160 



The change Is 

 in proportion 

 to the difference 

 oi temperature* 



Whence the 

 temperatures 

 will be in ge- 

 ometrical pro- 

 jgieflion, 



—and may be 

 reprefented by 

 the logarithmic 

 curve. 

 Figure con- 

 ducted. 



Comparifon of 

 the theory with 

 the •xperiment. 



COUNT RUMFORD'S NEW* EXPERIMENTS 



From reafoning which appears incontrovertible, and which 

 the refults of a great number of experiments appear to confirm, 

 it has been concluded that the celerity with which a hot body 

 placed in a cold medium is cooled, is always proportional to 

 the difference between the temperature of the hot body and 

 that of the medium. Conhdering this conclufion as eitablithed, 

 we may determine a priori what ought to be the gradation of 

 temperatures in the interior of a given folid cylinder furrounded 

 by air, one extremity of which is in contact with a coniidera- 

 ble body of boiling water, while the other is fimilarly in con- 

 tact with cold. 



We have feen that, if the furface of the cylinder were per- 

 fectly ifolated, the decreaie of temperature from the hotteii 

 extremity of the cylinder A to its other extremity E, which is 

 in contact with cold water would be in arithmetical progrejfion, 

 and it has juft been (hewn, that the decreafe rauft neceflarily 

 be accelerated by the action of the air and other furrounding 

 cold bodies. 



But the acceleration of the decreafe of temperature in thofe 

 parts of the cylinder which are toward the cold extremity, de- 

 pending on the action of the air and furrounding bodies, muft 

 be continually diminifliing in proportion as the temperature of 

 the furface of the cylinder approaches nearer and nearer that 

 of the air; and hence we may conclude, that if a given num- 

 ber of points at equal diftances from each other, be taken in 

 the axis of the cylinder, the temperatures correfponding with 

 thefe points will be in geometrical progrejfwn. 



We may reprefent the progrefs of the decreafe of temper- 

 ature by Fig. 2. PL VII. 



In a right line A E, reprefenting the axis of the cylinder, if 

 we take the three points B, C and D, fo that the diftance* 

 AB, BC, CD, and DE fhall be equal; and, erecting the 

 perpendiculars A F, B G, C H, D I, E K, take A F= the tem- 

 perature of the cylinder at its extremity A, BG=its tem- 

 perature at the point B, and fo of the reft ; the ordinates A F, 

 B G, &c. will be in geometrical progrefiion, while their cor- 

 refponding abfeifles are in arithmetical progreffion ; confe- 

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

 thefe ordinates muft neceflarily be the logarithmic curve. 



We will now fee, whether the refults of experiment agree 

 with the theory here exhibited or not. 



To 



