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A WEEKLY ILLUSTRATED JOURNAL OF SCIENCE.

To the solid ground
Of Nature trusts the mind which builds for aye."—WORDSWORTH.

No. 1068, VOL. 41.]

THURSDAY, APRIL 17, 1890.

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THURSDAY, APRIL 17, 1890.

indirect and inferential. He who trusts the rising of the mercury when the north-east wind is blowing may get a wetting. So also with the metaphorical weather-glass.

“ The property test is useful as far as it goes, but it is not THE GROWTH OF CAPITAL.

the only test,” says Mr. Giffen. Elsewhere, in his address The Growth of Capital. By Robert Giffen. (London : to the British Association, he has acted the part of a G. Bell and Sons, 1889.)

Fitzroy in considering together and interpreting in their CHE popular conception of what statistics are is connection the various tests and signs which economic

who describes an adept in that science stationing himself one particular instrument. early in the morning at the entrance to a bridge, This barometrical use of capital may involve the ne. and, after scrutinizing the passengers for several hours, cessity of correcting the estimates so as to take account triumphantly reporting that exactly 2371 widows have of changes in the value of money. It may happen, it has crossed during the day. This arithmetic of the street is happened, that in the last decade, as compared with the not the type of Mr. Giffen's calculations. His purpose is preceding period, the growth of capital estimated in more philosophical, his method more elaborate.

money shows a falling off, while the increase of money's The object which he seeks to measure is nothing less worth, of things, has not declined proportionately. To than the whole property, the accumulated exchangeable complete our measurement we must correct the measurwealth, of the United Kindom. In this problem, to appre-ing-rod. This is no easy or straightforward task. In hend even the question requires an effort of intelligence. the case of a real barometer we can mark the inches by "Imagination shrinks from the task of framing a cata- reference to the standard yard measure, which is kept in logue or inventory of a nation's property, as a valuator the Tower. But a similarly perfect measure of value is, would make it." Reason points out that the grand total in the phrase of an eminent living economist,“ unthinkis not so much the value of the whole, which in its able." The present generation finds itself, with respect entirety cannot be considered saleable, as the sum of to the variations in the value of money, in the sort of the values of all the parts, any one of which may be sold difficulty which must have occurred to the primæval man by its proprietor. The attribute of accumulation, as well when first he may have noticed that a perfect measure of as that of exchange, requires careful definition. Mr. time was not afforded by the length of day and night, Giffen, differing from some of his predecessors and con- and before there had been constructed a more scientific temporaries, does not regard the labourer himself as a chronometer. Even Mr. Giffen has to content himself species of capital. He does not, with Petty, attempt to with such rough and rather arbitrary corrections as the determine the " value of the people," nor, with De Foville, present state of monetary science affords. to effect "the evaluation of human capital.” However, As the object sought, the measure of accumulation, is some items which are of an incorporeal nature seem to somewhat hazy and difficult to envisage, so the method enter into his account. Presumably, that part of the by which it is approached is indirect and slippery national capital which he reckons by capitalizing the The business man must not suppose that the estimates income of public companies-multiplying it by a certain of a nation's capital can be totted up with the precision number of years' purchase-represents the value, not only of a commercial account. The physicist is better preof land and plant, but also of an immaterial something, pared to appreciate the character of the computation, which, in a broad sense, may be described as "custom" conversant as he is with observations which individually or "good will." Mr. Giffen doubts whether public debt are liable to a certain error, while, put together, they should be admitted as an item of capital. He is certain afford certainty. But even physical observations, liable that tenant-right should be excluded.

