1892.] facilitating the Reduction of Tidal Observations. 331 



"We may say that formerly there were about 800,000 operations 

 (writing and addition), and that in the present method there will be 

 about 140,000. This estimate does not include a saving of several 

 thousands of operations in obtaining the tides of long period. I am. 

 therefore within the mark when I claim that the work formerly be- 

 stowed 011 one year of observation will now reduce at least five 

 years. 



It has been found that the manufacture of my computing strips of 

 xylonite is rather expensive, but as it formerly cost in England 

 rather more than 20 to reduce a year of observation, the cost of the 

 apparatus will be covered by the saving in the reduction of a single 

 year, and it will serve for any length of time. 



12. On the completion of the record for short gaps and long gaps. 



In any long series of tidal observations there are usually some 

 breaks in the record in consequence of the stoppage of the clock of 

 the tide gauge, or from some other cause. Now the process of elimi- 

 nation by grouping depends essentially on the completeness of the 

 record, and it is therefore necessary to fill in blanks by interpo- 

 lation. 



Such interpolation has not been usual in the operations of the 

 Indian Survey, and it might be thought that the complete omission of 

 the missing entries is the proper course to take ; but it is easily shown 

 that this treatment is exactly equivalent to the assumption that the 

 water remained stagnant at mean sea level during the whole time of 

 stoppage of the gauge. It is obvious, therefore, that any conjectural 

 values are better than none. 



The process by which it is proposed to interpolate is best shown 

 by an example. 



At Port Blair (beginning April 19, 1880) the column of 6 h from 

 days 99 to 112 gives the heights shown in the first column of the 

 table below. I suppose that the tide gauge broke down on day 103, 

 and only came into action again on day 110.* There was really no 

 break down, and the actuality during the supposed hiatus is shown 

 in the last column but one. 



Now if we look back about a month we find that the water stood 

 about the same height at the same hour of the day (viz., 6 h ). Then 

 the " previous record " (which is complete) beginning at 69 d is en- 

 tered in the next column. Similarly a " subsequent record " is found 

 about a month later, and is entered in a third column. The mean of 

 the previous and subsequent records is then taken as giving the 

 values to be interpolated. 



* The days are here numbered from 1, instead of from 0. This has been the 

 usage in India hitherto. 



