Prof. TyndalPs Notes on Scientific History* 25 



whether we strengthen the arguments or objections against B, 

 or strengthen the force of the inference of B from A. If it be 

 held that this inference is certain, i. e. that y=l, then the odds 

 in favour of A are w{\ — X) to 1 — w 3 and every argument against 

 B tells with equal force against A. Let us take a numerical 

 illustration. 



Let w=^$q, y=i, and X= 1 9 q; then tvyX.= 2 * oo r oj an ^ tne 

 probability of A is ^y§t, i. e. the odds in its favour are less than 

 55 : 1. With this value of y, the probability of A cannot be 

 reduced below -f^ T} its value when X=], the odds being then 

 49 1 to 1. But if y = fo, then w?/X == ^y^-, and the odds in 

 favour of A are reduced to 1881 to 100, less than 19 to 1. What- 

 ever be the value of w, if 2/ = J and X>J, then the common 

 denominator is <1— \w } and the odds in favour of A are less 

 than \w to 1 — w. Thus if y=§, and X = §, the odds are only 

 \w to 1— w. 



IV. Notes on Scientific History. By John Tyndall, F.R.S.* 



1. 



TWO years ago, in a Friday evening discourse at the Royal 

 Institution f, I drew attention to the scientific labours 

 of Dr. Julius Robert Mayer, and since that time the knowledge 

 of his writings has been widely diffused by the publication in 

 English of four of the five memoirs which he completed before 

 his health gave way. A translation of Mayer's first paper (date 

 1842) will be found in the Philosophical Magazine, S. 4. vol. xxiv. 

 p. 371. A resume of this paper, written by myself, appears in the 

 Philosophical Magazine, S.4.vol. xxv. p. 378. A translation of his 

 third paper (date 1848) will be found in the Philosophical Maga- 

 zine, S. 4. vol. xxv. pp.241, 387, 417. A translation of his 

 fourth paper (date 1851) in the Magazine, S.4. vol. xxv. p. 493. 

 No translation of his second paper (date 1845) has yet been 

 published. Circumstances have recently compelled me to refer 

 to this Essay ; and pending its full translation, I would ask per- 

 mission to make such a resume of its contents as will give the 

 readers of this journal some notion of its merits. The extracts 

 will show the relationship of its author to other writers with whom 

 he has been recently compared. Prom the works of these writers, 

 moreover, I shall extract the portions on which their claims 

 mainly rest, and thus the public will be enabled to form an in- 

 dependent estimate of this passage in scientific history. 



* Communicated by the Author. 



t Proceedings of the Royal Institution, June 1862. Phil. Mag. vol. xxiv. 

 p. 57. 



