THe authors investigate the spin-¹/₂ Ising model with nearest-neighbour interactions on the four-dimensional simple hypercubic lattice. High-temperature series expansions are studied for the zero-field susceptibility chi ₀ and the fourth-field derivative of the free energy Xi ₀⁽²⁾ up to order nu ¹⁷. The series are analysed for singularities of the form t^-1 mod 1nt mod ^p where t is the reduced temperature. For chi ₀ it is found that p=0.33+or-0.07 when q=1, in good agreement with the prediction p=¹/₃, q=1 of renormalisation group theory. The critical temperature is estimated to be nu _c^-1=6.7315+or-0.0015. Results for chi ₀⁽²⁾ are more slowly convergent but are not inconsistent with the renormalisation group prediction p=¹/₃, q=4.