T. Russell — Prediction of Cold-waves. 469 



HA+LZ+L^F— E = 0. A, I and l n are the unknown quantities 

 and, E, the extent of cold-wave ; PI and L, are the measured 

 extents of high and low pressure. As regards F, the number 

 expressive of the density of the isothermal lines, it was de- 

 rived in the following way. 



Consider two contiguous areas, between three successive 

 isotherms. The tendency is for the wind to blow from the 

 high area towards the low, and carry the air from places of low 

 temperature to those where it is high. The mean temperature 

 of a strip between two isotherms as compared with a strip 

 adjoining it is ten degrees different, the one to the west and 

 north being the lower. If the area of higher temperature is 

 of less extent than the lower one, there is a possibility of all 

 the air from the lower one overflowing the higher, and that 

 the fall in temperature will be equal in extent to the area of 

 the higher multiplied by one, their difference of temperature 

 being ten degrees. If the area of lower temperature is less 

 than the higher one, it is not likely that it will change the 

 temperature any more than the area of the lower multiplied 

 by the difference of temperature unless there is cold air com- 

 ing from above. Consider a third area with respect to the 

 one of highest temperature. The fall of temperature pro- 

 duced by it may be taken in extent, as equal to the area of the 

 smaller one of the two areas multiplied by two, the difference 

 of their mean temperatures being twenty degrees, but some- 

 what less than this on account of the two areas being farther 

 apart than in the case of the first two considered. Part of the 

 low temperature is expended in lowering the temperature of 

 the intervening area. It is not known what the law is, accord- 

 ing to which this effect diminishes with distance of the areas 

 apart. There is some reason, however, for believing that it is 

 inversely as their distance apart. The effects of the areas, in 

 causing extent of fall, have been taken as inversely propor- 

 tional to their distances apart expressed in units of one hun- 

 dred miles. Considering all the other areas with respect to 

 the area of highest temperature, in a similar manner a series 

 of numbers will be obtained, expressive of the possible extent 

 of temperature-fall. The next area of temperature below the 

 one of highest temperature, will in like manner give a similar 

 series of numbers, and likewise a third area considered with 

 respect to all those below it will give a series, and so on, until 

 the last two areas are taken into account which give a single 

 number. The sum of all these numbers gives a total number 

 expressive of the possibility of temperature-fall, provided 

 there is sufficient of a low area to induce such a circulation of 

 the air, that the air from places of low temperature will reach 

 places where it is high. The more extensive and deep the 



