106 
Miscellanea 
the fifth leaf. Let us find the hoiiiotyposi« of the series as a whole, correcting for differen- 
tiation. 
We have : p = -0300 ± -01 62. 
In other words, when we do not pay attention to differentiation the homotyposis is almost 
zero. Clearly the small leaves on the spray could not be disregarded even by a moat careless 
gatherer, without the result being very manifest when the correlation is determined. 
Now let us allow for this gross case of differentiation by the above formula. We have 
p= -03001 -0162, 
(72 = 7-28052, o-.„» = 3-88274, 
o---o-.v- = 3-39778. m = 4. 
Hence: ?•= 0643 + '3809 
= •4452. 
Considering the comparative paucity of the material — only 144 sprays — -I think this result 
may be considered fairly satisfactory. Namely, we find, that judged by the first two leaves the 
homotyposis is -55, agreeing closely with the earlier determination ; judged by the first four 
leaves of the spray the homotyposis is -45. The probable error of either result is certainly not 
less than -04 to -05* and we conclude that the homotyposis in beecli leaves cannot diverge much 
from -5. Experience seems to show that the wider range of homotypes taken, if we allow for 
differentiation, the better the result will be. The present paper is also of interest as showing 
that a slight differentiation such as that between the first and second leaves, even if it should 
escape detection, would not radically modify, still less vitiate the results obtained. To get final 
numbers probably 1000 sprays of four leaves ought at least to be dealt with. The present study, 
however, will indicate how the student of homotyposis can investigate and allow for differentiation 
due to position. Other instances are given in the memoir in the R. S. Proceedings, Vol. 71, 
pp. 288-313. 
(iv) A paper has been recently published by Miss Tine Tammest in which two tables are 
given for the number of veins on beech leaves, having regard to their position on the year's 
shoot {Jahrestriebe). The authoress gathered 15 shoots with 9 leaves and 6 shoots with 8 leaves, 
— all off the same tree. She sought shoots with the same number of leaves as they had inter- 
nodes : " Diese waren, obgleich die Zahle der Internodien bei dem \'erschiedenen Trieben 
ziemlich stark variirt, an dem grosscn Bauine ohne viel Miihe zu finden " (p. 78). Further the 
shoots taken were those which had the greatest number of internodes. 
She found for this single tree : 
Position of leaf from base of shoot 
1 
G 
8 
9 
Mean No. of veins on 15 shoots 
„ „ 6 shoots 
9-8 
10-0 
11-7 
11-7 
13-1 
13-3 
13-5 
13-8 
13 1 
13-7 
12-7 
12-8 
11- 9 
12- 0 
10-6 
no 
9-5 
Now what is quite clear from this table is that (i) the nature of the shoots dealt with by 
Miss Tammes is both for number of leaves and number of veins to the leaf entirely different to 
what would be obtained by a random collection of year's shoots on the Chiltern beeches. That 
(ii) had she made such a random collection, her law of periodicity in growth would not have 
recei\'ed confirmation from the beecli tree at all. 
* For example, with a deviation of p from -03 equal only to about its probable error, the first term 
in r will be raised to -10 instead of 06 and thus r would be sensibly -5. 
t Verhandelingen der Koninklijke Akademie van Wetenechappen te Amsterdam (Tweede Seetie), Deal 
ix. Die Periodicitiit murphologischer Erscheinungen bei den Pfianzen, pp. 1 — 148. Maart, 1903. 
