128 REPORT— 1870. 



In the first Table the values of h represent the height of the tide due to 

 this component, referred to mean sea-level (A^, of analyzed series) ; in the 

 second Table they are referred to a fictitious level, R^ feet (0-56), below the 

 mean level. Supposing the value of aU the amplitudes of the tide-factors to 

 be so added throughout the whole of the Tables, the resulting correction to 

 the summation of tide-heights found for any time will be A^ — SE,. This 

 method gets rid of all signs and renders the work of the calculator much 

 lighter. 



59. The true hour-angle of each of the fictitious stars was then found for the 

 commencement of the series of tide-heights proposed to be computed (1869, 

 April 24** O"" Greenwich mean time). Lcven-ier's places of the sun and 

 Hansen's places of the moon have been used throughout these reductions. 

 Each hour-angle was then found in its proper column in the Table of hour- 

 angles formed at the commencement of these reductions, and which can be 

 found within a small fraction of a degree in a Table extending through 369 

 days. The consecutive hour-angles in the Table will be the correct argu- 

 ments for the heights for 1869, April 24^ 1^, 2^, &c. The height (/i) was 

 then taken from each Table in succession, using the true hour-augle as found 

 above for argument. The sum of the nine values of h thus found, together 

 with the correction A^— SE., will represent the height of the water above the 

 datum-line at first chosen, neglecting the long-period tides, wliich for Liver- 

 pool (§ 63) were found to be very small. A series of heights for every hour 

 of the day for 13 days was thus formed and compared with the heights taken 

 from the diagram-sheet (§ 56), and the difi'erences taken. The average dis- 

 crepancy was about -j^ foot and the maximum 2 feet. The difi'erences 

 showed considerable regularity of disagreement ; and it appeared probable 

 that the tide-components, varying with the inclination of the moon's orbit, 

 did not vary strictly according to the law of the equilibrium theory. It was 

 thought advisable to reduce another year for the determination of the law of 

 change, and a period of 369'' S^, commencing 1866, January 23<* 0'', was 

 chosen for this purpose. This period gave very nearly a minimum inclination 

 of moon's orbit to earth's equator, whilst the first year (1857-58) gave nearly 

 a maximum value. The results of the dcclinatioual tide-factors obtained from 

 the analysis of this year were not very diff'erent from what would have been 

 obtained from the values for the previous years according to the equilibrium 

 theory, but nevertheless indicated that these tides varied to a less extent than 

 what that theory gave. 



60. The results for Liverpool for 1866-67 are as foUows ; — • 



Ao = i6'8998. Average inclination of Moon's orbit to Earth's equator =: i8° 21'. 



L N 



0-6015 2-1608 

 i24°-o8 3oi°-59 



