This paper attempts to do two things: one is to give a precise analysis of the relationships between public goods and externalities; the other is to provide a formulation of a model involving public goods which covers the so-called mixed cases, i.e. those goods which lie somewhere between the extremes of the pure private good and the pure public good. There has been a tendency in the literature on external economies to ignore the public good aspect of externalities and a tendency in the literature on public goods to identify the two concepts with each other. The view taken here is that they are two distinct concepts, but that many externally produced commodities have the character of public goods. A theory of external economies must therefore take this feature into account. This paper attempts to show how this can be done by using the original Samuelson formulation [11]2 of a public good. It has been conceded by Samuelson himself [12] that many goods commonly termed public goods do not strictly fit his definition. There are some goods which seem to have a mixture of the characteristics of a public good and a private good. This paper attempts to resolve the confusion that has arisen in discussing these mixed goods by showing how a simple extension of the Samuelson model can accommodate them. It also demonstrates the effect that their presence has on the necessary conditions for Pareto-optimality.