822 



REPOBTS ON THE STATE OF SCIENCE. — 1920. 



harmonic prediction could be obtained from comparisons of the predictions made 

 independently for the Admiralty and by the United States Coast and Geodetic 

 Survey. One would naturally expect that j^redictions ostensibly obtained from the 

 same harmonic constants would be fairly concordant, even if slightly different mean 

 values were used, and that the lengthier the series of observations and analyses the 

 better would be the correspondence in prediction. But an examination of the 

 independent predictions shows that this is not so. The following table was prepared 

 by taking one month's predictions from the Admiralty tables and comparing 

 with the corresponding predictions published in the United States tables. The 

 maximum difference and average difference, taken without regard to sign, are given 

 for the heights and times of high and low waters. 



In the case of Aden, the range of tides on certain days is small, so that the time; 

 of high and low water is uncertain ; these days have been ignored. 



The above table in itself bears testimony to the unsatisfactory state of harmonic 

 prediction, even if we had no further evidence. We are not at the moment con- 

 cerned with the cause of any discrepancy between the two independent predictions 

 so much as with the general results. Where, as in the case of Liverpool, we may 

 have two different predictions, each supposed to be authoritative, which differ 

 occasionally by nearly a foot and on an average by five inches in height, then one's 

 confidence in the accuracy of prediction is badly shaken. The differences in times 

 are also serious and are considered so by all authorities ; these provide the best test 

 of the accuracy of prediction in all cases, since the height differences are naturally 

 small when the mean range of spring tides is small. 



While the maximum and average differences are conclusive, there is also much 

 interest in a fuller examination of the differences that do occur. It is found that 

 there are periodic differences of some magnitude in practically all cases. For 

 Liverpool, on certain days both high waters have a positive difference and both low 

 waters a negative difference ; that is, there is a semi-diurnal oscillation (in the 

 differences), of which the amplitude is about seven inches ; moreover, there are 

 diurnal oscillations also present in the differences, as is shown by one set of high- 

 water differences being consistently lower than the alternate set, e.g. 



4,8,0,4, -4, -1, -7, -3 inches. 



Similar results are found in the differences in times of high and low water. As 

 another example, in the case of St. John, N.B., there is a semi-diurnal oscillation of 

 nearly a foot on certain days, as is shown by the following series of differences in 

 heights for successive high and low waters : — 



-7, 12, -12,11, -8, 12, -11, 12 inches. 



The effects vary with different machines, but, generally speaking, for all the ports 

 there are systematic differences which should not be allowable. 



Enough evidence has now been given to show why it is considered that harmonic 

 predictions are not at present satisfactory ; two independent methods of judging 

 them have been considered, the first being based upon the experience of tidal 

 authorities in comparing predictions with observation, and the second being based 

 upon the disagreements that exist between two sets of predictions calculated inde- 

 pendently of one another. 



