32 EEPOUT— 1870. 



gram. The correspondence was equally good at all periods, for which trial was 

 made, between 12 and 16 hours, some parts agreeing better at the shorter, and 

 others at the longer period. The former period is selected for discussion in this 

 memoir. The data are derived from those of the continuous weather-records lately 

 published by the Meteorological Committee for the first quarter of 1869, so far as 

 they refer to Falmouth. The correspondence of the 12-hour period av. wind vel. 

 curves for Falmouth, with the barogi-am, is fairly satisfactory. The flexures of the 

 two curves are, on the whole, simultaneous, since neither curve habitually antici- 

 pates the other ; but they are seldom absolutely simultaneous. They correspond 

 in extreme positions as closely as in near ones, proving that it is not the absolute 

 height of the barometer, but the variations in its height, which indicate changes of 

 weather. The dominant influence of the wind-velocity upon the barometer was 

 made manifest by underlining with difierent colours the epochs of polar and equa- 

 torial winds, and showing that the correspondence of the two curves was, on the 

 whole, much the same, whatever might be the quality of the wind. 



The reason of this correspondence of the barogram with a 12-hour av. vel. curve 

 was then discussed, and was described as similar to that which causes a suitably 

 constructed barometer, when plunged intojtroubled water, to sympathize, not solely 

 with the height of wave exactly above its cistern, but also with that of every point 

 in a surface area whose diameter is a function of the depth of immersion. So the 

 barometer sympathizes with the condition of the air for some distance on all sides 

 of it ; and as there is a general easterly movement of the air over England, it 

 appears that the diameter of the circle of air which aflects the' barometer is such 

 as to require, on the average, 12 hours to pass over an observatory. A barometer 

 would therefore be afiected by an atmospheric wave of exceptional magnitude 

 before it reached the observatory. According to this argument, the efiects of the 

 independent variables, temperature, and damp must be treated on the same system 

 of 12-hour period of average as the wind's velocity. Consequently the following 

 formula is easily deduced. Let A, k be two successive barometric heights, at an 

 interval of 6 hours, a the 6-hour interval that precedes h, b the 6-hour interval 

 between h and k, and c the 6-hour interval which succeeds k. Call Va, ta, da the 

 6-hourly average during the period a of wind-velocity, temperature, and vapour- 

 tension, and use a similar notation for h and c. The units adopted were himdredtha 

 of an inch for barometer and vapour-tension miles per hour for wind-velocity, and 



degrees Fahr. for temperature. The general formula was 



a b c 



^-/';=»i(«a+6-<^6+c)+"(^a+i-^6+c)+K<^«+J-'^A+c)' 



The coefficient vi was found = — 2 by taking a number of selected equations in 

 which neither t nor d had materially varied during the period discussed ; n was 

 found = — 1 by taking the extreme range of the barometer under the influence of 

 changed temperature alone, the other variables being constant ; and d was assumed 

 = — 1 also, that is, it was taken at its real value, but with a negative ordinate ; all 

 the ordinates are negative, because v, t, and d all decrease as h increases. Now 



and similarly for t and d, whence 



h~k={Vc-Va) + l{tc-ta)-\-l{dc-da)fOr 

 Vo={h-k)-^Va-^l{ta-to) + lida-do). 



It will be observed that t)j is necessarily eliminated. Comparison was made 

 hetween the value of Vc as predicted by this equation with its value as ascertained 

 by fact. About 100 casos of marked changes of weather were taken, and it appeared 

 that the average error was one-third greater than if Cc had been predicted as simply 

 equal to Vf,. The reason why the average error is so large, notwithstanding the 



