Chapter III. Population

CHAPTER III POPULATION § I. More People, less Land per Head. To an Isolated Man in possession of the whole world there could be no question of Population-of too many or too few human things. If we suppose the world inhabited by large numbers of isolated men, men that is to say who did not co-operate, the question would be present, but in a very simple form. Each luan could only be benefited by the existence and consequent actions of the others in an incidental way, as, for example, he would be benefited by their killing off tigers or snakes to protect themselves. On the other hand, he would be injured by their occupation of land and catching of beasts which would be useful to him, and the greater their numbers the worse his position would be: obviously, the more numerous the human beings, the less land there would be for each, so that each man would have a smaller command of space and materials for agricul ture and other industry. It would seem probable that this disadvantage of large numbers would nluch more than counterbalance its incidental advantages in all ordinary circumstances.

The existence of co-operation modifies the situa 40 NOT ENOUGH LAND 4I tion very greatly without making any fundamental alteration. The ad~tage of having a number of neighbours becomes more than a matter of freedom from attack by wild beasts killed by those neighbours entirely for their own purpose. Co-operation being established, people enjoy the advantages of it, which we have already described, and the more people there are the greater can be the advantages derived from it. But there must always be a point at which the advantages are just counterbalanced, and beyond which they are more than counterbalanced, by the disadvantage of less space and materials per man. The disadvantage of putting II too many" people on a given space of ground has been observed from the very earliest times. '~ Abram," we are told, II was very rich in cattle ... and Lot also, which went with Abram, had flocks and herds and tents, and the land was not able to bear them, that they might dwell together . . . and they separated them selves the one from the other." .If people had imagined they could live in unlimited numbers on any given area they would have squeezed themselves all into a fertile field just outside the Garden of Eden, or on the slope of Ararat, or wherever the original home of the human race may have been, instead of spreading all over the globe. If it is thus obviously possible to have over-population on a portion of the earth's surface, it must also be possible to have it on the earth as a whole, which is only made up of its several parts.

Put in this way the theory of population 'seems to be little more than a very obvious generalization POPULATION which scarcely admits of discussion. But it has a' rather complicated history, without some knowledge of which it is difficult to understand the form which modern treatment of the subject usually takes in economic works. We need not go back very far. The ancient Greek philosophers regarded population from a point of view which was quite different from that of the modem economist. They were interested in what are called political rather than economic questions, and their politics were the politics of small city states. So they inquired how tpany people could be prop~rly governed in a city st~te, but not how many 'should live on a given spac~i of land in order to bring about the best economic results. The population of any considerable territories known to them probably did not increase perceptibly enough to make them ask whether it should ever stop, and if so, when. In the Middle Ages, too, throughout Europe population did not increase fast enough to make people think about the question whether it was desirable that it should go on increasing indefinitely. What we find is very frequent complaints of depopulation couched in such a form as to imply that no one could possibly imagine depopulation to be a good thing. In the seventeenth century growth of population was visible in England, and persons interested in the coloniza tion of Virginia tried to show that it would be much better if large numbers of people were shipped across the Atlantic, but their arguments did not lead to the emergence of any general theory. In the eighteenth century the great wars led each nation POSSIBILITIES OF MULTIPLICATION 43 to desire the largest possible population without thought for the economic consequences. As one who Wrote towards the close of that century ob serves, U Population! Population! Population at all events!" was the universal cry throughout Europe.

§ 2. Th~ Possibiliti~s of Multiplication obs~"v~d and used as an Argument against Utopias. The history of the population theory, in fact, only goes back to the middle of the eighteenth century, when its origin is to be found in the con troversy which then took place between certain scholars about the population of the world, or rather the "populousness of ancient nations." Some writers contended that the number of people was much greater in ancient than in modem times. Others, among whom Hume ~as pre-eminent, took the opposite view. It was only natural that some of the disputants should, in the course of discussion, hit on the plan of enforcing some argument by show ing how rapidly population would increase if human fecundity had full scope and mortality were normal. Robert Wallace did this in 1753 with the object of showing that there ,vas no difficulty in supposing that the population had increased so much between the Deluge and the time of Alexander the Great as to be greater at the end of that period than it actually was in the eighteenth century. He constructed a table showing that if we suppose six children to a marriage and a mortality which destroys two of them before they have time to become fathers and POPULATION mothers, the total population will increase in I,233 years from two persons to over four hundred and twelve milliards (4I2,316,860,416). Such a table makes it very obvious that, as Wallace says, " there has never been such a number of inhabitants on the earth at anyone point of time, as might have been easily raised by the prolific virtue of mankind." It also leads to the inquiry, It What are the circum stances which have repressed the growth of popula tion ?" and to the further inquiry, It Can these repressive influences be removed? "

