TRANSACTIONS OF THE SECTIONS. 157 



These compound units are the sources of frec[uent faUacies; thus if the popula- 

 tion is compared with the deaths in a quarter, a week, a day, or any short interval 

 of time, the apparent mortality is reduced to any extent. In reckonin» interest 

 and profit-rates, £1 under investment a year is the double unit ; if the dividend 

 on £100 is £2 half-yearly, the rate of profit is £4 a year. 



The rate of profit is found by dividing (1) the profits by (2) the capital multi- 

 plied into (3) the thne. 



Inattention to this principle is the source of some of the common fallacies on 

 the income-tax. Thus if two persons are taxed equitably on their property, they 

 are taxed in proportion to its amount and to the time it is under the protection of 

 the State : if A pays £1 on £1000 in a year, B is not fairly treated if he is made to 

 pay £1 every three months. The sophist assm-es B that he pays at the same rate 

 as A, keeping out of view the fact that the taxable unit is compounded of value 

 and time. Income is an indication, but not a measure, of property, yet if A has 

 a sum under investment in one way, he may have to pay at the rate of 6d., while 

 B with the same amount of property may now ha-ce to pay 10, 20, 30 sixpences as 

 his quota of the year's taxation. A life income of £1000 a year on men of 20 and 

 upwards, at 5 per cent., is on an average worth £11,712; while at the same interest, 

 the same income in perpetuity is worth £20,006. The owners of two properties 

 taxed upon the same unit of value, pay £11712 and £20-000 as their quota of the 

 year's tax ; under an income-tax the same premium is exacted from properties of 

 totally diflerent values. 



The first step in every statistical inquiry is to determine the value of the units 

 to be employed, be they single, double, or multiple. Thus if you find that the 

 mines of a country yield 5000 tons of copper ore, while the mines of another ^aeld 

 10,000, these are only preliminary units ; the final statistical unit is the ton of 

 copper. So of all the minerals the ton of metal is the final unit. The heating 

 power of coal is the element of value, and as it can be measured, it should supply 

 the final unit. 



In the statistics of products it is necessaiy to take time and space into the final 

 units of value ; thus coal at the pit's mouth is worth say 5s. a ton, and at this 

 price 40,000,000 tons are worth £10,000,000; but the consumer pays 10.s., 20*., 

 30s., 40s. a ton for this coal, and its cost in consumption maybe £40,000,000. This 

 comprises the profit of the coal merchant, the interest of capital, the coal dues, 

 and the cost of transport, which varies with the supply of horses, roads, canals, 

 railways. Our exports and imports difier in value in the home and foreign market. 

 The value of products should be determined at every stage ; thus we should follow 

 wheat from the market tiU it becomes (1) flour and (2) bread, and take care that 

 in all these cases the units are so like in all their aspects as to admit of compaiison. 

 It does not foUow that two countiies which have the same numbers of cattle are 

 equally rich in that kind of stock ; the herds of cattle may diiFer in size, in age, 

 in their amounts of produce of milk, butter, and meat — in the quality of all tlieir 

 products. Horses differ still more in excellence. In Smithfield sheep are not 

 bought by the head, but by the stone ; the oftal is sunk, and the price varies from 

 6(7. to 8d. per pound in inferior and prime sheep. The butcher gets at, and the 

 statist uses, the pound of saleable meat as the final unit. All the elements which 

 the statist wants here are taken into account in the value of stock and of its produce; 

 with this he gets comparable units in every climate. Again, take land : land-mea- 

 sures vary. Statists gain a step by employing as their imit a hectar, or a square 

 of 100 metres to the side; it is a large acre, o'f which om- present acre is foui- teutlis. 

 The United Kingdom contains (31,367,507) thirty-one million hectars of laud, 

 rather more than a hectar to each person. This is the proportion of land to people 

 in a populous country; and the hectar is a convenient unit of area. England hns 

 15, Scotland 8, and Ireland 8 million hectars of land ; the popidation being 20 mil- 

 lions in England, 3 millions in Scotland, and 6 in Ireland. The proportions in 

 ten are — England 7, Ireland 2, Scotland 1 ; on areas related as 2, 1 and 1. Ireland 

 has still twice the population of Scotland. Italy has 26, Pmssia 29, Spain 51, 

 France 54, Austria 64 million hectars. 



We come to States of a very diflerent magnitude; the United States of America 

 hold 440, Turkey 474, Russia "in Europe 544 million hectars. Including the whole 



