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The theory behind a new, three-dimensional analysis technique for the measurement of time-integral, perturbed angular correlation (IPAC) functions is presented. The new technique is described in relation to existing methods and in terms of its specific application to a large, Ge-detector array. The effective application of the new technique is demonstrated with results from an experiment where the g factors of excited states in ²⁵²Cf, secondary fission fragments were determined. A ²⁵²Cf source, sandwiched between two iron foils and placed in a saturated magnetic field at the centre of the Gammasphere detector array, was used to make IPAC measurements of prompt γ rays in order to deduce Larmor precession angles of stopped fragments in iron. The g factor of the I^π &equal; 2⁺ state in ¹⁰⁴Mo was thus measured to be g &equal; +0.248(22). This new measurement shows a factor-of-5 improvement to the precision which has previously been attained in more conventional experiments.