192 Professor Whewell on the 



16. It will be more simple to suppose the successive quanti- 

 ties of exports Se„ Se z , Se 3 , &c. to be known. In this case the 

 calculation will stand as follows. 



Let n-i+JBlArtfcfcfc^, 



gx ffi 



namely, the ratio of the gold originally in the country + the 

 value of the exports in the t th year, to the original gold; the 

 exports being reckoned at the original price. Also, let the ex- 

 ports = ng,. Then we have, by equation (1) 



g t+1 = m,g t - ng lt 



which may be easily reduced to calculation when the number of 

 terms m„ m„, m 3 , &c. is not large. 



Let the exports and imports reach their equilibrium in three 

 years ; we then have the equations 

 gs=m l g 1 -ng } 



g*=*tg»-*iTv 

 Hence g A = \ »h »», m, - (m 3 m 9 + m t + 1)*} g t ... (8). 



For instance, let the value of the imports be originally ^ of 

 the value of the currency of the country : and let the exports 

 be, in the first year -r of the same value; in the two successive 

 years let the exports be so diminished in quantity as to be - 

 and r. if estimated at the same price: therefore Sp^, = -g n Sp t e s 



tj 1 5 6 7 



Here » = gj »i-j m *~s> mi ~ $■ 



