. The 

 author also shows that the error of the mean, on account of this limi- 

 tation is never likely to be greater than six sevenths of the mean of 

 all the errors divided by the square root of the number of obser- 

 vations. 



The author then proceeds to the application of the doctrine of 

 chances to matters of literature and history. He shows that with 

 respect to the relation of two languages, nothing can be inferred 

 from the coincidence of the sense of any single word ; that the odds 

 would be 3 to 1 against the agreement of two words ; but if three 

 were identical, it would then be more than 10 to 1 that they were 

 derived from the same parent language. Six words give 1700 

 chances to 1, and eight near 100,000 ; so that, in these last cases, 

 the evidence would approach certainty. 



In regard to history, Dr. Young remarks, that the mention of a 

 single number found indisputably correct may afford strong evidence 

 of the veracity of a historian. 



There is a manuscript of Diodorus Siculus, in which, describing 

 the Egyptian funerals, he gives forty-two for the number of persons 

 who sat in judgement on the merits of the deceased ; and in a mul- 

 titude of ancient rolls of papyrus, lately found in Egypt, forty-two 

 assistants of Osiris are delineated on a similar occasion. Hence it 

 is 100 to 1 that this manuscript is more accurate than others which 

 have been collated ; that Diodorus Siculus was a faithful historian ; 

 that the inscriptions related to some kind of judgement ; and that 

 the hieroglyphics have been truly interpreted. 



The second section of Dr. Young's letter relates to the mean den- 

 sity of the earth. 



Before we admit that the excess of density of the central parts of 

 the earth, compared with its superficies, renders it probable that the 

 whole was once fluid, we should inquire into the exclusive effect of 

 pressure in augmenting the mean density. From this inquiry, Dr. 

 Young makes it evident, that the general law, of a compression pro- 

 portionate to the pressure, is amply sufficient to explain the greater 

 density of the interior of the earth ; and that this law, which is true 

 for small pressures in all substances, and with regard to elastic fluids, 

 in all circumstances, requires some little modification for solids and 

 liquids, the resistance in them increasing somewhat faster than the 

 density ; for no mineral substance is light and incompressible enough 

 to afford a sphere as large as the earth, and of the same specific 

 gravity, without some such deviation from the general law. A sphere 

 either of water or of air would be much denser : indeed the moon, 



