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 ; lmt 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 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 hir. 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 ofl'er 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.
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
