The history of the concentric cylinders apparatus for measuring the shear viscosity of liquids, and its attribution to Maurice Couette, have been explored. Examination of the Nineteenth Century literature has revealed that the concept goes back to Stokes and later Margules, the design and execution of the apparatus, apparently independently, to Perry, Couette, Mallock, and Schwedoff. Mallock's and Schwedoff's measurements were the most accurate and were within 1% of the viscosities derived from Poiseuille's measurements on the basis of no slip at the tube walls and cylinder surfaces. Measurement of fluid viscosity was closely linked to the adoption of the no-slip boundary condition at solid-fluid interfaces. (C) 2005 The Society of Rheology.