A spherical galaxy with reduced surface brightness, J=B({alpha})/B_e_, obeying the r^1/4^ law, logJ=-3.3307 ({alpha}^1/4^-1), where {alpha} is the reduced radius, {alpha}=r/r_e_ (r_e_ is the effective radius), is deprojected to find the corresponding space density, mass, mean density, force, potential, escape velocity, and potential energy at each point in the galaxy. Numerical tabulations to five significant figures are given for 124 points in the range 10^-6^<=R/r_e_<=260. In addition the projected surface brightness B({alpha}) and integrated luminosity within {alpha} are tabulated for the range 10^-6^<={alpha}=r/r_e_<=260. Conversion factors to cgs units and to M_{sun}_, pc, km/s, L_{sun}_ units are given. Asymptotic expansions for the space density {rho}(s) in the ranges s=<10^-4^ and s>=10^-1^ are derived, and it is demonstrated that the projection of the expansion for s<=10^-1^ is almost indistinguishable from the r^1/4^ law itself, apart from a small excess of luminosity in the central regions. Formulae and numerical tables of the luminosity distribution are given for use in galaxy photometry. Relations between the total galactic mass M_T_, the effective radius r_e_, the velocity dispersion {sigma}_v_, the central density {rho}_c_ and the mass M_N_ and radius R_N_ of the nucleus are derived. Here the "nucleus" is defined as the region within which stars having a velocity equal to the mean velocity dispersion in space, {sigma}_v_.