8 REPORT 1860. 



faint, I could not consider the preceding explanation as well-founded. Upon 

 attending to the circumstances under which they were now seen, I observed that 

 the human footprints were all covered with dry sand that had been blown into them, 

 so that they were much brighter than the surrounding sand, and than the dark side 

 of the impression next the sun ; and hence it is probable that they appeared to be 

 nearer the eye than the dark sand in which they were formed, and consequently eleva- 

 tions. After repeated examinations of them, I found the footprints appeared as 

 elevations as far as the eye could see them ; and they were equally visible with one 

 or both eyes. But whenever the eye rested for a little while on the nearest foot- 

 print, it resumed its natural concavity. 



I have observed other illusions of this kind, which are more easily explained, 

 though they differ from any hitherto described. In the Church of Saint Agostino 

 in Rome, there is above each arch a painted festoon suspended on two short pil- 

 lars; but instead of appearing in relief, as the painter intended, by shading the one 

 side of them, they appeared concave, like an intaglio. In other positions in the 

 church they rose into relief. Upon a subsequent visit to the church, I found that 

 the festoon, or suspended wreath, was concave when it was illuminated, or rather 

 when the observer saw that it was illuminated, b)' a window beneath it, and in re- 

 lief when the eye saw that it was illuminated by a window above it, the object 

 being similarly illuminated in both cases. In the common cases of inverted per- 

 spective, the eye is deceived by looking at the inversion of the shadow in the 

 cameo or intaglio itself; but in the present case the eye is deceived by perceiving 

 that the body painted, supposed to be in relief, is illuminated by a light either above 

 or below it. 



An optical illusion of a different kind presented itself to me in the Church of 

 Santa Giustina at Padua. Upon entering the church we see three cupolas. The 

 one beneath which we stood appeared very shallow ; the next appeared much 

 deeper, and the third deeper still. They were all, however, of the same depth, as 

 we ascertained by placing ourselves under each in succession, and observing that it 

 was always the shallowest. 



On Microscopic Vision, and a Neiv Form of 3Iicroscope. 

 By Sir David Brewster, K.H., F.R.S. 



la studying the influence of aperture on the images of bodies as formed in the 

 camera, by lenses or mirrors, it occurred to me that in microscopic vision it might 

 exercise a still more injurious influence. Opticians have recently exerted their 

 skill in producing achromatic object-glasses for the microscope with large angles 

 of aperture. In 1848 the late distinguished optician, Mr. Andrew Ross, asserted 

 " that 135° was the largest angular pencil that could be passed through a micro- 

 scopic object-glass," and yet in 1855 he had increased it to 170° ! while some 

 observers speak of angular apertures of 175°. In considering the influence of aper- 

 ture, we shall suppose that an achromatic object-glass with an angle of aperture 

 of 170° is optically perfect, representing every object without colour and without 

 spherical aberration. When the microscopic object is a cube, we shall see five of 

 its faces ; and when it is a sphere or a cylinder, we shall see nine-tenths or more of its 

 circumference. How then does it happen that large apertures exhibit objects which 

 are not seen when small apertures with the same focal length are employed ? 

 This superiority is particularly shown with test-objects marked with grooves or 

 ridges, and obliquely illuminated. The marginal part of the lens will enlarge the 

 grooves and ridges, and they will thus be rendered visible, not because they are 

 seen more distinctly, but because they are expanded by the combination of their in- 

 coincident images. Hence we have an explanation of the fact — well known to all 

 who use the microscope, — that objects are seen more distinctly with object-glasses 

 of small angular aperture. In the one case we have, with the same magnifying 

 power, not only an enlarged and indistinct image of objects, but a false representa- 

 tion of them, from which their true structure cannot be discovered ; while in the 

 other we have a smaller and distinct image, and a more correct representation of 

 the object. 



But these are not the only objections to large angular apertures and short focal 

 lengths. 1. In the first place, it is extremely difficult to illuminate objects when 



