PEOCEEDINGS 
OF THE 
ROYAL SOCIETY OF EDINBURGH. 
Monday, ^th January 1884, 
THOMAS STEVENSON, Esq., Vice-President, in the Chair, 
The following Communications were read : — 
1 Approximation to the Boots of Cubic Equations by help 
of Eecurring Chain Tractions. By Edward Sang. 
{Ahstract)\ 
In the progression of fractions here used, each new term is got by 
corresponding multiples of the three preceding terms, thus : 
this mode of formation being applied separately to the numerators 
and denominators of the fractions. 
For the cube root of 2 there is given the progression 
for which the multipliers are r=l, <1 = ^ , p = 3, and also a more 
rapidly converging series 
VOL. XII. 
1883-84. 
No. 116. 
rA -1- gB +pC = I) , 
rB + gC + pH = E , 
rC + gH +pE = F , and so on, 
1 0 1 4 15 58 223 
0 ^ 0'^ I ^ 3 ' 12^ 46’ 177’ 
= 
- 1 0 5 286 16287 
~d’ 0 ’ 4 ’ 227 ’ 12927 ’ 
having the multipliers 1 , - 3 and 57. 
VOL. XII. 
