I consider the multivariate Alexander polynomial $\Delta(t_1,\ldots,t_n)$ for a $n$-component link (defined using e.g. the Fox derivative). If we wish to construct a 1-variable polynomial $A(t)$, we can project using $t_i \rightarrow t$.

On the other hand, the Alexander-Conway polynomial is defined by $$\nabla L_+ -\nabla L_- = (t^{1/2}-t^{-1/2}) \nabla L_0.$$

But these two polynomials differ by a factor of $(1-t)$ in case there are more than 1 component $$\nabla_L = \frac{A(t)}{1-t}=\frac{\Delta_L(t,\ldots,t)}{1-t} \text{ (up to multiplication by $\pm t^k$)}.$$

I figured this out experimentaly and am trying to find a reference to this fact if it is even true in general. In this post I asked about the existence of such a "projected" polynomial and now I am wondering about the difference with the Conway version of the polynomial.