The writer is not attempting to construct a new system of dynamics, but merely to present in a clear form what he believes to be the principles of our existing system, and he ventures to hope that such a presentation may be of some use to those teachers of dynamics who are not specialists, and perhaps to older students. The paper is not intended for experts.

It has appeared to him that in the various text-books written on this subject, these principles are at times forgotten, with the result that there are to be found many faults, some due to incompleteness, some to vagueness, some to reasoning in a “vicious circle,” and some to the attempt to make one equation give us two or even three unknowns.