This research project consists of an extensive technical examination of a Paul Gauguin painting from Smith College called The Market Gardens at Vaugirard, 1879. The research was conducted in conjunction with research on Gauguin's early techniques by art historian Vojtech Jirat-Wasiutynski and paintings conservator Travers Newton. The examination of the painting in question is important for the understanding of Gauguin's early technique and the influence of the Impressionist painters. It was during this period that Gauguin was collecting Pissarro's work which had a marked influence on his own. Of particular interest is his palette and brushwork. Methods of investigation include x-ray fluorescence spectroscopy, infrared reflectography, and x-radiography. In addition cross-section samples of the paint film and pigment dispersions have been made, examined, and analyzed for elemental vontent. Other methods of analyses include scanning electron microscope, Fourier Transform infrarred spectroscopy, gas chromatography, and high pressure liquid chromatography. The results from these analyses were used for a comparative study for known techniques and materials used by Pissarro in contemporary works. A comparison has also been made with techniques and materials from early Gauguin paintings.