378 Mr. V. N. Nene. On a Method of Tracing 



22. The three results which we have found above are very im- 

 portant, and we shall now show their utility, and discuss some more 

 cases from them which we have not yet discussed, by taking some 

 particular examples by which we can show our method of tracing 

 unknown periods. 



Suppose we have at our disposal a long series of daily means (say) 

 of barometer observations, and we suspect in it a period of about 

 25 days. The first thing that we shall do is, that we shall take a small 

 series of daily means and curve it on a curve form, and see generally 

 the period of duration of turning points between successive maxima 

 or between successive minima. Suppose the duration of the period found 

 was from 5 to 10 days, then we shall take the least period of 5 days, 

 that is, we shall adopt 5 as our working value of m, and work the 

 processes as already discussed with the whole series of daily means, 

 until generally each mean of the last mean series is less than 2 (say) in 

 the last place of figures.* We shall take then for further treatment the 

 sum of all the mean series instead of the original series. The sum of 

 all the mean series will be found directly by subtracting the last 

 remaining series from the first daily mean series. We shall take this 

 series for a second set of operations. The number we shall take for 



operations is 25 ^ — - — nearly 36, but we shall take 35 because 



the operations are simpler for odd number than for even number. Now 

 we shall have 35 as our working value of m, by which we shall con- 

 tinue the operations, say up to 5th, and then curve the 5th remaining 

 series on a curve form. If there be only one period in the series from 

 about 17 to 35 days, we shall begin to get simple harmonic waves in 

 the fifth or in some further remaining series ; but if there be more 

 than one period the result will be compound, about which we shall 

 discuss presently. But first suppose that there is only one period. 

 If we do not find definitely the duration of simple wave curve in 

 the 5th remaining series, then we shall continue the process on to 

 the 6th remaining series and curve on the same curve form and 

 with the same zero line, until the duration of simple wave curve is 

 definitely found. It may here be mentioned, that if the period is not 

 of an exact number of days, we should have a long series to begin 

 with, so that we shall take some exact number of waves from the last 

 remaining series and find the number of days in them, and divide the 

 days by the number of waves, and the result will be the number of 

 days in the period. We must also remark that if there should be no 



* We always have some limit of accuracy of observing the instruments and re- 

 ducing the observed values ; for example, we observe barometer to a nearest 

 thousandth of an inch, and also reduce daily means to a nearest thousandth of an 

 inch. By less than two in the last place of figures, in this case, we mean less than 

 two thousandths of an inch of barometer, and so on. 



