In some physical researches it is required to measure the dimensions of a regular solid, whether parallel-sided, cylindrical, or spherical-ended, with the greatest possible accuracy. Again, in the regular work of a metrology bureau, accurate comparison of the size of an end-standard of length with reference to a line-standard is required. Until 1906 the only apparatus available for these purposes was the measuring machine made for comparing engineering gauges. In that year the writer described a machine based on the principle of electric touch, which was much more delicate than the older mechanical machines. It also had facilities for exploring the solid under test, to prove its accuracy of figure. This machine has been installed and used in the National Physical Laboratory since 1909. Improvements in it were described later. The present paper gives an outline of an improved machine of the same type embodying the experience gained in using the 1906 machine. The chief novelties are: (1) greater strength in the supporting parts, and consequent rigidity of the whole apparatus; (2) larger and much improved table to carry the solid under test; (3) improved measuring-ends; (4) an innovation for making absolute measurements, whereby the line-standard moves but the reading microscope remains fixed; (5) side girders to relieve the bed of load and so reduce friction, abrasion, and strain.