To exert power is for some principle to cause some potential to become actual. For example, a tree has the power to grow, but it does not have the power to burn. A man, by contrast, cannot make a tree grow, but can only cooperate with the tree in this regard. But a man has the power to burn a tree. The tree has no potential to burn without this (or some similar) external power. So, the potential to burn follows from the will of a man as its principle. Power and potential are not identical terms: 'Power' refers to the relation of an object's potential to the principle of that potential. Hence a tree has the potential to burn, but it does not have the power to burn.
Authority is the principle by which power is ordered to its proper end. A man may have the power to burn a tree without the authority to do so. Likewise, a man may have the authority to burn a tree without the power to do so. Authority serves to direct power to its end both by informing an agent in power (e.g. by issuing legal commands) and by ensuring the agreement of the application of power with order (e.g. through prudential consideration). Hence, the ordinary expression of authority is law. Power without authority degenerates itself but, with authority, is preserved and increased. Authority does not necessitate acts of power; rather, power is the means of fulfilling the aim of authority.
