on certain Equations in the Analytical Theory of Heat. 431 



temperature has previously been assumed constant throughout 

 any section perpendicular to the axis, this amounts to assuming 

 the temperature uniform throughout the whole bar. The 

 equation (1) then takes the form 



^ v Pi 



cp^- = — <-.h.v. 



Or, multiplying both sides of equation by I, the length of the 

 bar, and writing more generally for v on right side/(v), 



cplq^ = -plh.f(v). 



Or, writing m for plq, and s for the whole surface of the bar, 

 including the two ends, 



cm~=-s.h.f(v) (2) 



The bars used in these experiments to determine the form 

 of f(v) were about 26 or 27 centim. long and 1*9 centim. 

 diameter. They were nickel- plated, so as to give them the 

 same smooth even surface. At the extremities of a diameter 

 in the middle of the length of the bars, two small holes, about 

 *7 millim. diameter and 2'5 millim. deep, were bored, and 

 into them an iron and a German-silver wire respectively were 

 soldered. The other ends of these wires dipped into mercury- 

 cups, in the circuit of an aperiodic Wiedemann's galvano- 

 meter. The mercury-cups being provided with thermometers, 

 the arrangement formed a thermo-circuit, and from the de- 

 flexion of the galvanometer and the temperature of the 

 mercury-cups the temperature of the bar at any time could 

 be found. The deflexion was read off by means of a tele- 

 scope and scale situated 2'5 metres from the galvanometer. 

 The correction of the extreme deflexion for the assumption 

 tan 20 = 2 tan 9 is less than '3 per cent, and is neglected. 

 The bars were at first suspended horizontally in the room by 

 means of two threads, and the temperature of the air observed by 

 means of a thermometer situated vertically under the bar and 

 protected from radiation by a small paper screen. On account of 

 the air-currents in the room, and the "lag" of the thermometer- 

 indications behind the actual temperatures of the air, the 

 cooling was ultimately carried out in a water-jacket 55 centim. 

 diameter and 75 centim. long. The change of temperature of 

 the jacket was then slow and regular, and the correction for 

 this change could easily be applied. The bars were heated 

 in an air-bath surrounded by water at 100° C. for three or 

 four hours, and at the end of that time the temperatures of 



2 K2 



