320 THE SOUTH AFRICAN NATIONAL DEBT. 



to suspending the sinking fund, it destroys the precaution taken 

 with respect to all past debts ; but if it abandon the system of 

 paying part cost out of revenue, it does not do so much harm, as 

 the past expenses are already to some extent provided for. (2) If 

 it were once recognised that good finance demands payment of 

 part cost out of revenue, it would not be easy to depart from 

 the system, for the fault would be glaringly obvious. Any 

 government that said it could not meet the needed expense out 

 of revenue would have to face the retort, " Then don't spend the 

 money." Indeed, the system proposed is more elastic than the 

 sinking fund, for in bad years it is only necessary to stop spend- 

 ing on public works and the demand on the revenue stops auto- 

 matically without the canons of good finance being infringed. 

 It need hardly be added that the suggested plan is equally 

 applicable to other countries. If it were adopted generally, the 

 loan market would come to expect it, and look askance on loans 

 that were not so safeguarded, and thus a wholesome check would 

 be imposed on governments inclined to extravagance. 



APPENDIX. 



If a sum in be borrowed at a rate of interest a and a fixed 

 charge of nib per unit time be provided to meet it, then after time ;/ 

 the fraction outstanding, z will be given by 



HI 



(a) If a constant sum ni„ be borrowed each unit of time, then 

 the accumulated debt / at the end of time N from the first loan will 

 be 



/ = / m n z dn = ;//,, / — 



/// bn in„(b — a) f „ , , . , 

 ' / e" ' dn 



" J 



a 



bn . b — a „ v , „ v 1N ) (bn b—a 



= m, ] - + — - e«» (c « N — 1) = m - - !fZZ U**— 1) ' 



"l.fl (i \ 1 ,1 a- K 



