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as Melandrium album (Lychnis  vespertina), Hyoscyamus niger, 
Galanthus nivalis, many Papilionaceae and Epilobium angustifolium. 
In the second place I think it may be useful to refer briefly to 
the so-called nectarless plants, because it might be argued that these 
do not support the truth or general validity of the hypothesis, put 
forward above. 
I have already had an opportunity of pointing out, that some 
plants, which do not contain nectar, have their ovarian-wall covered 
with war, and others with glands secreting mucilage; to these 
secretions the same biological significance is attached as that, which 
I think should be attributed to nectar-secretion. Furthermore, I have 
already mentioned a number of plants, which are recorded as nectar- 
less, but which, nevertheless, must certainly be reckoned among 
those containing nectar, namely species of Anemone, Clematis, 
Pulsatilla, and Paeonia in the order of Ranunculaceae, also Helian- 
themum vulgare and the various species of Verbascum and Hibiscus. 
I will only add, that it can be easily shown by chemical means, 
that the so-called nectarless Rosaceae: Rosa, Poterium, Agrimonia, 
Aruncus and Spiraea have been wrongly included in this class. 
Here indeed the nectar is often difficult to observe, but it is none 
the less present, as in other Rosaceae. If the flowers are extracted 
with water, so that the nectar, which has been thickened by evapo- 
ration, passes into solution, the presence of glucose may readily he 
demonstrated in all these plants. Finally it may be pointed out in 
this connexion, that very many plants do not require a special 
protection by nectar, either because the ovary continues its growth 
without interruption, (on account of early fertilisation, which often 
already takes place in the bud) or because it is not exposed to the 
air during the flowering period. 
The latter case occurs especially in the genera Plantago and 
Luzula, in Nymphaea alba and Erythraea Centaureum, in Luncus, 
in most Grasses and in other anemophilous plants. 
Mathematics. — “On a theorem of Painrevé’s.” By Prof. W. Kaprnyn. 
1. Parninve, in his well-known memoirs on differential equations 
of the first order, investigated the question when the integrals 
possess a definite number of values or branches if the independent 
variable turns round the critical parametric (not the fixed) points. 
For differential equations of the first degree 
BY — ul 1259 ) : (1) 
TE EEC NEN 
