Wages, capital: Substitution and Output Effects

Consider a CES production function $$Y=f(K,L)$$ with elasticity of factor substitution $$\sigma>0$$.

The substitution effect of higher real wages naturally implies a shift along the isoquant to more $$K$$. The rise in costs will reduce output. The total effect of $$w \uparrow$$ on $$Y$$ and $$K$$ is the sum of this substitution and output effect.

I'm interested in the link between the value of $$\sigma$$ and the strength of these two effects. Does anyone know a good reference, or lecture notes on the algebra of these effects in the CES context?