TRANSACTIONS OF SECTION A. 461 



I have here fjiven the train of thought which led to this investigation ; but I 

 ought to say that the results obtained do not depend upon the exact truth of every 

 step of this train of reasoning. This is in reality a matter-of-fact investigation 

 undertaken with the view of ascertaining whether or not there is any recognisable 

 connection between these two weathers in Great Britain. The result obtained, I 

 may add, was reported to the Solar Physics Committee, and by tliem communi- 

 cated to the Royal Society. In order to avoid as much as po.ssible the influence of 

 locality I obtained, through the kindness of the Meteorological Council, the diurnal 

 temperature-ranges at Stonyhurst, Kew, and Falmouth for the years 1871 and 

 1872. I obtained likewise, through the Idndness of the Kew Committee, the 

 diurnal ranges of magnetic declination at the Kew Observatory for the same two 

 years, e.xcluding disturbed observations. The temperature-ranges discussed are 

 therefore the means of those at the three observatories above mentioned, and still 

 further to tone down or equalise individual fluctuations the daily numbers ex- 

 hibited are each the sum of four daily ranges, the two before and the two after. 

 Finally, the object being to repreisent fluctuations of range rather than their 

 absolute values, a daily series representing the mean of twenty-five daily numbers, 

 has been obtained. Each daily number is thus compared with the mean of 

 twenty-five daily numbers, both columns being symmetrically placed with regard 

 to time, and the dilfei-ences, whether positive or neg.ative, between the two columns, 

 is taken to represent temperature-range fluctuations. 



A precisely similar course has been taken with re.spect to the Kew declination 

 ranges. 



By this means two years of daily numbers, sometimes positive and sometimes 

 negative, representing temperature-range weather, and two years of daily numbers, 

 sometimes positive and sometimes negative, representing declination-range weather, 

 have been obtained. 



The ne.ict object is to compare these two .series with one another. 



Now when two series of waves representing elevations and depressions come 

 together, it is well known that we shall have the greatest result when the crests 

 of the one series coincide with the crests of the other, and the smalle.st result- 

 perhaps none at all — when the crests of the one series coincide with the hollows of 

 the other. This, indeed, is the well-known explanation of musical beats. 



Now if there be any marked likeness between the two weathers, and if it be 

 true that declination-ranire weather precedes temperature-weather, the algebraic 

 sum of the two sets of fluctuations representing these weathers will be greatest 

 when the declination is pushed forward in point of time, so that the declination 

 fluctuation of to-day shall be summed up with the temperature fluctuation six or 

 seven days after. For suppose that the declination fluctuation of to-day is repre- 

 sented by a very large positive number ; if the above theory be true, the temperature- 

 fluctuation six or seven days afterwards will be represented by a large positive 

 number also; so that we shall have the addition of two large po.sitive numbers, 

 whereas if we add the declination-weather of to-day to the temperature-weather 

 of to-day it may chance that we are really adding a lai-ge positive to a large nega- 

 tive quantity, in which case the result will be very small. 



It may also happen that this amount of precedence of declination-weather is 

 greater at one season of the year than at another. 



We have therefore to pursue a plan somewhat of the following nature. Take a 

 month's temperature-weather, say, for the month of August, and add to it a month's 

 declination-weather, extending, say, from July 21 to August 21 ; let the sum be 

 262. Here the declination-month has been pushed forward eleven days ; next push 

 it forward twelve days, and let the sum be 273 ; then thirteen dajs, and let the 

 sum be 276 ; next, fourteen days, and let the sum be 270. It thus appears that 

 the greatest sum is got Ijy pushing the declination forward thirteen days, and we 

 may therefore presume that at this season of the year thirteen days denotes the 

 precedence of the declination weather. On this principle the following table has 

 been constructed. 



