A method is suggested for setting up analytic atomic wave functions which form good approximations to Hartree's functions. These functions are of the form $\ensuremath{\Sigma}c{r}^{n}{e}^{\ensuremath{-}ar}$, where the exponent $a$ as well as $c$ and $n$ vary from one term to another. The constants are determined for 1, 2, and 3-quantum electrons by fitting Hartree's values numerically for five selected atoms, and interpolation methods are presented for dealing with the intermediate atoms. A method is suggested for setting up exactly orthogonal functions, with no loss of accuracy. It is shown that the analytic wave functions are the solutions of central field problems in which the field is slightly different for different quantum numbers, on account of the inaccuracy in the function, but a table shows that the discrepancy between this and the correct field is small over the region where the wave function is large. Suggestions are made for future work, on the one hand in extending the tables, on the other in using the wave functions in investigating atomic energies, exchange integrals, etc.