A method and apparatus for analyzing fluids by means of x-ray fluorescence. The method and apparatus are applicable to any fluid, including liquids and gases, having at least one component that emits x-ray fluorescence when exposed to x-rays. The apparatus includes an x-ray source (82) including an x-ray tube (64) having improved heat dissipating properties due to the thermal coupling of the x-ray tube with a thermally-conductive, dielectric material (70, 1150). The x-ray tube also includes means for aligning (100, 2150, 2715) the x-ray tube with the x-ray source housing whereby the orientation of the x-ray beam produced by the x-ray source can be optimized, and stabilized various over operating conditions. The method and apparatus may also include an x-ray detector having a small-area, for example, a PIN-diode type semiconductor x-ray detector (120), that can provide effective x-ray detection at room temperature. One aspect of the disclosed invention is most amenable to the analysis of sulfur in petroleum-based fuels.