Some of the circumstances, Wallace decided, were physical, and independent of the volition of man. Others were due to the errors and vices of mankind, and might be largely removed by better government. But they could not be altogether removed even by a perfect government. It Under a perfect government," he says, It the incon veniences of having a family would be so entirely removed, children would be so well taken care of, and everything become so favourable to populousness, that though some sickly seasons or dreadful plagues in particular climates might cut off multitudes, yet in general mankind would increase so prodigiously that the earth would at last be overstocked, and become unable to support its numerous inhabitants." Even if " some extraordinary method of support ing" the people were discovered, the inevitable would only be postponed, since soon It there would not even be sufficient room for C{)ntaining their bodies upon the surface of the earth." It is " cer tain that limits are set to the fertility of the earth, MALTHUS 45 and that its bulk, so far as is hitherto known, hath continued always the same, and probably could not be much altered without makin~ considerable changes in the solar system." Therefore II the greatest admirers of such fanciful schemes must foresee the fatal period when they would come to an end" in a II catastrophe." Barbarous and un natural regulations would have to be introduced, and mankind would never agree about them, but would fall to fighting over them.

§ 3. Malthus' theory that Population tends to out run Subsistence. In his Essay on the Principle of Population, 1798, Malthus borrowed this argument from Wallace to use it against the~. Utopian anarchism of William Godwin. .Population, or u-the' principle of popula tion," as he sometimes expressed it, must, he thought, be kept in check, and all checks resolved themselves into vice or misery, so that no Utopia could be possible. But he was not content, with Wallace, to suppose there must at last be a catastrophe. He thought that (( the difficulty, so far from being remote, would be imminent and immediate." He thought so because he was imposed upon by a mis leading mathematical jingle which he had invented. n Population," he said, II when unchecked, increases in a geometrical ratio. Subsistence increases only in arithmetical ratio." His one example of an increase in geometrical ratio was doubling every twenty-five years, and his one example of an arith metical ratio was increasing by an amount equal . I POPULATION it appear highly probable. It might seem highly probable to reasonable persons that the produce of Great Britain could not be quadrupled in fifty years, and certain that it could not go on being doubled every twenty-five years thereafter. They might even be tolerably sure that it could not be increased every twenty-five years for the next century by more than an amount equal to the produce in 1798, and certain, though Malthus does not suggest this rather obvious reflection, that it could not go on indefinitely increasing, even by equal amounts every twenty-five years.

§ 4. "The Law of Di1ninishing Returns." But some one might object, " I With every mouth God sends a pair of hands,' as the proverb says, so why should not the increased number of-people be able to grow a proportionately increased amount of produce? Or even more, seeing that they would be able to draw greater advantage from division of labour?" Malthus' argument gives no answer to these questions except what is obscurely implied in "it would be contrary to all our knowledge of the qualities of land." Common knowledge of the "properties of land" tells us that it would be impossible to get an infinite amount of produce from any limited area, even if we could increase the amount of labour expended on that area indefinitely. It also tells us, which is more important for practical purposes, that the amount of additional produce which can be got by equal additional amounts of labour expended on the limited area will begin to POPULATION to the original amount every twenty-five years. If these two series, I, 2, 4, 8 ... and I, 2, 3, 4, 5 ... are placed side by side, it is obvious that after the second term the first series increases much more rapidly than the second series, and Malthus inferred that there must consequently be " a strong and constantly operating check on population from the difficulty of subsistence." For the doubling of population in twenty-five years he relied on the experience of North America, and here he was on firm ground, since whether the period he gives is longer, as he supposed, or· shorter than the reality, there is no doubt that an (( unchecked" population would double itself in some short number of years.

