By Mr. Thomas Tredgold. 



571 



of different liquids are at such different temperatures that 

 we may vary the ultimate temperature of the heating surface 

 from 100 to 600 degrees, that of water being 212°. This 

 mode of considering the subject opens a new source for 

 speculation and for improvement, which it will be desirable 

 to consider more in detail after analyzing the laws of the 

 motion of liquids by heat. 



7. A general investigation, embracing all the circumstances 

 concerned in the motion, would be extremely intricate, and 

 hence I shall not attempt to include more than those which 

 are of sufficient importance to have an influence on the results 

 requiring attention in practice ; and, for a like reason I adopt 

 the most simple formula of hydraulics that apply to the 

 case. 



Put / = the sum of the lengths of the pipes in feet. 



h = the depth of the liquid in the boiler in feet below 



the centre of the upper pipe. 

 e = the expansion due to the mean difference of tem- 

 perature at the extremes of the apparatus. 

 / = the friction of the liquid against the surface at the 

 mean temperature for one foot in length and one 

 inch in diameter. 

 d = the diameter of the pipe in inches ; and, 

 v = the velocity in feet per second. 

 The friction of a pipe is as its surface, and the square of 

 the velocity directly ; and, the equivalent head is inversely 

 as the area of the section of the pipe, consequently, 

 7854 d(° " 5=8 A ~^T~ ~ tne nea< * equivalent to the friction. 



