356 Mr. W. J. M. Rankine on the Causes of the Excess of the 



M. Renou himself and by M. Babinet, that the solar heat, ab- 

 sorbed and re-radiated by the bed of the river, is the principal 

 cause of the elevation of its temperature, M. Renou cites the 

 fact, that he has frequently observed a sudden elevation of tem- 

 perature in the river immediately follow the appearance of the 

 sun ; but on the other hand it is to be remarked, that M. Renou 

 has also observed great elevations of temperature take place in 

 the water when the sun was not visible. 



It is worthy of note, as tending to show that the solar radia- 

 tion is not the principal cause of the excess of the temperature 

 of rivers over that of the air, that according to the table of the 

 monthly means of M. Renou's observations in 1851, this excess 

 greatly exceeded its mean amount in November and December, 

 months in which the solar radiation is weak ; and that in De- 

 cember the monthly mean very nearly reached its maximum, 

 having been 2°'95, while its actual maximum, in iNIay, was 3°*09. 

 It is also to be observed, that while the mean dim-nal variation 

 of temperatm'e was 8°'03 for the air, it was only 0°"65 for the 

 river. 



^lien we consider that it has been proved experimentally by 

 Mr. Joule, that the heat developed by the friction of all sub- 

 stances (including in that term the consumption of power by the 

 agitation of fluids) bears a certain definite proportion to the 

 mechanical power consumed, it appears probable that friction is 

 an important cause of the elevation of the temperature of rivers 

 above that of the contiguous air. 



Let us suppose that a river flows in a uniform channel, 

 having a uniform inclination, with a uniform velocity ; and let 

 i denote the rate of inclination of the channel; 

 V the velocity of the current ; 

 then iv represents the height through m hich each mass of water 

 descends during unity of time, and also the mechanical power 

 due to the descent of unity of weight of water during unity of 

 time along the channel of the river in question 



INow as the velocity of the cuiTcnt is uniform, this mechanical 

 power must be entirely consumed by friction; that is to say, 

 transfonned into heat. Let 



K denote the dynamical specific heat of liquid Mater ; that is 

 to say, the height through which a given weight mixst descend 

 in order to produce mechanical power sufiicient to elevate the 

 temperature of the same weight of water by one degree ; then, 

 according to Joule's experiments, 



K = 1390 feet per Centigrade degree. 



VI 



and ==- 



A. 



