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We demonstrate that a common-line method can assemble a 3D oversampleddiffracted intensity distribution suitable for high-resolution structuresolution from a set of measured 2D diffraction patterns, as proposed inexperiments with an X-ray free electron laser (XFEL) (Neutze {\it et al.},2000). Even for a flat Ewald sphere, we show how the ambiguities due toFriedel's Law may be overcome. The method breaks down for photon counts belowabout 10 per detector pixel, almost 3 orders of magnitude higher than expectedfor scattering by a 500 kDa protein with an XFEL beam focused to a 0.1 microndiameter spot. Even if 10**3 orientationally similar diffraction patterns couldbe identified and added to reach the requisite photon count per pixel, the needfor about 10**6 orientational classes for high-resolution structuredetermination suggests that about ~ 10**9 diffraction patterns must berecorded. Assuming pulse and read-out rates of 100 Hz, such measurements wouldrequire ~ 10**7 seconds, i.e. several months of continuous beam time.

Crystallography without crystals I: the common-line method for assembling a 3D intensity volume from single-particle scattering