Non-standard scales for fundamental measurements obtained by a change of operation of concatenation satisfy the axioms in the same manner as standard scales. One possible change of operation for length measurement is from linear juxtaposition to rectangular juxtaposition. Some argued that the choice between standard and non-standard scales can be guided by no other reason but simplicity of science and convenience. Non-standard scales for length measurement however, would require either change of laws, or introduction of a universal force or a change of all other scales which would preserve the laws, and a complicated practice which consists of many partial measurements that affect the precision of measurement. The set of permissible scales for length measurement divides naturally into two subsets: symmetric and asymmetric scales. The set of permissible scales can be reduced to the symmetric scales by either adding an axiom or by stating a symmetry requirement as a law dictated by the nature of the magnitude under consideration (length).