July 7, 1887] 



NATURE 



219 



Murchison's on page 103, in connexion with the Aymestry 

 limestone. 



The author mentions, but does not definitely accept, 

 Prof. Hull's correlation of the Devonian rocks. Through- 

 out]the work, and particularly in the Carboniferous section, 

 great care has been taken to show and where possible give 

 the origin of the economic value of the rocks. A little more 

 stress should have been laid on the relations of the Coal- 

 measures to the underlying rocks, and one might notice 

 here the absence of the Dudley, Sedgeley, and other 

 inliers from the South Staffordshire coal-field on the map. 

 An important feature consists in the description of Palaeo- 

 zoic rocks from all the deep borings (a list of these forms 

 the first appendix) ; and a good section to express the 

 present state of knowledge on the deep-seated geology of 

 the London Basin is given on page 202, 



The Permian and Lias form a single system, the Poiki- 

 litic, which is included in the Mesozoic, the author being 

 guided by the widespread discordance between it and 

 the older rocks. It is not quite easy to understand all 

 the tables (pp. 2S6, 470), but these only echo the difficul- 

 ties which exist in the rocks themselves. It would have 

 been as well if the Yorkshire Cornbrash had found a place 

 afterthe Upper Estuarine on page32i. A good opportunity 

 was missed of discussing the anomalous beds of Faring- 

 don and Blackdown, particularly in relation to Mr, 

 Starkie Gardner's recent papers on kindred questions ; 

 and we should have liked to see the grit phases in the 

 Jurassic clays of the eastern counties more accurately 

 defined. A section might have been introduced to show 

 the thinning of the Gault and growth of the Cambridge 

 nodule beds ; and Mr. Sollas's work on flints ought not 

 to have been omitted. 



The Upper Eocene beds are classed as Oligocene, but 

 the Brockenhurst bed is put in its true place in the 

 Headon. 



There are some very suggestive remarks on the con- 

 nexion bstween health and geology, between villages and 

 springs and consequently the outcrop of porous rocks, 

 and on the effects of percolation of spring and sea water 

 through rocks. The section on igneous rocks is of neces- 

 sity somewhat vague and unsystematic from its brevity, 

 but room has been found to treat the volcanic rocks 

 historically ; the Nuneaton diorites are intrusive in pre- 

 Carboniferous rocks only. There are concluding chapters 

 on metalliferous deposits, and on scenery and geology, 

 the latter containing a useful list of hills, valleys, plains, 

 and forests. 



A little more space might with advantage have been 

 spent in indicating with greater fulness what is known of 

 the physical geography of the different periods, and 

 epochs of earth movements, their dates, directions, and 

 effects should have been more fully dealt with in the last 

 chapter. A capital synopsis of the animal kingdom is 

 furnished in an appendix by Mr. Edwin T. Newton ; and 

 a grand index, occupying 45 pages of three columns each, 

 and giving the dates of the birth and death of authors 

 referred to, closes the volume, which is an excellent 

 summary of the present state of our knowledge of British 

 geology. The author has worked conscientiously and 

 well, and that we have been able to suggest so few addi- 

 tions clearly shows that his labour has not been in vain. 



W. W. W. 



A TREATISE ON GEOMETRICAL OPTICS. 



A Treatise on Geotnetrical Optics. By R. S. Heath, 

 M..A., D.Sc, Fellow of Trinity College, Cambridge, 

 Professor of Mathematics in the Mason College, Birm- 

 ingham. Demy 8vo, pp. xvii. 356. (Cambridge : Uni- 

 versity Press, 1887.) 



"T^HIS treatise is based on the conception of a beam of 

 *- light as consisting of a system of rays, which obey 

 the laws of reflexion and refraction. The transformations 

 of such a system and the construction and properties of 

 optical instruments are deduced, so far as the latter are 

 capable of explanation from this point of view. 



In confining himself to geometrical optics in this sense, 

 the author follows the mode of division of the science 

 which has been usually adopted in text-books in this 

 country, through the succession of Cambridge treatises 

 by Coddington, Grififin, and Parkinson, and Lloyd's 

 " Treatise on Light and Vision." The subject then splits 

 up naturally into the theory of reflexion and refraction of 

 systems of rays, which is in fact a department of geo- 

 metry ; and the more special discussion of the nature of 

 optical instruments and the forms and positions to be given 

 to their refracting surfaces to diminish spherical and 

 chromatic aberration, which allies itself with the technical 

 science of optical construction. 



The book begins with a short chapter on the nature 

 and properties of light, in which the theory of illumina- 

 tion is worked out as a consequence of the experimental 

 fact that self-luminous surfaces appear equally bright in 

 all directions and at all distances. The second and third 

 chapters contain the statement, in geometrical and ana- 

 lytical form, of the laws of reflexion and refraction, and 

 the investigation of conjugate foci for direct pencils. 



In Chapter IV. the subject of refraction through lenses 

 and systems of lenses is treated, use being made of the 

 symmetrical analysis, by means of the convergents of con- 

 tinued fractions, to determine the principal points of a 

 system whose refracting surfaces are specified. Free use 

 is also made of the cardinal points of the system in the 

 semi-geometrical manner introduced by Mdbius. The 

 following chapter is devoted to an account of the general 

 analytical investigation by means of which Gauss placed 

 the whole theory on an independent basis. The notion 

 of the equivalent lens is here introduced to some practical 

 purpose, for the investigations of this and the preceding 

 chapter enable the author to specify the exact character 

 of the equivalence that can be secured by a single lens or 

 a single refracting surface : viz. that if the lens or surface 

 occupied the position of one of the principal planes of the 

 system, it would refract any beam incident along its axis 

 into the same configuration as it actually possesses when 

 it emerges through the other principal plane of the instru- 

 ment ; so that, neglecting aberrations, the equivalence 

 holds in every sense except as regards the displacement 

 along the axis, and is therefore complete for most practical 

 purposes. 



The theory of caustics is treated, chiefly by analytical 

 methods ; and the existence of wave-surfaces, which cut 

 the system of rays at right angles in an isotropic medium, 

 is established geometrically. 



Chapter VII. is devoted to the discussion of the 

 spherical aberration of direct pencils, which is perhaps 



