The laws which are to be imposed on these ideal representations are in the first instance largely at our choice. Any scheme of abstract dynamics constructed in this way, provided it be self-consistent, is mathematically legitimate; but from the physical point of view we require that it should help us to picture the sequence of phenomena as they actually occur. Its success or failure in this respect can only be judged a posteriori by comparison of the results to which it leads with the facts. It is to be noticed, moreover, that all available tests apply only to the scheme as a whole; owing to the complexity of phenomena we cannot submit any one of its postulates to verification apart from the rest. It is from this point of view that the question of relativity of motion, which is often felt to be a stumbling-block on the very threshold of the subject, is to be judged. By "motion" we mean of necessity motion relative to some frame of reference which is conventionally spoken of as "fixed." In the earlier stages of our subject this may be any rigid, or apparently rigid, structure fixed relatively to the earth. If we meet with phenomena which do not fit easily into this view, we have the alternatives either to modify our assumed laws of motion, or to call to our aid adventitious forces, or to examine whether the discrepancy can be reconciled by the simpler expedient of a new basis of reference. It is hardly necessary to say that the latter procedure has hitherto been found to be adequate. As a first step we adopt a system of rectangular axes whose origin is fixed in the earth, but whose directions are fixed by relation to the stars; in the planetary theory the origin is transferred to the sun, and afterwards to the mass-centre of the solar system; and so on. At each step there is a gain in accuracy and comprehensiveness; and the conviction is cherished that _some_ system of rectangular axes exists with respect to which the Newtonian scheme holds with all imaginable accuracy. A similar account might be given of the conception of time as a measurable quantity, but the remarks which it is necessary to make under this head will find a place later. The following synopsis shows the scheme on which the treatment is based:-- _Part 1.--Statics._ 1. Statics of a particle. 2. Statics of a system of particles. 3. Plane kinematics of a rigid body. 4. Plane statics. 5. Graphical statics. 6. Theory of frames. 7. Three-dimensional kinematics of a rigid body. 8. Three-dimensional statics. 9. Work. 10. Statics of inextensible chains. 11. Theory of mass-systems. _Part 2.--Kinetics._