Royal Society. 57 



ticable number of surfaces we may introduce as arbitrary constants ; 

 but it is practically perfect, when the residual error is" a quantity 

 less than that which the eye can appreciate. The separation of the 

 markings of the Pleurosigmata and other analogous objects, is found 

 to depend on good defining power associated with large angle of 

 aperture. 



The Podura scale appears to be a compound structure, consisting 

 of a very delicate transparent lamina or membranS, covered with an 

 imbricated arrangement of epithelial plates, the length of which is 

 six or eight times their breadth, somewhat resembling the tiles on a 

 roof, or the long pile of some kinds of plush. This structure may 

 be readily shown by putting a live Podura into a small test-tube, 

 and inverting it on a glass slide ; the insect should then be allowed 

 for some time to leap and run about in the confined space. By this 

 means the scales will be freely deposited on the glass, and being 

 subsequently trodden on by the insect, several will be found, from 

 which the epithelial plates have been partially rubbed off, and at the 

 margin of the undisturbed portion, the form and position of the 

 plates may be readily recognized. This structure appears to be ren- 

 dered most evident by mounting the scales thus obtained in Canada 

 balsam, and illuminating them by means of Wenham's parabolic re- 

 flector. The structure may also be very clearly recognized when 

 the scale is seen as an opake object under a Ross's y^th (specially 

 adjusted for uncovered objects), illuminated by a combination of the 

 parabola and a flat Lieberkuhn, as the writer has elsewhere de- 

 scribed*. The underside of the scale thus appears as a smooth 

 glistening surface with very slight markings, corresponding probably 

 to the points of insertion of the plates on the contrary side. The 

 minuteness and close proximity of the epithelial plates will readily 

 account for their being a good test of definition, while their promi- 

 nence renders them independent of the separating power due to large 

 angle of aperture. 



The structure of the second class of test- objects above mentioned 

 differs entirely from that above described ; it will suffice for the pre- 

 sent purpose to notice the valves of three species only of the genus 

 Pleurosigma, which, as arranged in the order of easy visibility, are, 

 P.formosum, P. hippocampus, P. angulatum. 



These appear to consist of a lamina of homogeneous transparent 

 silex, studded with rounded knobs or protuberances, which, in 

 P.formosum and P. angulatum, are arranged like a tier of round shot 

 in a triangular pile, and in hippocampus, like a similar tier in a qua- 

 drangular pile, as has frequently been described ; and the visibility of 

 these projections is probably proportional to their convexity. The 

 " dots " have by some been supposed to be depressions ; this how- 

 ever is clearly not the case, as fracture is invariably observed to take 

 place between the rows of dots, and not through them, as would na- 

 turally occur if the dots were depressions, and consequently the sub- 

 stance thinner there than elsewhere. 



This in fact is always observed to take place in the siliceous lorica; 

 * See British Association Keyorts for 1850. 



