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It is proved in this paper that there is a fine correlation between thevalues of $|\zeta(1/2+i\vp_2(t))|^4$ and $|\zeta(1/2+it)|^4$ where $\vp_2(t)$stands for the Jacob's ladder of the second order. This new asymptotic formulacannot be obtained in known theories of Balasubramanian, Heath-Brown and Ivic.

Jacob's ladders and the asymptotic formula for the integral of the eight order expression $|\zeta(1/2+i\vp_2(t))|^4|\zeta(1/2+it)|^4$