The research originated in an attempt to re- establish the apparently critical ratio of width to thickness which Barba found to give, in the case of flat test -bars of mild steel, a maximum of extension on fixed or constant gauge -lengths, but the scope of the investigation ultimately became much wider. The main object of the experiments discussed in this Thesis was to determine the nature of the influence of width of specimen upon the results of tensile tests of mild steel and rolled copper. The test -bars were cut from 1/4-inch and 1/8-inch steel boiler plates and from 1/8-inch copper plate, and were machined to give widths varying from 1/4 inch to 4 inches, the range of the ratio width/thickness in the thinner specimens being approximately from 2:1 to 30 :1. The results indicate the influence of width of specimen on the strength, on the extension of fixed lengths, on the extension of three types of variable gauge-length, and on the reduction of area and certain other quantities involving the final transverse dimensions. For the most part, the equations were derived from the results obtained from the specimens of the high-grade 1/8-inch steel plate. Further research on similar lines carried out on 1/4-inch, 3/8-inch, and 1/2-inch mild steel plates, all of which were rolled from slabs cut from the same ingot, gave evidence definitely corroborative of the views latterly expressed by the writer; but to avoid unnecessary repetition no record of that investigation has been included in the present exercise.