Periodicities when the Periods are unknown. 



387 



of distribution must not be greater than half a day, and so the mean 

 of the 9th and 10th values, which was found more appropriate to 

 9th column than any other column, was entered in the 9th column. 

 Similarly up to the mth horizontal line, the values will be entered by 

 properly combining two values for entering in one column as many 

 times as need be in the course of entering the series in the manner 

 stated above. Also the sums and means of each vertical column are 

 taken in the same way as in the preceding example. We will not go 

 into details, as in the preceding example, but can simply say that the 

 last numbers of our new form will be the variation of the period of 

 36*4 days with its almost full magnitude, and for 36 points, the 

 intervals between which from point to point will be 1^ days. 



40. We should remark that the process of difference and sum series 

 has also an obvious advantage in separating the observation series 

 into any number of difference and sum series without affecting the 

 series by the process. By affecting the series by the process, we mean 

 that in the former process for the remaining series and mean series, if 

 we take any arbitrary number as our working value of m, and if there 



should be periodicities lying between — and mc, we shall get the 



periodicities mixed up in both the series with a greater amplitude 

 than the original series. These separations are very useful for the 

 first trials when suspecting approximate periods. 



Application of the Process and Detection of a Period of about 9^ Months. 



41. For this purpose we have taken means of barometric pressure 

 at Bombay, from 1847 to 1872 and 1873 to 1878, thus forming our 

 Table I. The first part of monthly means is also given in Table I, 

 page 11, of the volume entitled " The Meteorology of the Bombay 

 Presidency," by Charles Chambers, Esq., F.R.S., Superintendent of 

 the Colaba Observatory, Bombay ; and the last part at the foot of 

 Tables I to VI, pages 58 to 63 of the " Bombay Magnetical and 

 Meteorological Observations, 1871 to 1878." The description of the 

 barometer and mode of observation, &c, are fully given in both the 

 volumes. With the numbers in Table I, we have performed one 

 operation to get the first difference and sum series by taking 12 as our 

 working value of m, and the result is entered in Table II. The 

 numbers in Table II are subtracted from the corresponding numbers 

 in Table 1 and entered in Table IIL At the foot of Table II we have 

 entered the mean for January in the 24 years, 1848 to 1871, the mean 

 for February in the 24 years, the mean for March, &c, &e., up to 

 December.* These means form the annual variation of barometric 



* Properly speaking, we should have taken the means of thirty years, 1848 to 

 1877, instead of 1848 to 1871 ; but first of all we have taken for our discussion the 