But for the" arithmetical ratio" of the increase of subsistence-for his assertion that the subsistence could only be made to increase by an amount equal to the original amount every twenty-five years, he had no warrant at all. He relied merely on a nebulous supposition. Turning his eyes away from his North American example, where, unless, which there was no reason to believe, the existing people were worse fed than their much less numerous ancestors, subsistence must have increased in the same geometrical ratio as the populations, he asked his readers to " take an,y spot of earth, this island, for instance, and see in what ratio the subsistence it affords can be supposed to increase." U If," he says, "I allow that by the best possible policy, by breaking up more land, and by greater encouragements to agriculture, the produce of this island may be doubled in the first twenty-five years, I MALTHUS 47 think it will be allowing as much as any person can well demand.

II In the next twenty-five years it is impossible to . suppose that the produce could be quadrupled. It would be contrary to all our knowledge of the qualities of land. The very utmost that we can conceive is that the increase in the second twenty-five years might equal the ol'iginal produce. Let us, then, take this for our rule, though certainly far beyond the truth, a.nd a.llow that by great exertion the whole produce of the island might be increased every twenty-five years by a quantity of subsistence equal to what it at present produces. The most enthusiastic speculator. cannot suppose a greater increase than this. In a few centuries it would make every acre of land in the island like a garden. Yet this ratio of increase is evidently arithmetical. It may be fairly said, therefore, that the means of sub sistence increase in an arithmetical ratio." It is doubtful if " enthusiastic speculators " would have admitted that the produce of Great Britain could not possibly be quadrupled in fifty years from 1798, but whether or no, Malthus does not prove his case, since it is clear that produce had doubled and quadrupled within the periods supposed in the North American colonies: if this ever happened anywhere, it must be wrong to lay down as a general proposition that the means of subsistence can only increase by equal amounts every twenty-five years.

If we confine the proposition, as we may suppose Malthus unconsciously did in his own mind, to countries already as thickly peopled as Great Britain was in 1798, he resembles the candidate in geometry who claimed that if he had· not exactly proved the proposition set before him, he had at least made DIMI~ISHING RETURNS 49 diminish before, and often, perhaps we might say generally, long before the point is reached at which additional labour would bring in no additional return at all. The truth was well expressed in a criticism which Turgot wrote upon an obscure essay sent in for a prize offered by the Royal Agricultural Society of Limoges about 1768. He says:"Seed thrown on a soil naturally fertile but totally unprepared would be expenditure almost entirely wasted. If the ground were once tilled the produce would be greater; tilling it a second and a third time might not double and triple but quadruple or decuple the produce, which will thus augment in a much larger proportion than the expenditure, and that up to a certain point, at which the produce will be as great as possible com pared with the expenditure. Past this point, if the expenditure be still increased, the produce will still increase, but less and less, and always less and less, until the fecundity of the earth being exhausted, and art unable to do anything further, an addition to the expenditure will add nothing whatever to the produce."

The statement, of course, applies to some or any one given time, so that it excludes the consideration of the changes in man's knowledge and other circum stances which will from time to time alter the position of the U certain point, at which the produce will be .as great as possible compared with the expenditure," and also the position of the ultimate point at which the fecundity of the earth is exhausted and art unable to do anything further, so that H an addition to the expenditure will add nothing what ever to the produce." In fact, the knowledge and circumstances of mankind are continually changing, / 50 POPULATION and very often, probably in the majority of cases, the change is of such a nature as to shift the points in the direction which is favourable to the pro ductiveness of additional labour. Hence common knowledge of the properties of land, while it does tell us that population cannot, at anyone time, be greater than a certain size without causing the returns to industry to be less than they might be, certainly does not tell us that population cannot double itself in twenty-five years, treble in fifty, and quadruple in seventy-five, nor even that it cannot double every twenty-five, quadruple in fifty, and octuple in seventy-five years without causing any diminution of returns. The most we can say is that such rapid progress is unlikely to go on long, and certain not to go on for ever.

