Accretion

“ Employing the term, then, in its usual sense, as applicable only to organisms, Life may be defined as—the co-ordination of actions. The growth of a crystal, which is the highest inorganic process we are acquainted with, involves but one action—that of accretion. The growth of a cell, which is the lowest organic process, involves two actions—accretion and disintegration—repair and waste—assimilation and oxidation. ”

“ So I have added to use the energy of effort, and the Lamarckian theory, completed, can be characterized as the theory of the origin of species, by effort, use, and disuse. A prominent cause of change of structure may be here referred to; and that is, change in consequence of excess or diminution of growth-energy, due to the action of use and effort in disturbing its equilibrium. That is to say, that excessive growth in one place has caused diminished growth in another, and vice versa. ”

“ The increment of length divided by the increment of time gives the absolute rate of growth at any part of the curve. As long as the growth is uniform, so long the slope of the curve remains constant. If a stimulating agency enhances the rate of growth, there is an immediate upward flexure in the curve; a depressing agent, on the other hand, lessens the slope of the curve.
I shall now give a few typical examples of the employment of the Crescograph for in­ves­ti­ga­tions on growth: the first example I shall take is the demonstration of the influence of variation of temperature. ”

“ For a great part of the difference, in regard to rate of growth, between one individual and another is a difference of phase,—a difference in the epochs of acceleration and retardation, and finally in the epoch when growth comes to an end. And it follows that the variability of rate will be more and more marked, as we approach and reach the period when some individuals still continue, and others have already ceased, to grow. ”

“ In particular we should like to know the meaning of that point of inflection, or abrupt change from an increasing to a decreasing velocity of growth which all our curves, and especially our acceleration curves, demonstrate the existence of, provided only that they include the initial stages of the whole phenomenon: just as we should also like to have a full physical or physiological explanation of the gradually diminishing velocity of growth which follows, and which (though subject to temporary interruption or abeyance) is on the whole char­ac­ter­is­tic of growth in all cases whatsoever. ”

“ It becomes necessary therefore to study the phenomenon of growth in successive small portions; to study, that is to say, the successive lengths, or the successive small differences, or increments, of length (or of weight, etc.) , attained in successive short increments of time. This we do in the first instance in the usual way, by the “graphic method” of plotting length against time, and so constructing our “curve of growth.” Our curve of growth, whether of weight or length (Fig. 3) , has always a certain char­ac­ter­is­tic form, or char­ac­ter­is­tic curvature. ”

“ Again, as to the cost at which nutriment is distributed through the body, and effete matters removed from it, "Each increment of growth being added at the periphery of an organism, the force expended in the transfer of matter must increase in a rapid progression—a progression more rapid than that of the mass." ”

“ Expansion not bounded by matter. The mind, having got the idea of the length of any part of expansion, let it be a span, or a pace, or what length you will, can, as has been said, repeat that idea, and so, adding it to the former, enlarge its idea of length, and make it equal to two spans, or two paces ; and so, as often as it will, till it equals the distance of any parts of the earth one from another, and increase thus till it amounts to the distance of the sun or remotest star. ”

“ For the equi­lib­rium or tendency to equi­lib­rium of fluid pressure in all parts of its interior while the process of imbibition is going on, the constant rearrangement of its fluid mass, the contrast in short with the crystalline method of growth where each particle comes to rest to move (relatively to the whole) no more, lead the mass of jelly to swell up, very much as a bladder into which we blow air, and so, by a graded and harmonious distribution of forces, to assume everywhere a rounded and more or less bubble-like external form268. ”

“ V. A top supported above its centre of gravity, or a body which would be in stable equilibrium if not spinning, precesses in the opposite direction to that of its spinning.
VI. The last two statements come to this:—When the forces acting on a spinning body tend to make the angle of precession greater, the precession is in the same direction as the spinning, and vice versâ.
Having by observation obtained a rule, every natural philosopher tries to make his rule a rational one; tries to explain it. I hope you know what we mean when we say that we explain a phenomenon ”

“ Response to feeble stimulus by acceleration of growth; (b) response to strong stimulus by retardation of growth; (c) response to medium stimulation—retardation followed by recovery. Down-curve represents acceleration, and up-curve retardation of growth (seedling of wheat) . range of the plant is inconceivably greater than ours; it not only perceives, but also responds to different rays of the vast ethereal spectrum. ”

“ A complete curve of growth, starting from zero, has the same essential char­ac­teris­tics as the regeneration curve.
Indeed the more we consider the phenomenon of regeneration, the more plainly does it shew itself to us as but a particular case of the general phenomenon of growth189, following the same lines, obeying the same laws, and merely started into activity by the special stimulus, direct or indirect, caused by the infliction of a wound. ”

“ Growth may cease at this limit, and a balance be struck; or the form of the unit may be altered and surface gained by flattening out, or very frequently by ramifying processes; or—and this the most frequent solution—the cell may divide, halving its volume, gaining new surface, and restoring the balance. ”

“ This synchronous excess of heat and water evidently produced the abnormal growth. And probably, as this matter is further studied, it will be found that these agents, rightly proportioned, operating synchronously, produce these thicker rings; while as one or the other is in excess, or absent, the growth is checked, and thus has time to condense and harden, and form these sub-rings ”

“ Where, then, as often happens, the generating curve of the shell is ap­prox­i­mate­ly a circle passing through the point of origin, we may consider the acceleration of growth along various radiants to be governed by a simple math­e­mat­i­cal law, closely akin to that simple law of acceleration which governs the movements of a falling body. ”

“ We have seen that a slow but definite change of form is a common accompaniment of increasing age, and is brought about as the simple and natural result of an altered ratio between the rates of growth in different dimensions: or rather by the progressive change necessarily brought about by the difference in their accelerations. ”

