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. VOL. nil.] PHILOSOPHICAL TRANSACTIONS. 41 



LII. ^n Essay towards Solving a Prollem in the Doctrine of Chances. By the 

 late Rev. Mr. Bayes, F. R. S. Communicated by Mr. Price, p. 370. 



This problem is to this effect : " Having given the number of times an un- 

 known event has happened and failed; to find the chance that the probability of 

 its happening should lie somewhere between any two named degrees of probabi- 

 lity." In its full extent and perfect mathematical solution, this problem is much 

 too long and intricate, to be at all materially and practically useful, and such as 

 to authorize the reprinting it here; especially as the solution of a kindred pro- 

 blem in Demoivre's Doctrine of Chances, p. 243, and the rules there given, 

 may furnish a shorter way of solving this problem. See also the demonstration 

 of these rules at the end of Mr. Simpson's treatise on " The Nature and Laws 

 of Chance." 



LI II. Of the Sea Pen, or Pennatula Phosphorea of Linna-us; also a Descrip- 

 tion of a Neiv Species of Sea Pen, found on the Coast of South Carolina ; 

 with Observations on Sea Pens in General. By J. Ellis, Esq., F.R.S. p. 41 9. 



This animal was well known to the ancients by the name of the sea pen ; many 

 of the old authors took it for a fucus or sea plant. This species has been found 

 in the ocean from the coast of Norway to the most remote parts of the Medi- 

 terranean sea, and not only dragged up in trawls from great depths of the sea, 

 but often found floating near the surface. Dr. Shaw, in his History of Algiers, 

 remarks that they afford so great a light in the night to the fishermen, that they 

 can plainly discover the fish swimming about in various depths oT the sea. From 

 this extraordinary property Linnasus calls this species of sea pen, pennatula phos- 

 phorea, and remarks, after giving the synonyms of other authors, habitat in 

 oceano fundum illuminans. 



The outward appearance of this animal is not unlike one of the quill feathers 

 of a bird's wing, but they are found of different sizes, from 4 to 8 inches in 

 length; the lower half of it is naked, round, and white, not unlike the quill 

 part of a writing pen ; the upper part represents that of the feathered part of the 

 pen, and is of a reddish colour. This upper half, which arises from the quill and 

 is feathered on both sides, is a little compressed, and becomes smaller and smaller 

 till it ends in a point at the top; along the back of this, in the same manner as 

 in the inner side of a common writing pen, there is a groove in the middle, from 

 the quill to the extremity; from each side of this upper part of the stem proceed 

 li^le parallel featherlike fins; these begin at the top of the quill part, very small 

 on each side at first, but lengthen as they advance towards the middle; hence 

 they shorten gradually on each side, till they end in a point at the top, their ter- 

 minations preserving on each side the figure of the segment of a circle. 



VOL. XII. G 



