The author, within twenty years last past, has had his attention called by two different persons, each ignorant of the efforts of the other, who were seeking to obtain Perpetual Motion by utilizing certain physical facts concerning Momentum and Energy. These facts and the principles out of which they grow are familiar to all who understand thoroughly, even the rudiments of physics; but to persons who are inclined to mechanics, but who have never had the advantages of the presentation of clear principles, they are confusing, and it is surprising that they have not become more fertile fields for Perpetual Motion workers. However, we are unable to find any written or printed account or description of a plan or device of that kind, and our information is confined to instances that have been brought to our personal observation, and concerning which the advice and counsel of the author was sought. The worker in each case was a man of more than ordinary natural intelligence, and with a bent for mechanical pursuits and reflection. Each had taken a course in what is conventionally called High School Physics. The idea in each case was so novel and interesting that we deem the presentation worth while. They were so nearly alike that instead of attempting to narrate what they said, we will endeavor in our own way to present the idea, and then to give our explanation, showing wherein lay their error. The following definitions and laws of physics may be regarded as established: Momentum _Momentum_ is the quantity of motion of a moving body, and is the velocity multiplied by the weight. Thus, a body weighing two pounds, moving at four feet per second, may be represented as having a momentum of eight. A body weighing two pounds moving at the rate of six feet per second may be said to have a momentum of twelve. A body weighing ten pounds moving at the rate of ten feet per second will have a momentum of one hundred--and so on. Now, a step further. A body in motion striking another body free to move will lose part of its motion, and will impart some of its motion to the body moved against. The aggregate momentum after the striking is the same as before--that is to say--if a body weighing ten pounds have a velocity of twenty feet per second, its momentum we will call two hundred. Now, if in moving it strike another body either larger or smaller its motion will be somewhat retarded, and the body struck will possess some motion.