Page:The New International Encyclopædia 1st ed. v. 10.djvu/598

INDEX KEWENSIS. 024 species with whioli he worked, provided the money for its eoiiipletioii. It was eompiled by ik-njamin Baydon Jackson (q.v.), wliose aim wa.s to record every genu-s and species of phaneroj;anioiis plants publislicd up to 1885; to follow Henthani and Hooker's Gincra I'lnnlarum as authority for the limitation of <;enera ; to add to each name, whether retained or .synonymie, a full reference to its place of piihlieation, retaineil names beinf; the earliest under which they were published in the recognized genus and not necessarily the ear- liest specific names; and, finally, to indicate the geographical distribution of each species. Two supplements, bringing the work down to 180."), and embracing specific names between Aaliusand Irika. appeared in 1002. In these the author was assisted by Theopliilus Durand of Hrussels. INDEX LAWS. See Exponent and Expo- NF.NTI.M.. INDEX NOTATION. See Notation. INDEX NUMBERS. An index number is a method adopted by statistical and economic writ- ers to exhibit the course of prices of a group of commodities or of commodities generally. A crude method of attaining this result is to add the prices of the various commodities togeth- er. The defects of such a procedure are apparent from the following simple illustration: INDEX NUMBERS. 2d date Cotton, por lb Flour, per bbl Fit; Iron, per tou (2000 lbs.).. In this comparison, where each article has an C(jual weight in determining the result, there appears to have been a fall in price of o.ti per cent.; while in the first statement, where pig iron predominated, a ri.se in i)rice if 1.2 jjor cent, ap- l)carcd, and in the second statement, where flour jircdominatcil, the fall in price appeared to be 7.2 per cent. It is obvious that the third state- ment or simple index number is a far better in- »'.ication of the course of prices of these articles thau the other two, where one article or the otiier dominates the result simply by reason of the fortuitous circumstance that its unit of measure- ment is relativelv large. The third statement is not, however, an abso- lutely exact measure of the total price change, since it is not ^if e<puil signifi<'ance that flour falls and that pig iron rises. To the individual consumer no doubt a slight fall in Hour is more important than an equal rise in pig iron. It may readily be assumed that he buys for his daily needs 10 times as many things afTected by the price of cotton as arc afTected by that of pig iron, and perb.nps four times as many afTecteil by the price of flour as are afTected by that of cotton. Ills relative consumption might be: jiig iron, 1 ; cotton, 10; flour, 40. Hence the price changes noted affect him in varying measure, and this must be accounted for in estimating tho significance of the total change. The calcula- tions are as follows: . Total »21.58 $21.83 If the sum be a criterion, it appears that there has been on the whole an advance in price of the group despite the fall in cotlim and flour. A little reflection will sliow that had pig iron been quoted l)v the pound instead of by the ton the result would have been different, as follows: Cotton. iM»r lb.... Flour, per bbl.... Pig iron, per lb.. Total l8t date S0.08 3.50 .009 $3,989 2d date $0.07 3.2.^ .00925 S3.32U25 But even here there are still great differences in the initial prices and the variations are meas- ured on very ditTcrent scales. The index number avoids this difficulty by re- ducing the initial ))rices to common terms. It establishes the variation of each price from its own starting-point, and then determines the aver- age variation. The assumed figures above given will serve the purpose of demonstration, and the following statement of relative prices is true for either of the series: Prioft at l8t date PrtceBt2d dat« in t4*rniR ot prfcp ut 1st dat«  $100 100 100 tPl 5 Pig Iron 102 8 Total $300 100 $2^3 ** Prlc6 Units of Impor- tance Product Cotton $87.5 92.9 102.8 10 40 1 875.0 Flour 3716.0 Pig Iron - 102.8 Total $283.2 941 51 ... 4C03.B 920 On the other hand, in the aggregate consump- tion of the nation the proportions of the differ- ent articles might be quite dilTerent, and hence also the significance of these combined changes in the wholesale market. Let us assume them to be: pig iron I, cotton 2, and Hour 4. We then have the following calculation : Price CnltB ot Impor- tance Product Cotton $87.5 92.9 102.8 2 4 1 175.0 371.6 Pig Iron 102 8 f Tntnl $283.2 94.4 7 M91 92.8 We have now determined by these slightly different methods the price of the group to have been at the second date, compared with the first, as 94.4, 02.0. and 02.8 respectively are to ,$100. and we have in these results from assumed figures a fair illustration of the methods of inde.x num- ber calculations, and the problems to which they give rise. The problems of a general index number are not dissimilar. The first is the choice of articles whose prices are to be included. Xo definite statement of what articles should or should not be comprised in the imlex can he made except that they shouhl be staple articles of general use. It would defeat the object of an investigation