368 ON THE THEORY OF VEGETABLE SPIRALS. 



state of our knowledge, or perhaps impossible, to arrive at an 

 explanation not based on morphological grounds or expressed in 

 morphological language. Yet it is certain that we ought not 

 to acquiesce in a merely morphological explanation of any phe- 

 nomenon, though it is going too far to say, that such explana- 

 tions are merely transitional or provisional, to be accepted only 

 until something else can be got. For teleological considerations, 

 whereof morphological are one kind*, neither exclude nor are 

 excluded by those which relate to actual genesis. The formal 

 and the final cause alike exist and coincide, if I may presume 

 to touch upon the subject, never to be mentioned but most 

 humbly and most reverently, in the Unity of the Divine Wis- 

 dom, from which both proceed, and the explanations derived 

 from either are, or rather would be, if our knowledge were com- 

 plete, equally and alike true, though in different ways. But to 

 return to the matter in hand. It seems reasonable to suppose 

 that when vegetable growth is proceeding according to any 

 given system, say for instance, that whose characteristic frac- 

 tion is 3%, the tendency to rhythmical recurrence on which the 

 whole depends still exists among the parts of which the whole 

 is made up, especially as these two parts are as we have seen 

 nearer in point of position to constituting a symmetrical spiral 

 than any other two portions into which the whole could be 

 divided. The first or last five, or the first or last eight are 

 within -jL of the circumference of going round the axis an integral 

 number of times. Now as we have seen, it is the larger portion 

 of a spiral which possesses a character of antagonism to the whole. 

 If the interval between adjacent points exceeds the limit towards 

 which this interval continually tends f, then that between adjacent 



* It is surely only from want of attention to the History of Philosophy that the 

 two are put in opposition to one another, whereas in the sense in which Aristotle 

 would have used the term, the doctrine of those who speak of the Unity and Modi- 

 fication of Types, and that of those who refer every thing to the advantage of the 

 individual or species, are alike based on the Final Cause. Moreover there seems 

 no sufficient reason for setting the two doctrines in opposition, still less for reject- 

 ing either. Truth comes to us in fragments, and so we must be content to accept 

 it, not letting ourselves be deterred by any antinomy from embracing all of it that 

 we can apprehend. 



t Namely four right angles multiplied by the positive root of the equation 

 x z + x=i. I use the word tend here in the mathematical sense of tendency to a 

 limit. It is, I believe, Bravais' doctrine that there is in reality but one angle of 



