382 Prof. G. H. Darwin. On an Apparatus for [Dec. 15, 



The last two columns contain a comparison between the interpo- 

 lation and what in the present case we know to have been actuality. 

 There is a mean error of O20 ft. Thus it is clear that a fair record 

 may be interpolated even with so long a break as a week. 



In this example I have only shown the interpolation for one 

 column, but of course all the other twenty-three columns would really 

 have to be treated similarly. 



I find by trial that the result would be a little improved by a 

 graphical method, but that process is slightly more troublesome than 

 the numerical one. 



Table of Interpolation. 



It may happen that the hiatus is too long for treatment in this 

 way. I do not think it would be safe to treat much more than a fort- 

 night by interpolation. 



It has been shown in 4 how the tides associated with S are to be 

 treated where the record is deficient, and it remains to consider the 

 other tides. 



In 7 are given the days with which we must stop in the analysis 

 of an incomplete year, and this table affords us the means of treating 

 a long hiatus in the observation. 



We may in fact omit all the entries between any two of the 

 numbers given in the table without seriously affecting the result. 



Let us suppose, as an example, that the tide gauge broke down on 

 day 210 and was only repaired and in operation again on day 226. 

 Now 210 is 148 + 62, and 225 is 222 + 3. 



Then we see by the table in 7 that in finding the means for 