to a considerable yet calculable extent of error, hardly The uses of such a valuation are manifold. Mr. Giffen parallel the fallibility of these economic or, if we night devotes a chapter to their enumeration. In the first coin a required word, metastatistical computations. In place, it is desirable to compare our resources with our estimating that fallibility, we may usefully employ the liabilities. It is satisfactory to find that the national analogy suggested by the theory of errors ; but we must debt compared with the national fortune is but a "baga- bear in mind the criticism to which this theory, even in telle." The amount of a country's accumulations, and its application to physics, was subjected by a witty mathethe rate of their increase, afford some measure of its matician: “After having calculated the probable error, capacity to endure the burdens of taxation, and, we may it is necessary to calculate the probability that your add, other kinds of pecuniary strain. It is observed by calculation is erroneous.” Newmarch, one of Mr. Giffen's predecessors in this The characteristic to which we draw attention is fully department of statistics, that the investment in railways, recognized by Mr. Giffen. Again and again he dwells on which produced such convulsions in 1847-48, would have the rough and approximative character of his method, been in 1863 almost unfelt and insignificant in com- “the wide margin of error," and the “limit of informaparison with the yearly savings which were being made tion available.” His cautions against reasoning too finely at the later epoch.

might have seemed superflous in their iteration, but that One use to which Mr. Giffen gives prominence may be he doubtless anticipated the irrelevant criticism which thus described. The comparative growth of capital at each departmental statistician might direct against details different epochs serves as a sort of barometer of nationallike the specialist in sculpture who, according to Horace, prosperity. Of course those who use a barometer must represents with peculiar accuracy the hair or nails, but remember that its indications of fair weather are but nescit componere totum. VOL. XLI.—No. 1068.

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The futility of a penny-wise precision, and even of that or diminishes both the numerator and denominator in criticism which sticks at a few thousand pounds where the same proportion is not operative on the result. If millions or tens of millions are the units of the scale, will all the data were based on income-tax returns, and the be apparent when we consider the construction of the same proportion of property escaped the net of the colossal account. The starting-point of the computation collectors at each epoch, the result would be undisturbed is afforded by the income-tax returns. The income under But all the data are not based on the income-tar ; dice, each head thus evidenced is multiplied by a certain num even if there were no increased stringency in the collection ber of years' purchase to form the corresponding item of of the tax as a whole, or any other general derangement, capital. Thus, in the valuation of 1885 there is, under could it be supposed that the defalcations under each the head of “Houses," the income £128,459,000, which, head observed an exactly uniform proportion. To estibeing multiplied by 15, the number of years' purchase, mate the effects of this unequal distortion, it will be gives £1,926,885,000 as the corresponding entry of capi- convenient to alter our statement by putting in the tal. Again, under “Farmers' Profits," the income is numerator, instead of lands in 1885, the expression£65,233,000, which, being capitalized at 8 years' purchase,

Lands in 1875 X

Lands in 1885 makes £521,864,000 capital. Now, of course, neither

Lands in 1875 are the income tax returns perfectly accurate, nor can the number of years' purchase proper to each category be with corresponding changes for the other entries assigned with precision. A further element of uncertainty Thus the quæsitum may be considered as a sort is introduced when, in the case of “Trades and Profes- of mean--a weighted mean-of the ratios between sions," we reduce the income-tax return by a somewhat the several items for the two years. In this exarbitrary factor, one-fifth, in order to take account only of pression the influence which the two elements, the that income which results from accumulated property as absolute quantities used as weights and the ratios, exer distinguished from personal exertion, Where the in- cise upon the error of the result is different. The inttucome-tax is no longer available for our guidance, the ence of error in the absolute quantities would be procedure becomes even more precarious. Thus “Movable comparatively small, if those quantities were tolerably Property not yielding income,” such as furniture of houses equal and the ratios not more unequal than they are and works of art, is estimated as amounting to half the But, unfortunately, the absolute quantities are extremely value of “Houses," that is, £960,000,000. Even the unequal. Out of the twenty-six items, "Lands" and most faithful follower of Mr. Giffen may be staggered "Houses " together make up more than a third of the when with reference to such entries he reads

sum-total. By a formula adapted to the case, it may be " The estimates of the income of non-income-tax calculated that, if each of the twenty-six quantities be paying classes derived from capital of movable property liable to an assigned error per cent. (exclusive of such not yielding income, and of Government and local pro- mistakes as, affecting the numerator and denominator of perty, are put in almost pro formå and to round off the the result in an equal proportion, disappear in the division', estimates, and not with any idea that any very exact then the percentage of error incident to the total result is figures can be stated.”

