The conservation laws are examined from the transformation properties of the Lagrangian. The energy-momentum complex obtained has mixed indices, ${{T}_{\ensuremath{\mu}}}^{\ensuremath{\nu}}$, whereas a symmetric quantity ${\mathcal{T}}^{\ensuremath{\mu}\ensuremath{\nu}}$ is required for the definition of angular momentum. Such a symmetric quantity has been constructed by Landau and Lifshitz. In the course of examining the relationship between these quantities, two hierarchies of complexes ${{T}_{(n)\ensuremath{\mu}}}^{\ensuremath{\nu}}$ and ${{\mathcal{T}}_{(n)}}^{\ensuremath{\mu}\ensuremath{\nu}}$ are constructed. Under linear coordinate transformations the former are tensor densities of weight ($n+1$) and the latter of weight ($n+2$). For $n=0$ these reduce to the canonical ${{T}_{\ensuremath{\mu}}}^{\ensuremath{\nu}}$ and the Landau-Lifshitz ${\mathcal{T}}^{\ensuremath{\mu}\ensuremath{\nu}}$, respectively.By requiring the energy-momentum complex to generate the coordinate transformations, and the total energy and momentum to form a free vector, one can identify the canonical complex ${{T}_{\ensuremath{\mu}}}^{\ensuremath{\nu}}$ as the appropriate quantity to describe the energy and momentum of the field plus matter. Similarly, by requiring the total angular momentum to behave as a free antisymmetric tensor, one can construct, in the usual manner, an appropriate quantity from ${{\mathcal{T}}_{(\ensuremath{-}1)}}^{\ensuremath{\mu}\ensuremath{\nu}}$. The angular momentum complex so defined differs from that proposed by Landau and Lifshitz as well as from an independent construction by Bergmann and Thomson.