438 PROCEEDINGS OF THE AMERICAN ACADEMY. 



It will be seen that the maximum variation of any minor average from 

 the total average is only 0°.004. The Tonnelot thermometer, standard- 

 ized by the Bureau Internationale des Poids et Mesures in 1894, gives 

 essentially the same result as the average of the three new thermom- 

 eters — a result which indicates in the clearest manner the excellent 

 quality of the work of the Bureau. The final result, 32°. 383, is only 

 0°.004 higher than the value found by one of us in 1898 — a difference 

 about equal to the average deviation of the older experiments from their 

 mean. If each experiment of the recent series is taken as of equal 

 weight, the "probable error" — of the total average is 0°.0007 ; while 

 if each minor average is considered as an observation, the " probable 

 error " becomes 0°. 001. These very small figures indicate that further 

 multiplication of observations is needless. The transition temperature 

 of sodic sulphate has been determined in terms of the international 

 standard to within the limit of accuracy of the standard itself. 



Before closing this report, it is perhaps worth while to emphasize in 

 comparison the possible uncertainties of the three fixed points in the 

 thermometric scale, — 0°, 32.383°, and 100°. 



The freezing point of water (an equilibrium of two phases) is depend- 

 ent upon three essential conditions : first, the pressure ; secondly, the 

 purity of the water ; thirdly, the homogeneity of the crystal form of 

 the ice. 



It is well known both theoretically and practically, that jjressure 

 lowers the melting point of ice, because this substance is more volumi- 

 nous than water. The temperature chosen for the international standard 

 of thermometry is not the true triple point of the substance, but a point 

 0°.007 lower, — the freezing point under atmospheric pressure. Ordi- 

 nary variations in this pressure cause an effect on the temperature smaller 

 than the necessary errors of observation ; hence the effect of changing 

 atmospheric pressure may be disregarded, as well as the effect of the 

 pressure of a few centimeters of liquid above the thermometer bulb. 



The second possible cause of deviation, impurity in the water, causing 

 a lower freezing point because of its osmotic pressure, is easily avoided. 

 Water is more easily purified than almost any other substance, and even 

 commercial ice often approximates the required purity within a i'ew 

 thousandths of a degree. Attention should be called, however, to the 

 danger of dissolving volatile impurities from the atmosphere. This 

 danger is much less when the interstices between the pieces of ice are 

 wholly filled with pure water; and it is obviously well to add water 

 which has been boiled in a platinum or silver flask and rapidly cooled, 



