The common application of the concepts of space and time results in the concept of _motion_, the science of which is called phoronomics. In order to make this new variable subject to measurement we must arrive at an agreement or convention as to the way in which to measure time. For since past time can never be reproduced we actually experience only unextended moments, and have no means of recognizing or defining the equality of two periods of time by placing them side by side, as we can in the case of spacial magnitudes. We help ourselves by saying _that in uninfluenced motions equal periods of time must correspond to the equal changes in space_. We regard the rotation of the earth on its axis and its revolution about the sun as such uninfluenced motions. The two depend upon dissimilar conditions, and the empirical fact that the relation of the two motions, or the relation between the day and the year, remains practically the same, sustains that assumption, and at the same time shows the expediency of the given definition of time. _Analytic geometry_, the application of algebra to geometric relations, occupies a noteworthy position, from the point of view of method, in the science of space. It yields geometric results by means of calculation, that is, by the application of the _algebraic_ material of symbols we can obtain data concerning unknown _spacial_ relations. An explanation is necessary of how by a method apparently so extraneous such results as these can be attained.