114 BULLETIN OF THE 



standing indebtedness together with the interest on the fund sup- 

 posed to be already accumulated. 



2. Had the annual contribution to the sinking fund been a fised 

 sum in addition to the interest on the fund, these annual contribu- 

 tions would have formed a series in geometrical progression of 

 which the common ratio would be the amount of one dollar for 

 one year at the rate of interest realized on the investment of the 

 funds ; but since the contribution instead of being a fixed quantity 

 is one per cent, of a diminishing quantity in addition to the in- 

 terest on the fund, the entire annual contribution will constitute a 

 geometrical progression, in which the common ratio is the amount 

 of one dollar at a rate of interest one per cent, less than the rate 

 at which investments can be made. For instance, if investments 

 can be made at the rate of five per cent, per annum the entire annual 

 contributions will progress at the rate of four per cent. 



3. The language of the law is as follows : 



Sec. 3694. The coin paid for duties on imported goods shall be 

 set apart as a special fund, and shall be applied as follows : 



First. To the payment in coin of the interest on the bonds and 

 notes of the United States. 



Second. To the purchase or payment of one per centum of the 

 entire debt of the United States, to be made within each fiscal year, 

 which is to be set apart as a sinking fund, and the interest of which 

 shall, in like manner, be applied to the purchase or payment of the 

 public debt, as the Secretary of the Treasury shall from time to 

 time direct. 



Sec. 3695. All bonds applied to the sinking fund, and all other 

 United States bonds redeemed or paid by the United States, shall 

 be cancelled and destroyed. A detailed record of the bonds so 

 cancelled and destroyed shall be first made in the books of the 

 Treasury Department. The amount of the bond of each class that 

 have been cancelled and destroyed shall be deducted respectively 

 from the amount of each class of the outstanding debt of the 

 United States. 



Sec. 3696. In addition to other amounts that may be applied to 

 the redemption or payment of the public debt, an amount equal to 

 the interest on all bonds belonging to the sinking fund, shall be 

 applied, as the Secretary of the Treasury shall from time to time 

 direct, to the payment of the public debt. 



Let Dx denote the amount of the public debt outstanding at any 

 time (x) ; and let Fa; denote the aggregate amount of the sinking 

 fund as accumulated to that time : 



