224 



rites, sulphate of iron, and alum, are commonly found in such mines ; 

 from which circumstances, together with the sulphureous odour 

 emitted by most of the mineral coals when burned, the agency of 

 sulphuric acid is strongly evinced ; and, as we have already observed, 

 the coals formed artificially from vegetable substances, by means of 

 sulphuric acid, bear a strong resemblance to the mineral coals, not 

 only in their external characters, but also in their other properties. 



Mr. Hatchett intends, he says, to relinquish any further prosecu- 

 tion of this subject for the present ; but he entertains such sanguine 

 expectations of its proving economically useful, that he strongly re- 

 commends the prosecution of the inquiry, particularly of that part 

 which relates to roasted vegetable substances and to peat. 



The Application of a Method of Differences to the Species of Series 

 whose Sums are obtained by Mr. Landen, by the Help of impossible 

 Quantities. By Mr. Benjamin Gompertz. Communicated by the 

 Rev. Nevil Maskelyne, D.D. Astronomer Royal, F.R.S. Read 

 February 13, 1806. [Phil. Trans. 1806, p. 147.] 



The nature of this paper is such, as renders it absolutely incapable 

 of abridgement. By way of introduction to it the author observes, 

 that having some years back, when reading the learned Mr. Landen's 

 fifth memoir, discovered the manner of applying a method of differ- 

 ences to the species of series whose sums are there obtained by the 

 help of impossible quantities, and having since extended that appli- 

 cation, he now ventures to offer it to the consideration of others. 



The practice of this method, in most cases, appears, he says, ex- 

 tremely simple, and on that account he is almost induced to imagine 

 that it has already been considered by mathematicians. And he ac- 

 knowledges that, since the greatest part of the paper was written, 

 he has, in Euler's Institutiones Calculi Integralis, met with two 

 simple series, which are in that work summed by multiplications 

 similar to those employed in the investigation of the principal theo- 

 rems contained in this paper. But whether that learned mathema- 

 tician has pursued the method any further, he has not been able to 

 ascertain. 



Mr. Gompertz has purposely considered some of the series summed 

 by Mr. Landen, in order to procure an opportunity of comparing both 

 the results and methods ; and as the series may have particular cases, 

 in which both Mr. Landen's means and those of our author fail, he 

 has added, towards the end, a general Scholium concerning the causes, 

 circumstances, and consequences of such failure. 



An Account of a small Lobe of the human prostate Gland, which has 

 not before been taken notice of by Anatomists. By Everard Home, 

 Esq. F.R.S. Read February 20, 1 806. [Phil. Trans.1806, p. 195.] 



The subject of this paper is a portion of a gland which, from the 

 smallness of its size, and the obscurity of its situation, has hitherto 





