470 T. Russell — Prediction of Cold-waves. 



area of low- pressure, the more this will be accomplished. 

 Accordingly, a term is included in the equation which gives 

 the temperature-fall, which is proportional to this number 

 multiplied by the extent of the low area and an unknown 

 quantity. This number expressive of density or sparseness of 

 isotherms in the case of different weather-maps preceding cold- 

 waves varies from 5 to 95. 



To establish the numerical relation between the extent of 

 cold-wave and the extent of high and low areas of pressure, 

 127 cases of cold-wave were selected from those that have 

 occurred in ten years. They were so chosen as to include the 

 greatest possible variety in extent of cold-wave from the 

 smallest to the largest, the greatest and least areas of high and 

 low pressure concerned in their production, cases in which the 

 " high " was in different positions with respect to the " low," 

 and cases of the greatest diversity of the isothermal lines pass- 

 ing through the low area. 



Normal equations were formed, and from them the values of 

 the unknown quantities derived : 



h = 2-75, I = 3-15, l t = 0-0547 



From the residuals obtained by substituting the values of the 

 unknown quantities in the observation-equations, the probable 

 error in the extent of a cold-wave derived by this method was 

 found to be ± 5. The average extent of cold-wave in the 127 

 cases was 20. The extent of different cold-waves varied from 

 5 to 60. 



Several different forms of equation were tried. The one de- 

 scribed, gave more satisfactory values of the residuals than any 

 of the others. From a consideration of the residuals in the 

 various methods tried, it was inferred that the fall of tempera- 

 ture in a cold-wave must be composed of two parts. One part 

 depends on the presence of a high or low area of pressure, and 

 the other on the transmission of air from places in the north- 

 west, where it is cold, to places where the temperature is high, 

 in the vicinity of the low area. The first part probably re- 

 sults from the intermixture of air near the ground with that 

 from a great altitude, this intermixture resulting from a great 

 diminution of temperature upward in the air. In Winter, on' 

 account of the greater lengths of the nights, there is excessive 

 cooling of the upper layers of air. The determining factor of 

 a convective interchange, is the upward diminution of temper- 

 ature. The air over a wide area of country being in unstable 

 equilibrium, a circumstance, such as a slight excess of heating 

 at the ground may be the cause of an intermixture of the strata 

 throughout a great height. Intermixture would cause the air to 

 become nearly uniform in temperature, which would cause a fall 



