A more general form of the Beer–Lambert law states that, for N attenuating species in the material sample, T = exp ⁡ ⁡ ( − − ∑ ∑ i = 1 N σ σ i ∫ ∫ 0 ℓ ℓ n i ( z ) d z ) = 10 ∧ ∧ ( − − ∑ ∑ i = 1 N ε ε i ∫ ∫ 0 ℓ ℓ c i ( z ) d z ) , or equivalently that τ τ = ∑ ∑ i = 1 N τ τ i = ∑ ∑ i = 1 N σ σ i ∫ ∫ 0 ℓ ℓ n i ( z ) d z , A = ∑ ∑ i = 1 N A i = ∑ ∑ i = 1 N ε ε i ∫ ∫ 0 ℓ ℓ c i ( z ) d z , where