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We introduce a class of currents which allows a new and very explicit form for the Massey product of a third order link as a line integral. The explicit form permits the introduction of an asymptotic Massey product analogous to that introduced previously for Gauss's integral by V. Arnold. The average third order asymptotic Massey product is shown to be equal to Berger's third order helicity for divergence-free vector fields in linked tori. A. CurvesAn integral expression on a tubular neighborhood of a curve is different than a line integral over the curve itself and, to our knowledge, the first to suggest the latter in this context were Evans and Berger in Ref. 5. We will rigorously derive their expression from Massey's formula in Sec. II by using Stokes's theorem. Denoting by ⍀ C i (X),iϭ1,2,3, the solid angle subtended by the curve C i from the viewpoint X, the result is a͒ Electronic

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