Notices respecting New Books. 443 



distance in front of the semi-lenses of the stereoscope. When 

 the lower pair are seen, by axial convergence, as a truncated 

 cone, the upper pair are seen separately and monocularly, 

 without the appearance of relief. For binocular combination 

 of the upper pair divergence of visual lines is required, assu- 

 ming an average pair of eyes and an average lenticular stereo- 

 scope, at least as found in New York. The truncated cone 

 now appears larger, deeper, and more distant. It is unneces- 

 sary to explain why the background dot should appear double 

 when the foreground circle is seen single, and vice versa. 



In the course of these experiments, extending over many 

 months, it has been found that, although the coordination of 

 muscular actions in the eyes is commonly directed only to the 

 attainment of perfect vision, their dissociation is largely under 

 the control of the will. Not only is it possible directly to 

 diverge the visual lines without employing any external 

 points of fixation, but I find it not difficult to contract the 

 ciliary muscle strongly, thereby destro}ang the distinctness of 

 distant vision, while the relation between the visual lines un- 

 dergoes scarcely any noticeable variation. Certain peculiar 

 visual effects result from this; but the discussion of them must 

 be reserved at present. 



40 West 40th Street, New York. 



LIY. Notices respecting New Books. 



Conic Sections treated Geometrically. By S. Holkee, Haslam, B.A., 



and J. Edwaeds, B.A. London : Longmans. 1881. Pp.137. 

 rf^HE authors start from the usual Eocus and Directrix definition 

 ■*■ of the curve, and call to their aid what they call the Auxiliary 

 Circle of a Point. This is the circle first used, so far as we are 

 aware, by Boscovich in his Sectionum Conicarum Elementa (1754), 

 but without a name : of its use he writes : — " Miruni sane quam 

 fcecunda est haec constructio, quam tyroni exercendo apta. Plu- 

 rima quidem ex ea inferri possunt theoremataet pleraque utilissima, 

 ac iterum fcecunda." Rediscovered by George Walker (1794), and 

 named by him the Generating Circle, it has again come to the front 

 in Mr. Charles Taylor's book, and there poses as the Eccentric circle 

 of a point. It certainly furnishes a very neat basis for operating 

 upon the Sections ; and its usefulness is extended in a neat way by 

 our Authors to what they call Focal Projection. The first five chap- 

 ters give the familiar properties of these curves ; the sixth treats 

 of curvature ; the seventh of the Right circular cone ; the eighth of 

 Transversals leading up to the above-named Eocal Projection in 

 chapter nine, and Orthogonal Projection in chapter ten. Six sec- 

 tions are devoted to Exercises at the end of the book. The proofs 

 have a freshness about them dependent upon the introduction of 