not likely to be less than gths of the error affecting each But whoever carefully considers the principles on which of the parts. That is, abstracting the inaccuracy of the Mr. Giffen has assumed the different coefficients entering ratios, which are of the forminto his computation-principles set forth more fully in a former essay--will be satisfied that he has in no case

Lands in 1885 - Lands in 1875. run a risk of overrating. We may therefore accept his Now any error in the ratios is more directly operative on estimate of the national capital in 1885 as a figure the result than the same degree of error in the absolute round indeed, but not exaggerated. That figure is quantities. But, on the other hand, it may be that the erron £10,000,000,000.

actually affecting the ratios is particularly small, owing Greater precision may be attainable where there is the favourable operation of that general principle which required, not the absolute amount of capital in 1885, but we have just now cited from Mr. Giffen's pages. The estithe ratio of that amount to the corresponding estimate mate of inaccuracy must, however, be increased to some for 1875, in order to compare the growth of the national extent by the error of the ratios. Altogether it would resources during that decade with the growth at a pre- seem that the whole chain or coil is not so much stronger vious period. We shall now be assisted by the important than the particular links or strands as is usual in the ca! principle which Mr. Giffen thus notices :

culation of probabilities. It would be a moderate es “According to well-known statistical experience, the mate that the percentage error of the compound ratio is comparison of the growth or increment may be reason- not less than a half of the error on an average affecung ably successful, if the same method is followed on each each of the components-lands, houses, &c.-in either occasion in working out the data for the comparison, although these data themselves may be unavoidably in- year, complete."

What degree of error, then, shall we attribute to cach

of these items? A precise determination of this con Let us put our quæsitum in the form of a fraction, efficient is, as we have already observed, impossible in thus :Lands in 1885 + Houses in 1885 + &c.

would be interesting to collect the estimates of competent

authorities. As a mere conjecture, for the sake of illusLands in 1875 + Houses in 1875 &c.

tration, let us entertain the supposition that the error the (using lands, &c., as short for value of lands, &c.). It is effective error in the sense above explained) of any one evident that any source of inaccuracy which exaggerates item is as likely as not to be as much as 5 per cent, and

may just possibly be 20 per cent. Then we should increase of capital, Mr. Giffen turns round and seems ascribe half this degree of inaccuracy to the figure 1'175, to reason from the increase of capital to the fall of swhich, according to Mr. Giffen's computation, is the ratio prices. of the total capital in 1885 to the total capital in 1875. It would be conceivable that the real increase, as measured of population is known to be at much the same rate

“If two periods are compared in which the increase by some superior being, is not 174 per cent., but as little throughout, and the increase of productive capacity may as 7, or as much as 27, per cent. Perhaps the defect is be assumed to be at the same rate, or not less, in one of a little more likely than the excess, if there exist any the periods than in the other, then, if the apparent accuconstant cause making for depression such as the in. mulation of capital in the one period proved to be less creased stringency of the tax-collectors in later years.

