68 Analyses of Boohs. 



but in the powers and capabilities of our numerical system to 

 express them. Mr. Powell then proceeds to discuss the views of the 

 earlier geometers and of later mathematicians. He points out the 

 misapprehension under which they all labour, from the common 

 mistake of considering that definitions describe the thing defined 

 instead of fixing the meaning of terms. He shews that the mistake 

 must be corrected before reasoning can be admitted on the subject. 

 The nature of abstract quantity is next ably treated of, and the paper 

 concluded in the same philosophic spirit which pervades it throughout. 



V. — The Transactions of the Linnean Society of London. Vol. 

 XVII, part 3rd, 1836. 



The number of communications in this portion of the transactions 

 amounts to 12, most of which are important. 



BOTANY. 



Remarks on some British Ferns. By Mr. David Don, Lib. L.S. 



The object of this paper is to determine how far some species of 

 ferns recently added to the British Flora, merit the rank which has 

 been assigned to them. 



Aspidium dumetorum, of Smith he has ascertained to be merely a 

 diseased state of A. dilatatum, which is shown by the sudden termi- 

 nation of the costae, and by the partial decay of the other segments. 



Nephrodium rigidum turns out to be the same with the plant of 

 Swartz. It differs from N. dilatatum and N . spinulosum, in having 

 larger and more crowded sori, and a broader and more depressed 

 indusiura. The fronds are lanceolate and both the stipes and rachis 

 are copiously clothed with long narrow ramentaceous scales, as in 

 aspidiu77i aculeatum. In dilatatum and spinulosum the rachis is 

 nearly naked, and the stipes is furnished with fewer and broader 

 scales. From N. filix mas it is distinguished by its more delicate 

 fronds, having the pinmdae pinnatified and a more scaly rachis. 



Aspleniumfilix foemina is observed in the shape of two different 

 varieties, but neither of them are entitled to be regarded as a distinct 

 form. 



Cystea dentata or Polypodium dentatum of Dickson, who first 

 distinguished it from fragilis, inhabits Clova, and appears peculiar 

 to the Scottish Alps. 



Cystea regia. Contrary to the opinion of Hooker, Mr. Don 

 considers this plant distinct from alpina, being characterised by its' 

 more compact frond, by its shorter, broader and cuneiform segments, 

 by the still more important characters of its more copious sori, and 

 of its narrower and tapering indusium. In the Alplna, the segments 

 are linear and the sori much fewer, being mostly solitary on the 

 lobes, and the indusium broader, truncate, and not taper pointed. 

 No British station now exists for this plant. 



{To be continued.) 



