## Abstract

As is well known, the stress in a polymer solution can be expressed in terms of the characteristic relaxation spectrum. Here the effect of polymer concentration on the relaxation spectrum is evaluated to the first-order approximation. It is then possible to calculate the Huggins constant k$_{\mathrm H}$ (in the viscosity equation $\eta_{\mathrm{sp}.}$/c = [$\eta$] + k$_{\mathrm H}$[$\eta$]$^2$ c) from this spectrum. It is found that k$_{\mathrm H}$ is related to its value k$_\Theta$ at the $\Theta$-point, thus: $k_{\mathrm H} = k_\Theta \alpha^{-4}_\eta + C_0z\alpha^{-5}_\eta$ where C$_0$ is a numerical constant, z is the customary excluded volume parameter, and $\alpha_\eta$ is the expansion coefficient (approximately measured by the intrinsic viscosity). This equation is compared with recent experiments by Nagasawa and by Inagaki, and good agreement is obtained. Thus two different polymer solutions give plots of adequate linearity for $\alpha^4_\eta$k$_{\mathrm H}$ against $M^{\frac{1}{2}}/\alpha_\eta$ (since z is proportional to M$^{\frac{1}{2}}$) with approximately the same intercept (k$_\Theta$ $\sim$ 0$\cdot$45).