152 Experimental Investigations 



hottest extremity of the cylinder, A, to its other extrem- 

 ity, E, which is in contact with cold water, would be in 

 arithmetical progression^ and it has just been shown that 

 the decrease must necessarily be accelerated by the ac- 

 tion of the air and other surrounding cold bodies. 



But the acceleration of the decrease of temperature in 

 those parts of the cylinder which are toward the cold 

 extremity, depending on the action of the air and sur- 

 rounding bodies, must be continually diminishing in 

 proportion as the temperature of the surface of the cyl- 

 inder approaches nearer and nearer that of the air ; and 

 hence we may conclude that, if a given number of points, 

 at equal distances from each other, be taken in the axis 

 of the cylinder, the temperatures corresponding with 

 these points will be in geometrical progression. 



We may represent the progress of the decrease of 

 temperature by Plate IV. Fig. 2. 



In a right line A E, representing the axis of the cylin- 

 der, if we take the three points B, C, and D, so that 

 the distances A B, B C, C D, and D E shall be equal, 

 and, erecting the perpendiculars A F, B G, C H, D I, 

 EK, take A F = the temperature of the cylinder at 

 its extremity A, B G = its temperature at the point B, 

 and so of the rest; the ordinates A F, B G, &c. will 

 be in geometrical progression, while their corresponding 

 abscisses are in arithmetical progression ; consequently 

 the curve, P Q, which touches the extremities of all 

 these ordinates, must necessarily be the logarithmic curve. 



We will now see whether the results of experiment 

 agree with the theory here exhibited, or not. 



To form our judgment with ease and, as it were, at a 

 single glance, of the agreement of our theory with the 

 results of the experiment of which I gave an account 



