208 H. S. CARSLAW. 
The amount of the tax on £75,000 will be seen to be 
£1,562 10s. under the first clause. 
§5. In the Land Tax and Income Tax Act, 1918 of West- 
ern Australia, it is enacted that an Income Tax shall be 
levied on the chargeable income of taxpayers, as follows:— 
‘“At the rate of twopence in respect to every pound 
sterling of income chargeable plus an additional rate thereon 
of ‘006 of a penny for every pound sterling by which the 
income chargeable from all sources exceeds £100. Pro- 
vided that the rate in the pound shall not exceed two 
shillings and sixpence.”’ 
From the above statement it is to be understood that, if 
the taxable income is £x and the amount of the tax is T 
pence, we shall have 
ES ey 298. when « =< 100, 
(ye =| 2 + («—100) 006} x, when 101 =a SenG0: 
(a1) Oho. when « = 4767. 
It will be found that the amounts paid by each successive 
pound from the 101st up to the 4766th, form an arithmetical 
progression of which the first term is 2°606 pence and the 
common difference °012 pence. 
The 4765th pound pays 58°574 pence. 
The 4766th pound pays 58:°586 pence. 
The 4767th pound pays 49:064 pence. 
The 4768th pound and all succeeding pounds pay 30 pence. 
pn 
The rate of tax (—) for the value of x which corres- 
ponds to the average rate 2s. 6d. (namely 47662) is 58°6. 
The Treasury of West Australia loses about 2s. 4d. on each 
pound of income over £4767, since each of these pounds 
should pay at the rate reached at the end of the progression. 
A similar error occurs in the New Zealand Acts dealing 
with Land Tax, Income Tax, and Special War Tax. 
