When we decide to throw the older theories into the melting-pot and make a clean start, it is best to relegate to the background terminology associated with special hypotheses of physics. Physical quantities defined by operations of measurement are independent of theory, and form the proper starting-point for any new theoretical development. Now that we have explained how physical quantities are to be defined, the reader may be surprised that we do not proceed to give the definitions of the leading physical quantities. But to catalogue all the precautions and provisos in the operation of determining even so simple a thing as length, is a task which we shirk. We might take refuge in the statement that the task though laborious is straightforward, and that the practical physicist knows the whole procedure without our writing it down for him. But it is better to be more cautious. I should be puzzled to say off-hand what is the series of operations and calculations involved in measuring a length of $10^{-15}$~cm.; nevertheless I shall refer to such a length when necessary as though it were a quantity of which the definition is obvious. We cannot be forever examining our foundations; we look particularly to those places where it is reported to us that they are insecure. I may be laying myself open to the charge that I am doing the very thing I criticise in the older physics----using terms that \PageSep{7} have no definite observational meaning, and mingling with my physical quantities things which are not the results of any conceivable experimental operation. I would reply--- By all means explore this criticism if you regard it as a promising field of inquiry. I here assume that you will probably find me a justification for my $10^{-15}$~cm.; but you may find that there is an insurmountable ambiguity in defining it. In the latter event you may be on the track of something which will give a new insight into the fundamental nature of the world. Indeed it has been suspected that the perplexities of quantum phenomena may arise from the tacit assumption that the notions of length and duration, acquired primarily from experiences in which the average effects of large numbers of quanta are involved, are applicable in the study of individual quanta. There may need to be much more excavation before we have brought to light all that is of value in this critical consideration of experimental knowledge. Meanwhile I want to set before you the treasure which has already been unearthed in this field. \PageSep{8} \Chapter{I}{Elementary Principles} \Section{1.}{Indeterminateness of the space-time frame}