§ 5. The theory that Growth of Population had caused an actual Diminution of Returns in Agriculture. Malthus himself never attempted to bring his theory of population into close relationship with the law of production laid down in the passage just quoted from Turgot. Though the law must have been latent in the mind of every prudent farmer with sufficient means to over-cultivate if he wished to do so, and though it was, as we see, clearly stated by Turgot in 1768, its history does not really begin till 1814. At that time much discussion took place in England about the new duties on the importation of corn which were supposed to be required in order to keep the price of corn up to what was considered a remunerative figure. Moderate men thought this DIMINISHING RETURNS 51 would be about 80S. the quarter for wheat, but most "agriculturists seem to have demanded a good deal 'more. The dispute led people to give some attention to the cost of cultivating the new land which had recently been taken into cultivation in consequence of the high prices which were brought about by bad seasons and increasing population, little or no importation being possible during the war. All authorities agreed that the cultivation of the new land was highly expensive. The high protectionists thought this a great argument in their favour, since, if the prices fell, the new land could not be kept in cultivation, and then, they said, less com would be produced and its price would rise again. To this Malthus, Ricardo, and a much less well known but excellent writer, Sir Edward West, all replied in effect that the recent rise of price was the result of the new land being worse than the old, and that if some com were imported, cultivation could be confined to better land on which t~e cost of produc tion and the price would be lower, so that the effect of allowing importation would be to lower rather than to raise the price.

To explain their thesis both Ricardo and West wrote brief imaginary histories of the progress of cultivation, illustrated with numerical examples, in which they supposed the most fertile and best situated land to be taken into cultivation first and then the less and less good in regular succession as population increased-and required larger and larger supplies. They recognized that the larger supplies could also be obtained by employing more labour 52 POPULATION on the old land, but whether they were obtained by labour on the new land or by additional labour on the old or, as would happen in practice, partly by one method and partly by the other, the returns to a given amount of agricultural industry would be diminished. West says:It The ... principle ... is that each equal addi tional quantity of work bestowed upon agriculture yields an actually diminished return, and, of course, if each equal additional quantity of work yields an actually diminished return, the whole of the work bestowed on agriculture ... yields an actually dimin ished proportionate return. Whereas it is obvious that an equal quantity of work will always fabricate the same quantity of manufactures."

This It principle" of West's received the rather unfortunate title of " the la\\r of diminishing returns in agriculture." The diminution of returns, it was seen, might be prevented from actually taking place by what were called" inlprovements," that is to say, inventions and the introduction of better methods, but it was supposed that the effect of these changes was merely temporary, and could not prevail in the long run against the general principle, so that diminishing returns was the general rule throughout history. This is so contrary to the results of direct observation that it seems difficult to believe that it could ever have been accepted, but it was supported by the erroneous theory of profits generally held at the time, which led people to suppose that the historical fall in the general rate of interest which had taken place was a proof of diminution of returns.

DIMINISHING RETURNS 53 The doctrine of 1814 that growth of population produces a (( tendency," in the sense of a general drift only temporarily interrupted by II improve ments," towards a diminution of the returns to a given amount of industry expended in agriculture was not a (( law" at all, but a hasty and erroneous generaliza tion founded on observations made in an exceptional period of English history. When the memory of that gloomy period began to fade away, writers began to point out that, as a matter of fact, in spite of the great increase of population, the returns to agricultural industry had, in the general course of history, increased enormously. One of them says:(f In 1389, in securing the crop of com from 200 acres, there were employed 250 reapers and thatchers on one day and 200 on another. On another day in the same year 212 were hired for one day to cut and tie up 13 acres of wheat and I acre of oats. At that time 12 bushels to an acre were considered an average crop, so that 212 persons were employed to harvest 168 bushels of grain, an operation which could be accom plished with ease in our time by half a dozen persons."

Statistics of this kind are difficult to obtain, and not always trustworthy, but no reasonable person can have any doubt that the productiveness of agricultural industry has enormously increased. The population of the civilized world is much better fed, and yet has to spend far less a proportion of the whole of its labour on the acquisition of food. If agricultural returns diminished, and yet the people continued to be equally well fed, a larger and ever w. F 54 POPULATION larger proportion of the world's labour would clearly have to be expended in producing food. § 6. The theory that Growth of Population had made Returns 'in Agr'iculture Less than they otherwise would have been, and this sufficiently to Over balance Increase of Returns in other Industry. When no longer able to ignore the historical in crease of returns to agriculture, those who were deter mined to take a gloomy view of the effects of growth of population shifted their ground by saying that they did not mean that it caused a tendency to diminution of returns in the sense of a general drift, subject only to temporary interruptions, towards diminution of returns, but that it tended to diminish returns in the sense of causing the returns to be less than they otherwise would be. The growth of population, it was supposed, always tended to diminish agricultural returns, although" improvements" or, as J. S. Mill said, " the progress of civilization," had in the course of history more than counteracted this force, so that though returns had actually increased, they would have been still greater if population had not increased.

