To date, most shear velocity heterogeneity models in the lower mantle have been derived using long period data. Comparatively little use has been made of the vast ISC database of shear wave arrival times, which covers the years 1964 to 1991. The aim of this study is to use this database to construct global models of shear wave heterogeneity in the lower mantle and compare it with existing P models using similar period data in order to evaluate the hypothesis that P and S heterogeneity are proportional. In order to reproduce the resolution operator inherent in these existing models, the same parameterization has been employed; lateral dependence is in terms of spherical harmonics up to degree and order 6, and radial dependence in terms of a quartic polynomial. The inversion uses data from over 4500 events selected according to criteria which minimize the bias introduced by uneven source receiver coverage. Despite having approximately one sixth of the amount of data the model correlates well with a P wave model computed using data from the same events, and this in turn is almost identical to models computed by other authors using similar inversion methods. Assuming proportionality of P and S heterogeneity, a joint inversion of the P and S data has been performed. The resultant model correlates extremely well with the P model of this study, and similar variance reductions are obtained for both the P and S datasets as were found in the original inversions. Several model parameterizations have been used to try to investigate the dependence of the model expansion on the results. Consequently, taking into account results from synthetic experiments and from experiments into trade-offs with other inversion parameters, the average ratio of relative S to P heterogeneity ^{d ln v_s}andfrasl;_{d ln v_p} throughout the lower mantle is constrained to be in the interval (1.8,2.1) with emphasis on higher values within these bounds. This value is in agreement with other studies using similar period data, and the upper bound is close to the optimum value of 2.27 obtained by Li et al., 1991 from normal mode data, suggesting that the ratio is at least only weakly dependent on frequency. In addition evidence is presented that the ratio is increasing with depth although attempts to extract specific gradients have failed because of the very poor distribution of S rays in the deepest mantle.