There are numerous problems in nuclear physics where it is important to measure quantitatively the amount of a particular element present in a solid sample even though that element is present to only one part per million or considerably less. Examples of such problems include the quantitative determination of the amount of calcium formed by radioactive decay of potassium (1), the amounts of samarium and gadolinium formed by radioactive decay of europium (2), the amount of fission products formed from nuclear fission, etc. (3, 4). In addition to such nuclear physics problems in which the mass spectroscopy group at Chicago has been primarily interested, there are a variety of other problems where such sensitivities are important. These include such things as trace quantities of elements in semiconductors, or more generally, problems of the solid state; trace element studies in geochemistry; trace quantities of radioactive elements present in materials for constructing geiger counters, etc. It is the purpose of this paper to point out the potentialities and limitations of two of the mass spectrometric methods of quantitatively measuring trace elements in the part per million range and below. The two mass spectrometric methods of solid chemical analysis which have been used extensively in Chicago are (1) the Dempster vacuum spark method and (2) the isotopic dilution method. The Dempster vacuum spark method is quite analogous to the optical spectrographic method in that it analyzes for all elements present in a solid sample in a single experiment. In contrast to this general property of the spark method, the isotopic dilution method, as it is generally used, analyzes for only one element per experiment. Its sensitivity, however, is such that, using the method, many problems can be solved which are insoluble by any other known method. Since Mr. Hippie is discussing the general techniques and recent developments in the Dempster vacuum spark method in another paper in this group, this method is not described in any detail here, but there will be given a few results obtained by Dempster which illustrate, the sensitivities obtainable. The isotopic dilution method is described in somewhat more detail.