Notation 1: CONVENTIONAL SIDE-BY-SIDE NOTATION OF A VOLTAGE DIFFERENCE ALONG A WIRE, OVER AN INTERVAL OF n meters, INCLUDING CROSSEFFECTS (THAT ARE PLAINLY MEANINGFUL, IN THE ALGEBRAIC SENSE, AT ANY FINITE SCALE.)

THE SIDE-BY-SIDE NOTATION IMPLIES MULTIPLICATION OF THE LENGTH INCREMENT, "n meters" UNDER ALL CIRCUMSTANCES.

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NOTATION 2: MODIFIED SUBSCRIPT (RATHER THAN SIDE-BY-SIDE) NOTATION OF A VOLTAGE DIFFERENCE ALONG A WIRE, OVER AN INTERVAL OF n meters, INCLUDING CROSSEFFECTS.

THE SUBSCRIPT NOTATION DOES NOT IMPLY MULTIPLICATION OF THE LENGTH INCREMENT, "n meters" UNDER ALL CIRCUMSTANCES.

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Algebraic simplification of notation 1, that assumes that "association and multiplication are the same" One does not know what the terms below the first line mean, and these terms fail two kinds of loop tests. (The wholes are not equal to sums of the parts. The same term does not mean the same, over all "permitted" procedures that involve change from one system of units to another.)

Algebraic simplification of notation 2, according to rules that avoid multiplying numerical values of increments times themselves. Natural law operators in terms are dimensionally correct for the terms in which they occur. Every term is associated with the SAME spatial increment ( of n meters). No assumption that "association and multiplication are the same" Every term makes physical sense. Every term passes all loop tests that can be rightly applied. (Wholes equal the sums of the parts. The same term means the same, numerically and dimensionally, over all "permitted" procedures that involve change from one system of units to another.)