14 Proceedings of the Royal Irish Academy. 



plane surfaces, X is 4Tr or 12'56 : for a square, A is 16 : for lobed and indented 

 plane figures, A becomes a large number. Eepresentative leaves of aU tbe 

 species and hybrids have been accordingly measured, the area being obtained 

 by the use of squared paper, and the perimeter by an opisometer or map- 

 measurer, which is run round the edge of the leaf. 



The significant numbers obtained by the measurements of the leaves of the 

 London Plane, of its descendants, and of the two parent species, eonfinn in a 

 striking way the hybrid theor}', and may be tabulated thus : — 



Parents :— 









occidentalis, 



21-39, 



average 



30 



orien talis. 



60-123 



11 



91 



1st cross : — 









acerifolia. 



31-44 



M 



37 



2nd generation : — 









pyramidalis, 



28-36 



„ 



32 



hispanica. 



37-56 



'I 



46 



cuneata. 



73-100 



„ 



86 



digitata. 



67-87 



„ 



( 1 



cantabrigensis, 



, 28-36 



„ 



32 



par\'iloba, 



25-34 



„ 



29 



The first cross is thus seen to be intermediate between the two parents ; 

 and the second generation ranges from one extreme to the other. 



The fruit afTords good specific characters. The number of fruit-balls on 

 each peduncle is characteristic, solitarj- in P. occidenialis, and numerous, 3-6, 

 in P. orieniaJii. It is rather variable in P. acerifolia, 2-3 in some trees, 2-5 

 in others. Of the second generation hybrids, P. hispanica is most like the 

 Americau species, the fruit-balls being usually solitary, occasionally 2, and 

 rarely 3. In P. pyramidalis they are predominantly 2, but are often solitary. 

 The size of the fruit-balls is also a specific character, as they are considerably 

 larger in P. occidentalis than in P. orienlalis ; while those of P. aceri/olia are 

 intermediate. The fruit-balls are very large in P. pyramidalis. The surface 

 of the fruit-ball in P. occidfiUalis shows on examination the heads of the 

 achenes tightly packed toirether, and not separated visibly by hairs. In 

 P. oricntalis the tips of the achenes are plainly separated by pubescence. In 

 P. acerifolia, hi^xpanica, aintata, and parriloba the achenes, though tightly 

 packed, are separated by a slight pubescence. In P. pyramidalis, cantahrigen- 

 sis, and digHaia the surface of the fruit-ball is like P. orienlalis. 



The achene (Plate IX, fig. 9) shows specific characters in the presence or 



