702 Convection of Heat and Similitude. 



although a slight correction factor be introduced for deviation 

 with diameter (d). 



Finally, Langmuir^", in his study of convection of heat, 

 quotes from Carpenter (' Heating and Ventilation of 

 Buildings,' Wiley & Sons, 1903) values for a 2 inch steam 

 pipe, sensibly the same size as Hughes's largest cylinder 

 (5'06 cm.). These convection values, calculated for a 

 temperature excess of 85° C, are plotted as asterisks in 

 fig. 2, and are seen to lie higher than the mean curve, 

 although the points given by Hughes lie lower. 



(3) Long Cylinders : thick and thin compared. 



Hughes gave the results for his cylinders in a form 

 H«rf' 5 V, where n varies with diameter from 0'55 to 0*7, 

 and shows signs of depending also upon the velocity itself. 

 Obviously, this is not a suitable formula for extrapolation. 

 King, working over a wide range of conditions, gave the 

 formula (10) above. It is better adapted for extrapolation. 

 Particularly, there is no sign of variation with velocity 

 apart from that under the root sign ; so we can work 

 with a wire of diameter within King's range, only extra- 

 polating the velocity. 



Let us take, then, two wires approximating to the smallest 

 and to the largest used by King, of diameter 0'003 and 

 0*015 cm. respectively. As with Hughes's cylinders, let 

 them work at 100° C, in air at 15° C, this being appa- 

 rently the temperature (deduced from his radiation data) at 

 which Hughes worked. Then, if we choose velocities to 

 give values of u vd " similar to those in Hughes's experiments, 

 we may calculate from King's constants the appropriate 

 heat-loss (H). We find for both wires 



when vd = 500, H - 0*46, 

 „ wJ=1000, H = 0-66. 



These points have been plotted on the graph of fig. 2, 

 where remarkable agreement is seen with the curve obtained 

 for cylinders 30 to 1600 times as thick. The extrapolation is 

 considerable, but we recall that the most satisfactory part of 

 the most satisfactory formula was chosen to stand the strain. 

 It would not seem possible to conduct experiments to test this 

 particular extrapolation, as the velocities are so great that 

 the fine wires would oscillate or break under the mechanical 

 strain. 



* Laiigmuir, Trans. Am. Elcctroclu.ni. Sue. xxiii. p. 324 (1913). 



