178 



Mr. Mallet on the Physical Conditions 



of the air surrounding it, and F that of the focus of heat, and x any abscissa 

 whose origin is in ]', then the integral of the differential equation 



dy d-y , 



which determines the momentary variation of y {a and b being constants, and 

 .'/ + iy) the temperature of the bar at the time t) becomes, on certain as- 

 sumptions — 



y = Y X {10)^^"' 

 wlience 



Log?/: 



:Log J 



._x_ lb 



M4a 



M being the modulus of the common logarithms. Applying this formula to 

 the results of experiment with a bar heated at one end, and furnished with 

 eight thermometers, at the distances apart given beneath, he found the follow- 

 ing temperatures for the several points along the bar : — 



In which experiment and calculation were found to square closely. The 

 figures in the third column show clearly the enormous difference in temperature 

 between the two ends of the bar, freely conducting heat. 



Blot's general differential equation does not precisely apply to the case of a 

 gun whose metal is heated from the interior and cooled from the exterior only, 

 being much the same as a bar (or elementary radial section of the metal of the 

 gun) heated at one end and cooled at the other only, and to which conditions the 