than in the other, it must be ascribed to some change in The growth of 17 per cent. in the decade under con

the money values.” sideration may appear surprisingly small compared with

This reasoning may appear circular to the formal logithe 40 per cent. recorded for the preceding decade. The cian. But, in the logic of induction, we submit that it is general accuracy of the contrast is, however, confirmed very proper for two arguments archwise to support each by a comparison of the growths in each item for the two other. The consilience of different lines of proof is decades. Mr. Giffen points out that in the former decade, indeed an essential feature of the logic of fact, as formuunlike the latter, there are no growths downwards. Also lated by J. S. Mill. We venture to interpret Mr. Giffen's the percentages which measure increase run mostly at a double line of proof by the following parable. Has it higher level for the earlier period. His detailed examina- never occurred to you, reader, on looking at your watch, tion of the figures leaves nothing to desire. For a sum- and finding the hour earlier than you expected, to suspect mary contrast between the two sets of percentages we that the instrument has played you false? You review might submit that a proper course would be to compare what you have been doing; recollect, perhaps, that you the medians of the respective sets of figures (the arith. began work or got up earlier than usual; and, on reflecmetic means would not be suitable owing to the very tion, see no reason to distrust your watch. You test the unequal importance of the figures relating to such miscel- watch by the time, and you measure the time by the laneous items). Operating in the manner suggested, we watch. Similarly, Mr. Giffen is quite consistent when find as the median of the first set of percentage growths he measures the extent of the growth of capital by the 50, and of the second 25, thus confirming Mr. Giffen's extent of the fall in prices ; and confirms the fact of a conclusion that the former movement is about double the fall in prices by the independently inferred fact of a latter.

considerable growth of capital. The conclusion that in the last decade our progress has In connection with the fall of prices we should notice been only half what it was in the preceding decade is at an important contribution which Mr. Giffen makes to first sight disappointing. But we must remember that as monetary science by defining the ambiguous term “appreyet we have accomplished only part of our calculation. ciation.” The readers of NATURE who may be more We have still to make a correction for the change in the familiar with physical than social science will smile when value of money which may have occurred between the they understand that there has been in economical circles two periods. This is a problem familiar to Mr. Giffen. a stiff controversy on the following question: Whether, In his classical computations of the changes in the volume if there is not now in circulation a sufficient amount of of our foreign trade he encountered and surmounted a money-in proportion to the quantity of commodities similar difficulty. In that case he ascertained the change circulated-to keep up prices to a former level, the cause in the level of prices at which exports and imports ranged of the fall is the scarcity of gold or the abundance of in different years without going beyond the statistics of goods. It is as if, when the shoe pinched, people should foreign trade, and by operating solely on the prices and dispute whether the shoe is too small, or the boot too quantities of exports and imports. It might be expected, large. The mirth of the physicist seems for the most perhaps, that he would pursue an analogous course in part justified. However, as Coleridge or somebody said, constructing a measure for the change of prices affecting before we can be certain that a controversy is altogether the volume of capital. He would thus have been led to about words, there is needed a considerable knowledge of adopt the very ingenious method of measuring changes things. The better class of controversialists in the matter in the value of money which has been proposed by Prof. before us have doubtless had a meaning, but a latent J. S. Nicholson. But, however cognate that original idea and undeveloped one, which it required our author, may be to the theory of the subject, it will be found in like another Socrates, to bring to birth. The issue practice not easy to apply to the present computation. appears unmeaning, as long as you consider the question At any rate, Mr. Giffen has taken his coefficients for the in Mr. Giffen's phrase "statically,” without reference to correction in question, not, as before, from the subject the rate at which the quantity of goods and gold are itself, but ab extra, from Mr. Sauerbeck, Mr. Soetbeer, growing. But “dynamically," if goods and gold cease to and the Economist. Averaging their results, he finds that move abreast, it is intelligible to attribute the separation money has appreciated to the extent of 17 per cent between the two to the operation of one rather than the during the interval under consideration. This correction other. As we understand the matter, using our own being made, the growth of capital in the period 1875-85 illustration, let us liken the constant growth of goods to proves to be about the same as the growth in 1865-75. the uniform velocity of a boat carried onward by a steady

The soundness of this conclusion is confirmed by some stream ; and the parallel increase of money to the movereflections which at first sight might appear open to ment of a pedestrian on the bank. If the pedestrian, criticism. After using the fall of prices to prove the after keeping abreast with the boat for some time, is at

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