For a discussion of what AAB means by a “law” please see Alice A. Bailey – What is a Law?
In addition to the Law of Correspondence (singular) there is a Law of Correspondences (plural) which appears much more often in AAB’s writings. Below are all the references I found to the singular form of Law of Correspondence.
This is a deep mystery and I fear it is not possible for me to express these ideas with greater clarity. However, under the Law of Correspondence or Analogy, the initiate can gradually come to a true perception of the significances involved.
The fifth kingdom in nature, the spiritual, will emerge out of the fifth root race. Such is the esoteric control of the Law of Correspondence.
There are not therefore four deaths, as the goal of our system during manifestation is “initiation or release into the air,” so that the bird of life out of time and space can fly free. The concept which the Law of Correspondence brings of the final death is covered by the words liberation, relinquishment and final initiation, and means little to humanity, for it concerns the planetary Logos and His life cycle.