380 Prof. G. H. Danvin. On an Apparatus for [Dec. 15, 



Tides of Long Period. 



method of grouping, considerable errors of incidence of the S hours 

 in the K time scale prevail for many days together, and the method 

 seems of doubtful propriety. The same is true of the P tide, and here 

 also the two methods give somewhat different results. 



The accuracy with which the very small Q tide comes out, whether 

 from 24 values or only from 12, is surprising, and may perhaps be, to 

 some extent, due to accident. It shows, however, that the present 

 method may be safely applied, even when the special time scale 

 differs considerably from mean solar time. 



The results for the tides of long period are quite as close to the old 

 values as could be expected. 



11. A comparison of the ivork involved in the new and old methods of 



reduction. 



It has been usual in the Indian reductions to use three digits in 

 expressing the height of water, and there have been 15 series, or even 

 more. Now 3 x 24 x 365 x 15 is 394000 ; hence the computer has had 

 to write that number of figures in reducing a year of observation. 

 This does not include the evaluation of the annual and semi-annual 

 tides, so that we may say that there have been about 400,000 figures 

 to write. 



I propose to express the heights by two digits, and they only have 

 to be written once. Thus, in the present plan, the number of figures 

 to write is 2x24x365, or 17,500. Thus the writing of 382,000 

 figures is saved. 



In the old method the computer had to add together all the digits 

 written, say, 394,000 additions of digit to digit. 



I propose to use 24 hourly values in three series, viz., S, M, and 

 MS, and 12 two-hourly values in eight others. Therefore, the number 

 of additions will be 3 x 2 x 24 x 365 + 8 x 2 x 12 x 365 or 123,000. Thus 

 270,000 additions are saved. 





