154 
DR. H. T. BARNES ON THE CAPACITY FOR HEAT OF WATER 
the temperature 0 1 of the outflowing water, warmed by the passage of the electric 
current. The temperature of the water increases rapidly from B to A, and gradually 
decreases from A towards P. 
Radiation .—The loss of heat through the vacuum-jacket will consist of the 
cooling of the surface of the glass in the flow-tube by radiation, by convection 
currents of residual vapour in the jacket, and by radiation from the molecules of the 
water itself. Provided the vacuum is good, these are all included in the h term of 
the general difference equation. This radiation term obviously should not vary, hut 
should remain independent of the quantity of water flowing, provided it can be 
assumed that the temperature gradient from B to A remains the same for all flows. 
This assumption can be justified only if the temperature gradient is linear. If it is 
not linear then we may have either one of two conditions :— 
1. When the distribution of heat in the water column AB is such that the 
water is hotter in the centre than the sides, in which case the temperature 
of the glass surface of the fine tube will be that represented in (1) fig. 2. 
and will depend on the thermal conductivity of the different layers of 
water between the centre and the sides, which will be conditioned by the 
rapidity of flow. This condition is fulfilled perfectly when the water 
column is receiving heat from a central wire conductor and flowing at 
velocities less than the critical velocity for the tube in question. In this 
case the water flows in parallel stream-lines, and does not mix. The 
higher the velocity of flow up to the critical velocity, the more gradual will 
be the slope of the temperature gradient of the glass surface from B to A. 
At A, the water is mixed around the thermometer bulb and the temperature 
of the glass suddenly increases. For any given temperature 6 X of the 
water, as indicated by the outflow-thermometer, the total heat-loss from 
the water will decrease with increasing velocity of flow in proportion to 
the slope of the temperature gradient along BA. 
2. The case where the sides of the water column are hotter than the interior, or 
where the water is receiving heat from the surface of the fine tube. The 
