Periodicities when the Periods are unknown. 



391 



ending with the 2nd January, 1852, as the year 1848 was the first 

 complete year when the system of hourly observations began 

 without interruption at the Colaba Observatory. The weekly means 

 were chosen in place of daily means for two reasons, first that as 

 no observations were made on Sundays and a few holidays, no 

 continuous daily means were available during the period ; second, to 

 save comparatively the labour of calculations of the processes. On 

 some occasions when there were atmospheric disturbances, or for 

 similar reasons, observations were made on Sundays and none on 

 Mondays. For this and similar other reasons the weekly means were 

 calculated from all the daily means from Sunday to Saturday. 



These means are given in Table IX, and curved in fig. 6 in an 

 interrupted line. With these weekly means we have performed 

 •5 operations to get the fifth series of remainders. The numbers in 

 the first and fifth series of remainders are also given in Tables X 

 and XI respectively, and curved with the interrupted line of fig. 6, 

 and with the same scale in dotted and continuous lines respectively. 



50. Looking at the continuous curve, it will be seen that from 

 24th week of 1848 to 8th week of 1849, we have 7 waves of simple 

 harmonic character, and equidistant in duration. Thus there are 

 36 weeks, or 36 X 7 days in 7 periods, so that the average duration 

 of a period is exactly 36 days. Again, from 8th week of 1849 to 

 24th week of 1850 there are 13 waves, also almost equidistant in 

 duration. Thus there are 68 weeks, or 68 X 7 days in 13 periods, so 

 that the average duration of a period is nearly 36"6 days. Again, 

 from 24th week of 1850 to 34th week of 1851 there are, we presume, 

 12 periods. It will be observed that out of these there are 7 periods, 

 viz., 1st and 7th to 12th, whose waves are quite prominent ; with 

 regard to the remaining 5 periods their waves seem to be almost 

 obscured by irregularities. Thus there are 63 weeks, or 63 X 7 days, in 

 12 periods, so that the average duration of a period is nearly 36*7 

 days. If we now add all the weeks and periods together, to get the 

 mean duration of the period we have 167 weeks and 32 periods, 

 therefore the average duration of the period is nearly 36*53 days. 



51. We should here remark that as we are dealing with weekly 

 values, there is a possibility of an error, either too much or too little, 

 of one week in the whole period of 167 weeks. If we take 166 weeks 

 for 32 periods, we get an average duration of 36'31 days ; and if we 

 take 168 weeks, we get 36' 75 days. Thus the period we have found 

 out is approximate to the extent above mentioned. We shall, there- 

 fore, say that the period is approximately 36J days instead of 36'53 

 days. 



52. The object of drawing three curves of weekly means on the 

 same zero line, and with the same scale, is the same as in the preced- 

 ing example of the curves of daily means. The formation into regular 



