THE convection of heat to or from the walls of a circular tube conveying fluid in turbulent motion has been studied by a long line of investigators, among whom may be mentioned Joule, Reynolds, Stanton, Nüsselt, Soennecken, Jordan, Stender, Heinrich, and Stückle. From dimensional considerations Rayleigh (NATURE, Mar. 18, 1915, p. 66) deduced a formula which, written in non-dimensional form, is equivalent to.where a = coefficient of transmission of heat. d = diameter of tube.V = mean velocity of flow. Ic = conductivity of fluid.= viscosity of fluid. v = kinematic viscosity of fluid = ,4p.h = diffusivity of fluid = k/sp. s = specific heat of fluid. -p = density of fluid. For gases Stanton (Tech. Report Adv. Committee for Aeronautics, 1912-13) gave a formula reducible to ad (vd) '" const. i k . (2) in which n = 0 75 approximately for smooth tubes.Niisselt (Z. V. d. I., 1909) proposed a formula for gases reducible to his later form: ad lVd\" a =const. Vd) ' k C .. (3) which is equivalent to (2) (n = 078). Formulae for water of the form: a proportional to Vn, . (4) have been proposed by Stanton (Phil. Trans. Roy. Soc., 1897), Soennecken (Forsch. Heft 108/109), Stender (" Wtrmeubergang an strdmendes Wasser," Springer, 1924), and others. These formulae do not make explicit mention of the conductivity. Stender finds that the index 'an' depends on an equivalent mean temperature r0 C. = 09Tm + 0-lTw, where Tm = mean water temperature and Tw wall temperature.Experiments with oil have been carried out by Heinrich and Stickle, but not fully analysed (Forsch. Arb. Heft 271). The object of the present note is to suggest a general formula applicable to all fluids, liquid or gaseous, under conditions of turbulent flow in circular tubes, namely: ad 0 0260(YA\ fQ%) k V * (5) in which f(k/ys) is given approximately by the following values: h/v=l/cls 0 01 0 10 0 40 1-30 f(h/t) =f(k/ls) 0-97 0 895 0-835 0-785 which lie well on a smooth graph.This formula agrees well with the experiments of Heinrich and Stfickle for oil, those of Stanton, Soennecken and Stender for water (r= 100 C. to 7=700 C.). It also agrees as well with the results of Jordan, Niisselt, Pannel, and others for air, as these agree amongst themselves. A crucial test of the value of formula (5) would be given by experiments with mercury for which the value of k/us lies outside the range of the experiments referred to above.A complete formula should take account of the ratio of length to diameter of tube, or else the ratio of initial to final excess temperatures, but (5) is put forward as a step towards the correlation of the results of diverse experiments in which the ratio of length to diameter of tube exceeds about 2