The compound interest law and plant growth
The compound interest law and plant growth
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DOI：
10.1093/oxfordjournals.aob.a089727
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发表时间：
1919-07-01
期刊：
影响因子：
4.2
通讯作者：
Blackman, VH
中科院分区：
文献类型：
--
作者：
Blackman, VH
在许多现象的变化中，自然的某些量是成正比的，我们发现过程与其本身的量成正比。某些数量的变化率与数量本身成正比。由于以复利形式支出的货币以这种方式增加——任何时候的增长率都明显与资本数量成正比——开尔文勋爵将这种过程遵循的法则称为“复利法则”。物体冷却的速度遵循复利定律，因为物体相对于周围环境越热，它失去热量的速度就越快。同样，大气压随海拔高度的变化遵循这一定律，化学反应的速度也是如此。早在 1850 年就发现的威廉定律，即“给定时间内的化学变化量与系统中存在的反应物质的数量成正比”，只是对复利定律的重述。19 17 年，作者结合与 F. Gregory 先生合作进行的一些黄瓜生长实验的结果，认识到了该定律对于正确评估植物生长的重要性。切森特实验站。很明显，对于普通植物来说，叶面积会随着生长的进行而增加，并且随着叶面积的增加，同化产生物质的速率也会增加；这又将导致更快速的生长，从而导致更大的叶面积和更多的同化物质生产，等等。如果单位面积叶面的同化速率和呼吸速率保持恒定，并且叶系统的大小与整个植物的干重保持恒定的关系，则以干重衡量的新材料的生产速率将与植物的大小成正比，即植物干重的增加将遵循复利定律。人们早已认识到，当不受外部条件限制时，单细胞生物数量的增加遵循规则的几何级数。许多工作者也指出动植物的生长过程与自催化有相似之处，如 J. Loeb、W. Ostwald、Robertson、FF Blackman、Chodat
IN change many of phenomena some quantity of nature is proportional we find processes to the quantity in which itself. the rate Since of change of some quantity is proportional to the quantity itself. Since money put out at compound interest increases in this way-the rate of increase being clearly proportional to the amount of capital at any time-Lord Kelvin called the law which such processes follow ť the compound interest law'. The rate at which a body cools follows the compound interest law, for the hotter the body relative to its surroundings the more rapidly it loses heat. Again, the variation of atmospheric pressure with height above sea-level follows this law, as does also the velocity of a chemical reaction. Wilhelmy's law, discovered as long ago as 1850, that'the amount of chemical change in a given time is directly proportional to the quantity of reacting substance present in the system', is simply a restatement of the compound interest law.The importance of this law for the proper appreciation of the growth of a plant was brought home to the writer in 19 17 in connexion with the results of some experiments on the growth of cucumbers carried out in association with Mr. F. Gregory at the Cheshunt Experimental Station. It is clear that in the case of an ordinary plant the leaf area will increase as growth proceeds, and with increasing leaf area the rate of production of material by assimilation will also increase; this again will lead to a still more rapid growth, and thus to a greater leaf area and a greater production of assimilating material, and so on. If the rate of assimilation per unit area of leaf surface and the rate of respiration remain constant, and the size of the leaf system bears a constant relation to the dry weight of the whole plant, then the rate of production of new material, as measured by the dry weight, will be proportional to the size of the plant, ie the plant in its increase of dry weight will follow the compound interest law. The fact that the increase in number of unicellular organisms, when not limited by external conditions, follows a regular geometric series has long been recognized. The resemblance also of the growth processes of animals and plants to an autocatalysis has been pointed out by a number of workers, as J. Loeb, W. Ostwald, Robertson, FF Blackman, Chodat