RICHARDS AND LAMB. — SPECIFIC HEAT OF LIQUIDS. G73 



result. The reason for this is, that we determine the fall in temperature 



of the warm Ii(juid by subtracting this equilibrium temperature of the 



mixture from the initial temperature of the warm liquid; while we also 



determine the rise in temperature of the cold lujuid by subtracting its 



initial temperature from the temperature of the mixture. Any error, 



then, in this latter temperature measurement has a double elFect on the 



specific heat. 



The accuracy of the thermometry, of course, depends primarily on the 



thermometers employed. It will suffice to say here, that, by comparing 



the thermometers with standards after every experiment, and taking the 



zero point of these latter, and making the correction when necessary for 



exposed thread and hydrostatic pressure, we have usually felt sure of the 



equilibrium temperature to within two or three one-thousandths of a degree. 



This, with the usual fall of temperature of 17 degrees, would correspond 



2 X .0025 

 to a percentage error of — —^~r , or about 0.03 per cent. 



The stationary condition of the thermometer is so favorable to precise 

 measurement of temperature that it seems by no means impossible that, 

 using still greater precautions in the temperature measurements, by 

 means of platinum resistance thermometers, one might be sure of the 

 temperature of the mixture to within less than a single one-thousandth 

 of a degree, which, with the same temperature fall of seventeen degrees, 

 would correspond to an uncertainty in the specific heat of less than 

 0.01 per cent. This would far exceed the accuracy with which the 

 varying specific heats of water are now known. 



As we have just implied, the accuracy of the method is directly 

 proportional to the temperature fall of the warm liquid, or the tempera- 

 ture rise of the cold one. But the specific heat which is measured is the 

 mean specific heat over the teiuperature interval employed, and since we 

 cannot be sure that the change of the specific heat with the temperature 

 is linear, it follows that the greater the temperature interval, the less 

 the certainty with which the specific heat at any given temperature is 

 known. The temperature interval here employed was about seventeen 

 degrees. 



The rise in temperature due to the work done by the actual fall of the 

 liquids from the pipettes can be easily calculated. Thus, the total weight 

 of the falling li(juids was about 350 grams ; the length of the fall about 

 40 cm. The kinetic energy conv(M'ted into heat, therefore, amounted to 

 40 X 350 X 981, or 13,700,000 ergs, which corresponds very nearly to 

 one-third of a calorie. This would have heated the 350 grams of mixture 



VOL. XL. — 43 



