1843.] Treatment of Geometry as a branch of Analysis. 127 



The application of a few abstract principles to geometrical ideas of 

 the simplest character enables us thus to develope the whole mass of 

 complicated properties founded on them, in a comprehensive and con- 

 cinnous mode ; justifying by the result the daring paradox of D'Alem- 

 bert, that the more abstractedly an investigation is carried on, the more 

 lucid and satisfactory does it become. It must not, however, be for a 

 moment forgotten that analysis is but the lever; the fulcrum of its 

 support lies in the ideas peculiar to the subject to which it is applied. 

 Without a vivid and distinct conception of them our labour is idle. 

 Professor Whewell in his tractates has done mathematical education 

 signal service by insisting on this point, and his own works on Mecha- 

 nics, with those of Professor De Morgan on Algebra and the Differential 

 Calculus, may be hailed as some of the most valuable gifts which the 

 thoughtful student has received from the hands of the masters of 

 science. 



Description of a new genus of Falconidcc. By B. H. Hodgson, Esq. 



In the Journal of the Society for April, 1836, p. 227, I described a 

 species of Eagle as Aquila pernigra, but without noticing its singular 

 peculiarities of form, as especially the unique foot, of which the outer- 

 most fore digit is even smaller, in proportion to the innermost, than in 

 the human hand. There is no such foot heretofore described in the 

 whole family. The rest of its structure, as the feeble legs and vast 

 floating wings, agrees with Milvus ; and, in sooth, our genus Hetero- 

 pus should stand inter Aquilinarum et Milvinarum stirpes, and be 

 thus characterized: — Bill and head small and undepressed, aquilo- 

 milvine. Figure slender, with very ample wings and tail, the former 

 rather exceeding the latter; their gradation aquiline, having the 

 greatest quills incurved. Tarsi short and plumed. Toes nervous, 

 unequal, the inner and hind highly developed, the inner being 

 nearly as long as the central and stouter, the outer being much the 

 shortest and feeblest : talons very acute, and unequal, but not highly 

 curved. Type, Aquila pernigra, Nobis, loc. cit. 



[N. B.— In Mr. Jerdon's Catalogue of the Birds of Peninsular India (Madr. Jl. 

 No. XXIV, 68,) that naturalist remarks, that—" On the summit of the Neilgherries 

 there is frequently seen a black Eagle, larger than the Wokhab (Aquila Vindhiana, 

 Franklin), but of which I was unable to procure a specimen. I have heard it is also 



