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



tl sin {(^+^366^ + 1^} 



sinM 



M sm 1 



2 



;inM 



366 



M 



36k 



2 _ 



+ I Un sin + P ^ + % 2 sin ^U w2 + p|0 + , &c. J 



r r/ M-i \ >sinM— g- 1 /g: +1 -iy 



+ ^ +lS in{(U w+1 +£^6& w+1 )+P5. +1 l — Z - x( — 2— J 



L IV a / ^Msin^+i 



2 



+ ,&c.]. 



And it can be shown that the last factors of the terms in the first 

 and the third pairs of brackets, where M is sufficiently great, reduce 

 to zero (see curve of factors in fig. 1). Thus the 36 mean values 

 found in the last horizontal line of our new form will represent the 

 variation of the 36- day period. 



38. Next suppose that the period which we have detected is not an 

 exact number of days but (say) of 36'4 days, we shall still take the 

 nearest integral number, viz., 36, as our working value of m, and by 

 it find (say) the 5th difference and sum series as already described. 

 In this case the amplitude of the variation of the period of 36*4 days 

 will be slightly reduced in the 5th difference and sum series. The 

 reduction of the 1st simple harmonic variation that is of the period 

 of 36-4 days will be (1--99954), that of 18'2 days will be (1--99954), 

 that of 12'13 will be (1 — "99954), and so on. The next thing is to 

 show how the series is to be combined, which we are going to show 

 in the following manner. 



39. In the first horizontal line of our new form, we shall enter first 

 36 values. In the second horizontal line 8 values, from the beginning 

 of the next 37 values, will be- entered up to the 8th vertical column, 

 but in the 9th vertical column we shall enter the mean of 9th and 

 10th values out of the 37 values intended for the second horizontal 

 line ; in the rest of the horizontal line the remaining values will be 

 entered. The object of combining the 9th and 10th values and 

 entering the mean result in the 9th vertical column of the second 

 horizontal line is that, since we are dealing with exact days only, we 

 must enter the values in the columns in such a manner, that the error 



