in the Value of Land. 149 



land of the colony and let it on long leases. Whether it 

 should do so or not is a political question that we have 

 nothing to do with. There seem to me to be many reasons 

 why it might do so with advantage ; but in this note I only 

 seek to call your attention to an obvious mathematical fact 

 that is commonly ignored in a most unaccountable manner. 



In reckoning the rate at which the value of land increases, 

 we must always adopt the methods of compound interest. 

 No one pretends that, if a piece of land during the present 

 year increases in value, this increment is at the end of the 

 year taken out of the land ; the increased value of the land 

 has to remain throughout the next year as the capital in- 

 vested, and the rate must be calculated upon that. To 

 calculate it every year upon the original price of the land 

 would be absurd. And yet this is what has been done by a 

 recent writer in the Melbourne Review, who seeks to prove 

 that the value of the land in Melbourne has increased at the 

 rate of 139 per cent, per annum. If this statement is put 

 forward by a well-informed writer, we may guess what 

 misconception prevails generally. If £100 had originally 

 been spent in the purchase of land, and it had increased in 

 this rate, the value in the second year would be £239, for 

 none of the increased value has been taken out of it. Now, 

 if it still increases at the rate of 139 per cent, per annum, 

 this must be reckoned on the £239, and not on the original 

 £100. To show how utterly astray the calculation is, I need 

 only mention that at this rate, even assuming so short a 

 period as twenty-one years, the present value of the land 

 of Melbourne would be £24,190,000,000,000 instead of its 

 real value, £8,286,000. 



I have no doubt that to any one conversant with mathe- 

 matics it will seem a very elementary proposition that the 

 method of compound interest is the only one allowable in such 

 a case, but I should like to have the matter discussed before 

 our society, so that the true method to be adopted may be 

 settled, and possibly our legislators prevented from rushing 

 into hasty measures grounded on fallacious reasons. 



The question of rents has come in as a disturbing element. 

 Not only here, but in England and France, it has been 

 tacitly assumed that, as a man gets from year to year, in the 

 shape of rent, what is reckoned as a fair interest, the incre- 

 ment can then be calculated as at simple interest. But I 

 need hardly point out to a mathematician how faulty such 

 a process would be. The only correct method is to calculate 