This is clearly untrue if it is applied to the whole history of mankind. It would be absurd to contend that the productiveness of agricultural industry would be greater now than it actually is if the population of the world had remained at two, or whatever other small figure we suppose it to have started from. The H improvements" which have taken place would certainly not have been disTENDENCY TO DIMINISHING RETURNS 55 covered and introduced if the population had re mained so small. But if the doctrine is applied, as Mill seems to have meant to apply it, only to fairly recent times, it does not appear to be possible either to prove or disprove it. Mill coolly assumed that all the improvements which have been made would have been made just the same if the population had not grown. We cannot assume that, and we have no means of finding out exactly what would have been the position in that respect in Mill's time if the population of the world had remained at the same figure as it had reached in 1800, nor what would be the position now if the population had become stationary at the figure it had attained when Mill wrote in 1848 and which he considered great enough.

Of course the question of the desirability or un desirability of increase of population cannot be settled entirely by its effect on the returns to agricultural industry. Man does not live by bread alone, but requires all sorts of other commodities. The law of diminishing returns was put forward as applicable only to agriculture and other cc extractive industries," such as mining, which were regarded as directly dependent on the fertility of the soil. In other industry, especially manufacturing industry, it was supposed that di 7ision of labour led to increas ing returns \vhen larger quantities of produce were raised by increasing numbers of workers. Thus it had to be admitted that an increase of population, while tending to diminish returns from agricultural industry, at the same time tended to POPULATION increase returns from manufacturing industry, so that a balance had to be struck between the effect of the two tendencies: the returns to all kinds of industry taken together would only diminish when the diminution in agriculture was great enough to outweigh the increase in manufactures. It seems difficult to believe that anyone could have supposed that this was ordinarily the case, but the theory of profits already referred to required those who held it to think that a diminution of returns, at any rate in all the industry which produces things for the labouring classes, was proved by the historical fall of the rate of interest, and the practice of identify ing wages with food which prevailed in the earlier part of the nineteenth century led to the weight of agriculture being grossly overestimated. Con sequently it was held that increase of population tended to diminish the returns to all kinds of in dustry taken as a whole, and the gloomier writers of the time believed that it had actually done so.

§ 7. The Point of Maximum Return to All Industries taken together. What is wanted now is to throw aside the sharp distinction which was drawn in 1814 between agriculture and manufactures. Turgot's law is just as true of manufactures as of agriculture. At any given time (or if the reader prefers, circumstances remaining unchanged) increase of labour up to a certain point is attended by increasing proportionate returns (called for short increasing retunis) and beyond that point further increase of labour is POINT OF MAXIMUM RETURN 57 attended by diminishing proportionate returns (called for short diminishing returns). Mankind cannot produce an unlimited amount of calico any more than an unlimited amount of wheat. It would be impossible to produce more than a certain amount however many persons were engaged upon the production: and long before that amount was reached, the amount of additional calico which could be produced by each unit of additional labour would begin to diminish. At any given time, or which comes to the same thing, knowledge and circumstances remaining the same, there is what may be called a point of maximum return, when the amount of labour is such that both an increase and a decrease in it would diminish proportionate returns.

It is a crude and barbarous idea of agriculture which represents it as almost entirely dependent upon original fertility of soil and foot-pounds of human muscular energy, and as scarcely affected at all by the world-wide co-operation of mankind which pro vides it with appropriate tools and suitable seed, and combines the products of different regions so as to make them wholesome or palatable to the consumer. The most we can say in contrasting agriculture and manufacture is that the advantages of producing a large aggregate quantity and therefore the advan tages of a large population to produce and consume the large quantity are more obvious in manufacture than in agriculture. If we measure returns from the starting-point of nil suggested by the historical progress of population and assumed by Malthus, 58 POPULATION West, and Ricardo in 1814, we can say that in both agriculture and manufacture returns increase up to a certain point, and beyond that point they decrease.

