Abstract
The International System of Units tries to find or construct something that does not change with time and place, since such constancy is the best possible ground for definitions of fundamental measurement units. This problem of constancy has received scant attention within the philosophy of science, but is the topic of the paper. The paper first highlights inevitable kinds of circularities, semantic and epistemic, that belongs to the search for constancy, and then discusses contingent dependencies between unit definitions. The New SI proposal is criticized for not paying due attention to the fact that it defines units for one kind of quantity by means of a constancy that belongs to another. This inattention flaws the kilogram definition. The New SI definitions of the mole and the second neglect the distinction between discrete and continuous quantities; which make the definitions refer to constancies that are not invariants of nature.