GROWTH UNDER CONSTANT EXTERNAL CONDITIONS. 82 1 
In this case, therefore, the third zone, where the maximum increase of growth took 
place, was at first at a distance of only 2 mm. from the apex. 
It is clear that if an organ is divided into zones of small length, each zone 
will in general contain a larger number of cells the nearer it is to the punctum 
vegetatwms, since the cells are longer the further they are from the apex. But from 
the point where growth ceases the number of cells in the successive zones of an 
organ of uniform structure will be the same. If therefore the zones are again 
designated by the numbers I, II, III, &c., the number of cells in them by N^, N,,, 
N3 ... N", then we have : — 
I II III IV V VI VII VIII 
N, > N, > N3 > N, > N, > N, > N, = N3. 
But the difference in the number of cells in the zones is very far from being 
the cause of the difference in the rapidity of growth that prevails in them ; as is 
seen at once if it is recollected that the number continually decreases from the apex 
throughout the growing region, while the rapidity of growth first increases and 
then decreases. This may be expressed by the following formula : — 
I II III IV V VI VII VIII 
N, > N, > N3 > N, > N, > N, > N, = N3. 
Ii < I2 < I3 < I4 < I5 > ^6 > I7 > zero. 
If it were possible to divide in the same manner a filament of Vaucheria, a 
root-hair of Marchantia, or a similar unicellular organ, into small zones, it can 
scarcely be doubted (as we may conclude from other circumstances dependent on 
growth) that we should find the same law to regulate the distribution of the rate of 
growth in individual cells endowed with a power of apical growth. Since the same 
law applies to roots and stems — whether zones i or 2 millimetres or, in the case of 
stems, I or 2 centimetres in length are observed — it is to be expected that this 
formula would hold good also if zones of only a tenth or hundredth, or even 
thousandth of a millimetre could be marked out and measured. In other words, 
we should find that the law of the grand period holds good for each single minute 
area of the surface of the wall of a young cell. 
If the power of any particular zone to attain a definite length is called its 
Energy of Growth^ then a zone which up to the time when its growth ceases reaches 
a length of 10 mm. would have a smaller energy than one which continues to grow 
until it has reached a length of 100 mm. Thus, for example, the successive inter- 
nodes of most stems each of which was at one period i mm. long, differ very 
greatly in length when mature ; the internodes first formed are short, the next 
longer, and finally we have one the longest of all, followed again towards the apex 
by shorter ones. If we designate the energy of growth of the internodes I, II, III, 
&c., by E^, E2, Eg, &c., we get the series — 
I II III IV V VI VII VIII 
E, < E, < E3 < E, > E, > E, > E, > E,. 
With this increase and decrease in the energy of growth of the various inter- 
nodes of a stem is usually associated a similar reladonship between the size of their 