If we can start from what I have called the point of maximum return, we can say of manufacture as well as of agriculture tha t returns diminish as we move in either direction from that point. If we suppose all difficulties about the measure ment of the returns to all industries taken together to be somehow overcome, we can see that at any given time, knowledge and circumstances remain ing the same, just as there is a point of maximum return in each industry, so there must be in all industries taken together. If population is not large enough to bring all industry up to this point, returns will be less than they might be; if, on the other hand, population is so great that the point has been passed, returns are again less than they might be. The course which the development of theory on this subject has taken has led to the use of a great deal of very unsatisfactory phraseology which ought to be discarded. '''riters have said that" the law of diminishing returns had not come into operation,"

when they only meant that returns had not begun to diminish, and they have spoken of the law It undergoing a temporary supersession" when they meant only that returns had left off diminishing for a time. They have talked of " commodities which obey the law of diminishing returns" when they meant commodities the supply of which could not at the moment be increased without a diminution THE OPTIMUM 59 of returns, and of U commodities which obey the law of increasing returns " when they meant commodities of which some increase of supply would be at the moment accompanied by increased returns. They have even imagined an intermediate class U obeying the law of constant returns." All these expressions involve misuse of the term " law." A scientific law should be true at all times and places, and should not be liable to "temporary supersessions" or failures to come into operation, nor capable of being suddenly replaced by a contrary la\v. No one says that the law of gravity had not come into operation in Newton's garden until the apple broke from its stalk, nor that the law would have undergone temporary supersession if Newton had caught the apple as it fell. Nor do we say that a falling balloon is "subject to the law of gravity," but ea rising balloon is "subject to another law, that of rising bodies," while a balloon which remains at the same level is II subject to the law of constant height."

If we want to preserve the phrase" diminishing returns" we must take the point of maximum return as the starting-point, and say that returns diminish in either direction, all commodities 0r industries being always and everywhere subject to this (( law of diminishing returns. J' § 8. The Optimum, or best possible Population. Great caution must be exercised in applying the idea of a point of maximum return to the' question what is the most desirable population. In the first place, it is very important not to fall into the error 60 POPULATION of supposing that the point of maximum return remains permanently fixed, either for particular industries or for industry taken as a whole. The position of the point is perpetually being altered by the progress of knowledge and other changes. The discovery of the princi pIe of rotation of crops and the invention of steam locomotion on rails, coupled with the provision of the requisite appli ances, not only made increase of population possible without diminution of returns and consequent deterioration of wealth, but also made or tended to make that increase desirable. These changes shifted the point of maximum return, pushing it farther along in the direction favourable to large population.

Hence it is quite possible that the world was over popula ted in some past age when there was not a tithe of the present number of people on the globe, and that all the same it is not over-populated now. In the meantime the point of maximum return may have been shifted. Secondly, we must remember that population is not so agile in its movements as to be able to follow every shifting of the point of maximum return immediately. We can easily imagine some change in knowledge shifting the point rather suddenly, while it is obvious that the number of living man kind cannot be altered except slowly by an alteration in the balance of births and deaths, and that an increase of workers will only follow from an increase of births after an interval of more than a decade, while deaths cannot be accelerated or retarded except in so far as the moral or religious principle that THE OPTIMUM 61 human life must be preserved as long as possible is not maintained in practice.

Consequently it is useless to condemn the popula tion of anyone point of time as too great or too small simply because if it were smaller or larger the returns to industry would be greater at that time. The population of any moment is dependent for its magnitude on the population of the past, and will in its tum affect the population of the future. We have no right to isolate it and pick it out in preference to the others. Very probably it could nOt be different from what it is without causing the past or the future population to diverge so much more from the optimum or best possible that the result on all the periods taken together would be worse than the actual state of things. So what we have to look for is not the best population at any particular moment without refer ence to what has gone before and what is to follow after, but the best at all the moments taken together. In other words, we have to treat the ideal or optimum in regard to population as being the right movement (i.e. increase or decrease) of population rather than define it in reference to one particular point of time.

The right movement is that which will give the largest returns to industry in the long run, the interests of the people of all the generations being taken into the account. Thirdly, the general population theory should not be rashly applied to national or other local or tribal subdivisions of mankind. Of course it could be applied without any modification at all to a sub62 POPULATION division which was entirely isolated from all the others, but in so far as movement of men and goods is possible between a subdivision and the outside world, it must take its share in the effects of the general movement. The smaller it is and the greater the mobility between it and the others, the more its position approximates to that of the individual family, which is unable to make returns to industry appreciably higher or lower by more or less rapid propagation.