284 THEORY OF HEAT. [CHAP. V. 



At the same time a vessel of porcelain filled with water heated 

 to 60 was allowed to cool in air at 12. The value of e~ H in 

 this case was found to be 0*98514, hence that of Hlog i0 e is 

 O006500. We see by this how small the value of the fraction 

 e~ h is, and that after a single minute each term multiplied by 

 e~ M is not half the ten-thousandth part of what it was at the 

 beginning of the minute. We need not therefore take account 

 of those terms in the value of v u. The equation becomes 



Hu Hu H IIu 



v - u= h^n &quot; -&quot;r+a^T- 



From the values found for H and A, we see that the latter 

 quantity h is more than 673 times greater than H, that is to 

 say, the thermometer cools in air more than 600 times faster 



than the vessel cools in air. Thus the term -j is certainly less 



fi 



than the 600th part of the elevation of temperature of the water 



above that of the air, and as the term , - ^ -y is less than 



n H fi 



the 600th part of the preceding term, which is already very small, 

 it follows that the equation which we may employ to represent 

 very exactly the error of the thermometer is 



Hu 



V U = 



T 

 fl 



In general if H is a quantity very great relatively to Ji, we 

 have always the equation 



Hu 



v u = -= . 

 /I 



300. The investigation which we have just made furnishes 

 very useful results for the comparison of thermometers. 



The temperature marked by a thermometer dipped into a 

 fluid which is cooling is always a little greater than that of the 

 fluid. This excess or error of the thermometer differs with the 

 height of the thermometer. The amount of the correction will 

 be found by multiplying u the actual height of the thermometer 

 by the ratio of H, the velocity of cooling of the vessel in air, 

 to h the velocity of cooling of the thermometer in the fluid. We 

 might suppose that the thermometer, when it was dipped into 



