This paper is a sequel of the work  where the notions of "physical size? and its "measure? are cleared up, and the use of the term "measure? in metrology, not only to appoint the measure standard, but also for the quantitative expression of a physical size, obtained experimentally or by calculation, is proposed. In the present work, as a result, the properties of the measure of the physical sizes on the basis of its general expression are determined. These properties will be used in the framework of future papers.