384 Mr. Y. N. Nene. On a Method of Tracing 



nb 

 ~2 



90° 



108° 



257° -4 



442° -2 



624° -6 



805° '8 



986° -4 



1167° -0 



1347° -6 



K 



(Period in 

 days). 



72 



60 



25 2 



14-65 



10-37 



8-04 



6-57 



5-55 



4-81 



1 



2 



•63622 



•50409 



- -21610 



+ -12640 



- -08850 



+ -06721 



- -05348 



+ -04368 



- -03626 



1 



e a 



•40478 



•25411 



•04670 



•01597 



•00784 



•00452 



•00286 



•00191 



•00131 





•59522 



•74789 



•95330 



•98403 



•99216 



•99548 



•99714 



•99809 



•99869 



(-.;)* 



•07471 



•2309 



•78732 



•92260 



•96140 



•97758 



•98583 



•99049 



•99346 



/ i \ iq 



(■-,?) 



•00558 



•05330 



•61987 



•85134 



•92428 



•95567 



•97186 



•98107 



•98697 





•00042 



•01230 



•48804 



•78551 



•88859 



•93423 



•95808 



•97168 



•98051 



In the above table, the periods less than mc of the type K which 

 we have selected are those that have maxima or minima valnes of 



their first factors of the type - so that their factors of the type ( i-Z-FV 



q Kg 2 / 



will have the greatest possible reduction, that is, factors for inter- 

 mediate periods will reduce at slower rates. 



36. We also see that when r is equal to 5, we have the factor cor- 

 responding to the period 72 days reduced to y 1 -^, and from this we can 

 infer that the factors corresponding to greater periods than 72 days 

 will be reduced to less than y 1 ^-. So that for all practical purposes 

 we shall make the operations 5, and assume practically that in the 

 fifth difference and sum series we have reduced all series of the periods 

 72 and greater than 72 days to zero, and retained in their full magni- 

 tude all the series of the periods less than 36 days, whilst the series 

 of periods intermediate between 36 and 72 days will be only partially 

 obliterated. Such a series may be represented by 



{u Y sin (Ui + Yb Y ) + u 2 sin (U 3 + Pb 2 ) + , &c. } 

 + | u n sin + p|^ + u n sin (lJ n2 + p|0 + , &c. j 



-f |^ +1 sin (U w+1 + P& K+1 )+^ w+2 sin (U„ +2 + P&„ +2 ) ^^!±|Ill^ +, &c. 



In the first pair of brackets of the above expression, we have 

 arranged those terms of the simple harmonic series whose periods are 

 less than the period of 36 days, but not any of the period of the 

 36 



form — where N is any integral number; in the second pair of 

 brackets of the expression, we have arranged those terms of the 



