794 



SCIENCE. 



[Vol. II., No. 40. 



that it would be in readiness to pass into Ji at the 

 same time as tlie lieat wliich originally came from B 

 is returned to li, though my arrangement of moving 

 screens readily accomplished this, as was admitted by 

 Prof. J. Willard Gibbs injhis^eriticism of my paper.i 

 Db H. T. Eddy, Ph.D. 



Area of a plane triangle . 



°In the Mathematical magazine (Erie, Penn.; tor 

 April, Mr. James Main imblishes, as a matter of curi- 

 osity, a collection of ninety-four expressions for the 

 area of a plane triangle. In Mathesis (Gand, Belgium) 

 for June this list is republished; and in the August 

 nvunber of the same journal the subject is taken up 

 again by M. Ed. Lvicas, who extends the collection, 

 and classifies into five groups. In the first group are 

 eleven 'unique' expressions for the area, i.e., expres- 

 sions that do not admit of other similar expressions 

 by permuting the letters; in the second group are nine 

 expressions, each admitting of two other similar ex- 

 pressions by permuting the letters ; in the third group 

 are eleven expressions, eaqh admitting of three other 

 similar exjiressions ; in the fourth group are seven ex- 

 pressions, each admitting of five similar expressions ; 

 and, last, the fifth group consists of a single formula, 

 admitting of eleven similar expressions. Thus we 

 have a hundred and thirty-six expressions for the area 

 of a plane triangle in terms of the sides, angles, per- 

 pendiculars, semiperinieter, and radii of the circum- 

 scribed, inscribed, and escribed circles. M. Neuberg 

 adds also three other unclassified formulae, with the 

 statement that many other such may be found. The 

 total number of expressions for the area of a plane 

 triangle, in this collection, is therefore a hundred and 

 thirty-nine, making it, perchance, the most complete 

 collection that has been jjublished. M. B. 



The Dora coal-field, Virginia. 



In the November number of The Virginias is con- 

 tained a review of the report on the mineral resources 

 of the United States, recently published by the U.S. 

 geological survey, which contains the following: — 

 " In Mr. Charles A. Ashburner's report on anthracite 

 coal, p. 32, is this statement concerning the Dora 

 coal-field : ' Of one of the reported anthracite locali- 

 ties In Virginia, that in Augusta county, recent tests 

 with the diamond-drill would seem to prove the pres- 

 ence of anthracite,' " etc. In exi^lanation of the 

 above, I would like to state, that, by referring to 

 the report reviewed, on p. 24 will be found a foot- 

 note as follows: " Mr. Ashburner's contribution and 

 statistics end here." I only stand responsible for a 

 portion of the statistics relating to the anthracite 

 region in Pennsylvania {pp. 7 to 24 inclusive). I 

 desire to make this explan.ation public from the 

 fact that I do not wish to be held accountable for 

 questionable data relating to a coal-field of a very 

 uncertain character, and which I have never ex- 

 amined. 



Charles A. Ashbuener, 



GeologUt in charge Perm, anthracite survey/. 

 Philadelpliia, Penn. 



Synchronism of geological formations. 



In Science of Deo. 7 your correspondent, Mr. 

 Nugent, takes issue witli me as to my conclusions 

 hearing upon the relative ages of geological forma- 

 tions, and contends that the geological and paleon- 

 tological researches of the last twenty-one years (i.e., 

 during the period that has elapsed since the publi- 

 cation of Professor Huxley's address referred to in 

 ' Science, i. 160. 



my communication before tlie Philadelphia academy 

 of natur.al sciences) have only tended 'to maintain 

 the logical basis' on which the distinguished English 

 naturalist rested. As the subject is a very important 

 one, and one that has not, it appears to me, received 

 its full measure of attention or discussion, I trust 

 that you will permit me a little space for fuller ex- 

 planation, even at the risk of repeating what has al- 

 readj' been said in your valuable columns. 



Professor Huxley, in his anniversary address de- 

 livered before the London geological society in 1862 

 {(c^art. journ., xviii. p. xlvi), maintains substan- 

 tially, — 



I. 'That formations exhibiting the same faunal 

 f acies may belong to two or more very distinct periods 

 of the geological scale as now recognized ; and, con- 

 versely, formations whose faunal elements are quite 

 distinct may be absolutely contemporaneous: e.g., 

 " For any thing that geology or paleontology is able to 

 show to the contrary, a Devonian fauna and flora in 

 the British Islands may have been contemporaneous 

 with Silurian life in North America, and with a car- 

 boniferous fauna and flora in Africa" {loc. cit.). 



II. That, granting this disparity of age between 

 closely related faunas, all evidence as to the uniform- 

 ity of physical conditions over the surface of the earth 

 during the same geological period (i.e., the periods 

 of the geological scale), as would appear to be in- 

 dicated by the similarity of the fossil remains belong- 

 ing to that period, falls to the ground. " Geographical 

 l)rovinces and zones may have been as distinctly 

 marked in the paleozoic epoch as at present; and 

 those seemingly sudden appearances of new genera 

 and species which we ascribe to new creations may 

 be simple results of migration." 



Now, without wishing to enter into the minutiae 

 of the question, I believe a little reflection will clearly 

 show, that if, as it is contended, several distinct 

 faunas (i.e., faunas characteristic of distinct geo- 

 logical epochs, and separated in age from each other 

 by possibly millions of years) may have existed con- 

 temporaneously, "evidences of inversion," to qxiote 

 my own words, "in the order of deposit, ought to be 

 common; or, at any rate, they ought to be indicated 

 somewhere, since it can scarcely be conceived that ani- 

 mals everywhere would have observed the same order 

 of direction in their migrations." Given the possible 

 equivalency in age, as hypothetically claimed, of the 

 Silurian fauna of Nortlr America with the Devonian 

 of the British Isles and the carboniferous of Africa, 

 or any similar arrangement, why has it never hap- 

 pened, it may be asked, that when migration, neces- 

 sitated by alterations in the physical conditions of 

 the environs, commenced, a fauna with an earlier life- 

 facies has been imposed upon a later one, as the De- 

 vonian of Great Britain upon the carboniferous of 

 Africa, or the American Silurian upon the Devonian 

 of Britain? Or, for tliat matter, the American Silu- 

 rian may have just as well been made to succeed the 

 African carboniferous. Reference to the annexed 

 diagram, where D represents a Devonian area, say, in 

 Europe, S a Silurian one in America, and C a car- 

 boniferous one in Africa, — all contemporaneous, — 

 will render this point more intelligible. 



Now, on the proposition here stated, reasoning 

 from our present knowledge of the antiquity of faunas, 

 and accepting the doctrine of migration, as main- 

 tained by Professor Huxley and others, to account for 

 the possible contemporaneity of distinct famias, it may 

 be assumed that S (or America) will receive its Devo- 

 nian fauna from TJ ; D (Europe), its carboniferous 

 from C; and C (Africa), a later fauna from some 

 locality not here indicated. In other words, a migra- 



