in common use as Test-Objects. 129 



this conclusion is not correct : for when the diagonal lines make, 

 with the transverse, an angle greater than 60°, the transverse 

 rows are more remote than the diagonal ; and when the angle 

 is less than 30°, the longitudinal rows are the more remote, and 

 easily detected. In the quincuncial structure, therefore, the 

 diagonal lines predominate only when the angle of inclination is 

 more than 30° and less than 60°; but the transverse and longi- 

 tudinal cannot both preponderate in the same species." 



I have therefore the satisfaction of believing that my view is 

 borne out, as far as the number of series of lines is concerned, 

 by one so competent to guide our judgment. The cause of the 

 predominance of the diagonal lines in P. angulatum and the 

 rectangular in P. balticum is thus made apparent to a certain 

 extent. But it will be observed that Professor Arnott evidently 

 considers the whole four sei'ies of lines as occurring upon the 

 same plane, the word "distant'^ bearing reference clearly to the 

 position of the lines as removed more or less from each other on 

 that plane, and the theory offered being, that the more distant 

 series of lines are most distinct, whereas the most closely 

 approximated are the reverse. 



Both as regards P. angulatum, P. hippocampus, and their allied 

 forms, the diagonal series of lines consist of alternate ascents 

 and descents along the angular edges of the raised facets, which 

 thus constitute a series of zigzag lines directly in the line of 

 vision, whereby they cannot be brought simultaneously into 

 focus at all points. In short, every portion of the two series of 

 lines which bound the elevations is arranged on the same plane, 

 whilst the lines which unite the facets arc not so. 



In P. formosum and P. ([uadratum the structure is analogous 

 to that existing in P. angulatum. In P. balticum and P. hip- 

 pocampus, instead of diamond-shaped elevations, we have four- 

 sided flattened pyramids, presenting, as in the former case, four 

 sets of lines; but here, as a natural consequence, the spaces 

 being bound by the longitudinal and transverse series, these 

 predominate. 



This is in accordance, moreover, with the lines of fracture 

 observable in both types, — a fragment of P. angulatum, for in- 

 stance, always having its edges defined in conformity with the 

 diagonal lines bounding the diamond-shaped elevations ; whereas 

 in P. balticum the edges follow the rectangular outline of the 

 boundary lines. In both examples, the lines of fracture occur 

 at the thinnest portions of the valves. No such lines of fracture 

 occur in Triceratiwn, hthmia, or Biddulphia. Of course, accord- 

 ing as we view these objects on tiicir external or internal aspects, 

 the eye receives the impression of elevations or depressions, the 

 markings — i. e. the elevated angular spaces — being confined to 



