Periodicities when the Periods are unknown. 



389 



marks are made on the upper side of the curve, while in the preceding 

 case on the lower side of it, to distinguish them from each other. 



43. We find from May, 1858, to October, 1866, that the occurrences 

 of these minima have disappeared. From December, 1848, to May, 

 1858, there are 12 periods, that is -y 1 -/ — 9J months for a period, and 

 from October, 1866, to April, 1877, there are 13 periods, i.e., -\^=9§ 

 months for a period. From this we might guess that to form such a 

 curve there must be two prominent periods, which may be as (say) 5 

 and 9J months. 



44. To clear this doubt, we have further taken the numbers in 

 Table VI, and performed five operations to get the fifth difference and 

 sum series by taking 5 as our working value of m. These numbers we 

 have given in Table VII and curved in fig. 4. Then the numbers in 

 Table VII were subtracted from the corresponding numbers in 

 Table VI and entered in Table VIII, and curved in dotted lines with 

 the corresponding curve of fig. 3, and with the same scale and on the 

 same zero line. Now, by looking at the oscillations of the dotted 

 curve, it appears that it is of a simple harmonic character, and it 

 confirms the 9J-monthly period as already described. But in both 

 these curves (continuous and dotted) there are a few exceptions to the 

 confirmation of the 9-|-monthly period. These exceptional periods 

 are — from March, 1857, to December, 1859; June, 1863, to September,. 

 1866; April, 1868, to January, 1871; and November, 1872, to the 

 end. 



45. We shall now turn to fig. 4. By looking at the oscillations of 

 this curve we again see that amongst the periods there is a great 

 predominance of a 4f -monthly period. This we have ascertained as 

 in the case of 9^-monthly period. If we count all the marks made on 

 the curve, we have 65 ; thus there are 64 periods in 302 months (from 

 June, 1850, to August, 1875), and ^=4*72, i.e., nearly 4J months,* 

 which is an average duration for the period. 



We should now here remark that, although in the continuous curve 

 of fig. 3 we found that the occurrences of the subordinate minima 

 have disappeared from May, 1858, to October, 1866, still they appear 

 in the 4f -monthly period curve of fig. 4. 



Application of the Method to find the Duration of an exact Period. 



46. The writer had taken a small series of dail} r means of barometer 

 observations, derived from hourly tabulations of barograph, uncor- 

 rected to standard barometer No. 58, from 1st December, 1875, to 

 31st December, 1876, for trial, when the method of detecting any 



* The writer found worth noticing that the period of 4f months is almost an 

 exact multiple of the 36|-day period which he has found further on in paragraph 

 50. 