“ This gives an ideal solid, which may be called the stress figure, whose height shows the distribution of stress over the surface which forms its base. A line drawn from g, the centre of gravity of the stress figure, parallel to the ordinates Aa, &c, determines the point c, which is called the centre of stress, and is the point through which the resultant of the distributed stress acts. ”

“ Disturbances of equilibrium, resulting in rock movements under gravity, may be caused by local loading, either natural or artificial. Natural loading may be due to unusual rainfall, or raising of water level, or increased barometric pressure. ”

“ A growth of new vital force—which yet was not a growth—everything pointed the other way, let me say a stock, was to be grafted into the decaying and wasting organism, permanent in its character, constant, without flux or reflux. ”

“ But why should the growth of every organism be finally arrested? Though the rate of increase may, in each case, be necessarily restricted within a narrow range of variation—though the increment that is possible in a given time, cannot exceed a certain amount ”

“ Similar discriminative effects of different rays of light in excitation of motile and growing organs.
CONTRACTILE RESPONSE OF GROWING AND NON-GROWING ORGANS.
I have shown (page 198) that a growing organ under stimulus, undergoes an incipient contraction as shown in the responsive retardation of its rate of growth; that this retardation increases with the intensity of the incident stimulus till growth becomes arrested. ”

“ Rate of growth is subject to definite laws, and the velocities in different directions tend to maintain a ratio which is more or less constant for each specific organism; and to this regularity is due the fact that the form of the organism is in general regular and constant. ”

“ In consequence of such disturbance to the equilibrium, active growth now takes place in the next group, leading to fresh irritation, and this group then reacts more strongly than all the others upon the tension which first stimulated its activity. ”

“ In seeking the answer it will be useful to ask ourselves another question. What should we have expected the drop to do? Well, to this I suppose most people would be inclined, arguing from analogy with a solid, to reply that it would be reasonable to expect the drop to flatten itself, and even very considerably flatten itself, and then, collecting itself together again, to rebound, perhaps as a column such as we have seen, but not to form this regular system of rays and arms and subordinate drops. ”

“ In the spiral shell we have a problem, or a phenomenon, of growth, immensely simplified by the fact that each successive increment is irrevocably fixed in regard to magnitude and position, instead, of remaining in a state of flux and sharing in the further changes which the organism undergoes. ”

“ When the recession has reached the point i, or, in other words, when the gradient of the stream below the fall crosses the junction of the beds of unequal hardness, as it ultimately must, effective undermining ceases, and the end of the fall is at hand. ”

“ That is to say, whenever we are examining the relation between cause and effect we are examining into conditions or states and not into equalities or inequalities of force. When a weight of a hundred pounds is raised a unit of altitude, the effect is a new position, and the force employed, which was one of the causes of the new position, is an action equal to the lifting of the weight as reaction. ”

“ When the stretch is of a certain amount, there is equilibrium—the action of the spring just balances the weight,—and if the spring be stretched further there will be a balance of pull developed tending to bring the system back towards the equilibrium position. ”

“ Cope founded his belief, that the adult characteristics were also the result of acceleration, if I rightly remember it, mainly upon the class of facts spoken of above in man where a sudden change into two organs may produce entirely new and unexpected differences in the whole organisation, and upon the changes which acceleration appeared to produce in the development of each succeeding species. ”

“ Would it not be simpler to consider the law of acceleration as a definition in all cases, and to regard the experiments in question, not as verifications of this law, but as verifications of the principle of reaction, or as demonstrating that the deformations of an elastic body depend only on the forces to which this body is subjected? ”

“ This skipping is the highest exemplification, or rather manifestation, of acceleration in development. In alluding to the history of diseases and inheritance of characteristics, you in your "Origin of Species" allude to the ordinary manifestation of acceleration, when you speak of the tendency of diseases or characteristics to appear at younger periods in the life of the child than of its parents. ”

“ It is a corollary that when the environment is changed, the equilibrium of functions is disturbed, and there must follow one of two results—either the equilibrium is overthrown or it is re-adjusted: there is a re-equilibration. ”

“ They deceive themselves. A careful study of the Falls from the trigonometrical points, even without instruments, and a comparison of what you see, with the map of 1842, would convince you that the recession during the past 30 years would fall inside of 15 feet. Let us take six inches a year as an approximation to the rate at which the Falls are eating back through the ledges of shale and limestone. The scale which answers to the last 30 years will apply to the channel from the Horseshoe to Ferry Landing, nearly half a mile. ”

“ In animals the function of accumulation comprehends those processes by which the materials containing latent energy are taken in, digested, and separated from other materials; the function of transfer comprehends those processes by which these materials, and such others as are needful to liberate the energies they contain, are conveyed throughout the organism; and the function of expenditure comprehends those processes by which the energy is liberated from these materials and transformed into properly co-ordinated motions. ”

“ Now that we have thus become acquainted with the physical cause of that movement of the earth's axis which gives rise to what is called the precession of the equinoxes, we have next to enter with somewhat greater detail into some of the results of the movement. ”

“ The incessant tendency of material forces is toward final equilibrium; and if the quantity of this tendency be finite, a time of repose must come at last. If one portion of the universe be hotter than another, a flux instantly sets in to equalise the temperatures; while winds blow and rivers roll in search of a stable equilibrium. ”

“ On these important subjects we shall scarcely touch; for our main purpose will be sufficiently served if we consider the char­ac­teris­tics of a rate of growth in a few illustrative cases, and recognise that this rate of growth is a very important specific property, with its own char­ac­ter­is­tic value in this organism or that, in this or that part of each organism, and in this or that phase of its existence. ”