AroisT 1 , 1900.] 



KNOWLEDGE 



183 



does, the same angle to us, whether on the horizon or 

 in the zenith, appears to us larger in the former and 

 smaller in the latter position, for, as pointed out by 

 Mr. John Turner,! " of two bodies of equal angular 

 magnitude, that which appeal's to us to be neai-er wc 

 think the smaller." 



The truth of this statement is, I think, exemplified 

 in a very striking manner by the accompanying photo- 

 graph (Fig. 1), which shows the foreshortened side of a 

 villa seen " under conditions different from those in whi'jh 

 our experience is usually gained." It is, in fact, a 

 photograph taken through a 3-inch telescope, magnifying 

 some 40 diameters, of the villa, distant about a mile 

 and a half, and mai-ked by an arrow in Fig. 2, which 

 represents the naked-eye view of the same. 



Now as this building is at a considerable distance from 

 the observer it.s near and far ends are seen under prac- 

 tically the same visual angle, or, as a draughtsman 

 would express it, the vanishing point of its lines is 

 infinitely remote. Instead of the lines of the roof and 

 first story appearing to converge as they recede, as 

 would be the case if the house were really as near the 

 spectator as the telescope apparently brings it, they are 

 here practically parallel, and our usual ideas of per- 

 spective are consequently upset. So much, indeed, are 

 we in the habit of mentally enlarging the reduced image 

 of the far end of the house (knowing it to be as large 

 as the near end) that in the present case, where the two 

 ends are of practically equal angular magnitude, we 

 still mentally enlarge the di.stant end so that the lines 

 of the roof and the first floor appear actually to diverge 



Fig. 1. 



as they recede from us. That this curious effect, how- 

 ever, is purely due to a mental deception on our part 

 is plainly shown by holding the picture in such a 

 position that the eye can glance obliquely down the 

 seemingly divergent lines, when it will at once become 

 apparent that they are practically parallel ; the slight 

 existing convergence towards the distant end being in- 

 appreciable. 



This instance of our mentally enlarging the more 



+ Journal B. A. A., Vol. X., p. 220. 



distant of two objects subtending equal angles seems to 

 me to have a distinct bearing on the problem of the 

 apparent enlargement of celestial bodies when seen near 



^ ^i!5 



tp^f 



1 ,(-,. 2 



the horizon ; while the tele-photograph itself illustrates 

 in a remarkable manner the truth, so often overlooked, 

 that the telescopic aspect of an object (which is but the 

 naked-eye view enlarged) is not identical with that 

 which the object would present to the naked eye at the 

 same apparent distance. W. Alfred P.\rr. 



34, Viale Principe Amedeo, 

 Florence. 



LICHEX GROWING ON QUARTZ. 



TO THE EDITORS OF KNOWLEDGE. 



Sirs, — The other day I was shown an entire piece 

 of quartz upon which was gi-owing a lichen — ParuaJia 

 Pryaodes. After carefully removing a small portion of 

 the lichen, I examined the uncovered part for earth 

 deposits but failed to detect any. 



It is clear that the plant is rooted to the quartz, and 

 what I am at a loss to know is from which source other 

 than the atmosphere does this plant derive its nutri- 

 ment ? 



I have observed lichens acting upon hard rocks, but 

 never quartz ; moreover, as you assert in your article 

 on " Plants and their Food," Knowledge, May, 1900, 

 that quartz is an insoluble network enclosing the 

 mineral constituents of plant food, the phenomenon be- 

 comes all the more egregious, and its explanation would 

 bestow a great favour upon J. Ale.x.vndre Cook. 



10, Grafton Square. Glasgow, 

 14th June, 1900. 



[Mr. J. A. Cook has rejjroduced in too con- 

 densed a form the remarks of Mr. Pearson in Know- 

 ledge, Vol. XXIII., p. 102, where quartz is stated to 

 surround the other minerals in granite, which otherwise 

 would yield up the constituents needed by plants. This, 

 however, does not affect the point he raises. I have 

 consulted Prof. J. B. Farmer, f.e.s., who allows me to 



