554 



NA TURE 



{April 17, 1890 



The futility of a penny-wise precision, and even of that 

 criticism which sticks at a few thousand pounds where 

 millions or tens of millions are the units of the scale, will 

 be apparent when we consider the construction of the 

 colossal account. The starting-point of the computation 

 is afforded by the income-tax returns. The income under 

 each head thus evidenced is multiplied by a certain num- 

 ber of years' purchase to form the corresponding item of 

 capital. Thus, in the valuation of 1885 there is, under 

 the head of "Houses," the income ^128,459,000, which, 

 being multiplied by 15, the number of years' purchase, 

 gives ^1,926,885,000 as the corresponding entry of capi- 

 tal. Again, under " F"armers' Profits," the income is 

 ;^65, 233,000, which, being capitalized at 8 years' purchase, 

 makes ^521,864,000 capital. Now, of course, neither 

 are the income-tax returns perfectly accurate, nor can the 

 number of years' purchase proper to each category be 

 assigned with precision. A further element of uncertainty 

 is introduced when, in the case of " Trades and Profes- 

 sions," we reduce the income-tax return by a somewhat 

 arbitrary factor, one-fifth, in order to take account only of 

 that income which results from accumulated property as 

 distinguished from personal exertion. Where the in- 

 come-tax is no longer available for our guidance, the 

 procedure becomes even more precarious. Thus " Movable 

 Property not yielding Income," such as furniture of houses 

 and works of art, is estimated as amounting to half the 

 value of " Houses," that is, ^960,000,000. Even the 

 most faithful follower of Mr. Giffen may be staggered 

 when with reference to such entries he reads — 



" The estimates of the income of non-income-tax 

 paying classes derived from capital of movable property 

 not yielding income, and of Government and local pro- 

 perty, are put in almost /r^ T^rwa and to round off the 

 estimates, and not with any idea that any very exact 

 figures can be stated." 



But whoever carefully considers the principles on which 

 Mr. Giffen has assumed the different coefficients entering 

 into his computation — principles set forth more fully in 

 a former essay — will be satisfied that he has in no case 

 run a risk of overrating. We may therefore accept his 

 estimate of the national capital in 1885 as a figure 

 round indeed, but not exaggerated. That figure is 

 £ 1 0,000,000,000. 



Greater precision may be attainable where there is 

 required, not the absolute amount of capital in 1885, but 

 the ratio of that amount to the corresponding estimate 

 for 1875, in order to compare the growth of the national 

 resources during that decade with the growth at a pre- 

 vious period. We shall now be assisted by the important 

 principle which Mr. Giffen thus notices : — 



"According to well-known statistical experience, the 

 comparison of the growth or increment may be reason- 

 ably successful, if the same method is followed on each 

 occasion in working out the data for the comparison, 

 although these data themselves may be unavoidably in- 

 complete." 



Let us put our qucEsitum in the form of a fraction, 

 thus : — 



Lands in 1885 -f Houses in 1885 -j- &c. 

 Lands in 1875 + Houses in 1875 -^ &c. 



(using lands, &c., as short for value of lands, &c.). It is 

 evident that any source of inaccuracy which exaggerates 



or diminishes both the numerator and denominator \n 

 the same proportion is not operative on the result. If 

 all the data were based on income-tax returns, and the 

 same proportion of property escaped the net of the 

 collectors at each epoch, the result would be undisturbed. 

 But all the data are not based on the income-tax ; nor 

 even if there were no increased stringency in the collection 

 of the tax as a whole, or any other general derangement,^ 

 could it be supposed that the defalcations under each 

 head observed an exactly uniform proportion. To esti- 

 mate the effects of this unequal distortion, it will be 

 convenient to alter our statement by putting in the 

 numerator, instead of lands in 1885, the expression^ 



Lands in 1875 X 



Lands in 1885 

 Lands in 1875' 



with corresponding changes for the other entries. 

 Thus the qucesitutn may be considered as a sort 

 of mean — a weighted mean — of the ratios between 

 the several items for the two years. In this ex- 

 pression the influence which the two elements, the 

 absolute quantities used as weights and the ratios, exer- 

 cise upon the error of the result is different. The influ- 

 ence of error in the absolute quantities would be 

 comparatively small, if those quantities were tolerably 

 equal and the ratios not more unequal than they are. 

 But, unfortunately, the absolute quantities are extremely 

 unequal. Out of the twenty-six items, " Lands " and 

 " Houses " together make up more than a third of the 

 sum-total. By a formula adapted to the case, it may be 

 calculated that, if each of the twenty-six quantities be 

 liable to an assigned error per cent, (exclusive of such 

 mistakes as, affecting the numerator and denominator of 

 the result in an equal proportion, disappear in the division), 

 then the percentage of error incident to the total result is 

 not likely to be less than fths of the error affecting each 

 of the parts. That is, abstracting the inaccuracy of the. 

 ratios, which are of the form — a 



Lands in iJ 



Lands in 1875. 



Now any error in the ratios is more directly operative on 

 the result than the same degree of error in the absolute 

 quantities. But, on the other hand, it may be that the error 

 actually affecting the ratios is particularly small, owing to 

 the favourable operation of that general principle which 

 we have just now cited from Mr. Giffen's pages. The esti- 

 mate of inaccuracy must, however, be increased to some 

 extent by the error of the ratios. Altogether it would 

 seem that the whole chain or coil is not so much stronger 

 than the particular links or strands as is usual in the cal- 

 culation of probabilities. It would be a moderate esti- 

 mate that the percentage error of the compound ratio is 

 not less than a half of the error on an average affecting 

 each of the components — lands, houses, &c. — in either 

 year. 



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

 of these items ? A precise determination of this co- 

 efficient is, as we have already observed, impossible. It 

 would be interesting to collect the estimates of competent 

 authorities. As a mere conjecture, for the sake of illus- 

 tration, let us entertain the supposition that the error (the 

 effective error in the sense above explained) of any one 

 item is as likely as not to be as much as 5 per cent., and 



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