308 Prof. GL H. Darwin. [June 19, 



T COS Y 1 " = ' pn COS 0, 



T sin YT = p n sin 0, 

 \vhere = 2fe 



The period under reduction consists in this case of an exact number 

 of quarter-lunar periods, and the following table gives the values of 

 pn and y3, according to the number of quarter-lunar periods : 



No. of i-lunar 



periods. III. V. VII. IX. XI. XIII. 



' logpn 9-5749 9-5628 9-5508 9-5303- 9'5009 9-4618 

 /3 20-20 33-66 47-13 60-59 74-06 87'52 



Ti is the sun's mean longitude at epoch, the formula for I is given 

 above, and i/, f are found from Baird's Manual in the tables applicable 

 to the tide K x . 



E. Rules for the Partition of the Observations into Groups. 



If the first event after epoch is a L.W., either omit it from the 

 reductions, or let the first tide be the H.W. which precedes epoch. 

 Thus we are to begin with a H.W.* 



The H.W. and L.W. are treated apart in separate tables. 



Each tide (H.W. or L.W., as the case may be) is numbered con- 

 secutively, from 1 onwards. 



The following are rules for partitions : 



* This is not necessary, but it makes the statements of the subsequent rules 

 simpler, as they have not to be given in an alternative form. 



