150 



RECORD AND RESULTS OF 



This form was also used by Mr. Whewell (Phil. Trans. 1834, Art. II) as a first 

 approximatioia, and was applied by me to the Van Rensselaer Harbor tides. For 

 short series it is quite sufficient, and in the present case the results found by it and 

 by the more rigorous form given below hardly differ by as much as one inch in 

 the extreme. 



To find the ratio of the solar and lunar tide we have the greatest or spring tide 

 range, 21.7 — 11.8= 9.9 feet, and the least or neap tide range, 19.3 — 14.3 =5.0 

 feet; the former being the sum, the latter the difference; 



hence the ratio ~^ = 0.329 

 7.45 



For substitution in our formula given at the head of this article, we take for //■ 

 the half of the difference between the highest and lowest high water, or the differ- 

 ence between the highest and lowest low water, which is 1.22, the corresponding h', 

 by means of the above ratio, is 3.72, hence the expression 



J[3.72^ + 1.22^ + 2 X 3.72 x 1.22 cos 2 (<p — U°)~\ and 



computing the inequality by this expression the mean of all the ordinates will be 

 found = 3.81, which constant we subtract to obtain the inequality itself; we have 

 therefore for high water the half-monthly inequality 



2/ = J[l5.33 + 9.1 cos 2 (^ — 13°)] —3.81 

 and for low water 



2/= J[l5.33 — 9.1 cos2(^ — 9°) 1—3.83 



The comparison between observed and computed heights is shown in the follow- 

 ing table and by diagrams. The observed inequality was found by subtracting 

 the mean of the whole from each single value. The results computed by the 

 approximate formulse are marked " app.;" those by the more rigorous formula are 

 marked "ri<r." 





Half-monthly-iiic 



quality in 



height. 









In higli water. 



lu low water. 



C's tran. 



Observed. 



Computed 

 app. 



Computed 

 rig. 



Difference. 



^ 's tran. 



Observed. 



Computed 

 app. ^ 



Computed 

 rig. 



Difference. 



Qh 27" 



+ 1«.15 



+ 1«.17 



+ l«.ll 



0«.0 



Oh 2^m 



—V\0 



1ft. 2 



— 1«.3 



+ 0«.3 



1 29 



4-0.75 



+ 1.14 



+ 1.09 



—0.3 



1 29 



—0.9 



—1.1 



—1.1 



+ 0.2 



2 29 



+ 1.05 



+ 0.79 



+ 0.81 



+ 0.2 



2 29 



—0.9 



—0.7 



—0.6 



—0.3 



3 29 



+ 0.65 



+ 0.24 



+ 0.33 



+ 0.3 



3 28 



—0.3 



—0.1 



0.0 



—0.3 



4 28 



—0.35 



—0.37 



—0.27 



—0.1 



4 28 



+ 0.5 



+ 0.5 



+ 0.6 



—0.1 



5 30 



—0.85 



—0.91 



—0.90 



0.0 



5 27 



+ 0.8 



+ 1.0 



+ 0.9 



—0.1 



6 30 



—1.25 



—1.18 



—1.28 



0.0 



6 26 



+ 1.5 



+ 1.3 



+ 1.1 



+ 0.4 



7 26 



—1.25 



—1.15 



—1.24 



0.0 



7 26 



+ 1.4 



+ 1.1 



+ 1.0 



+ 0.4 



8 22 



—0.75 



—0.85 



—0.83 



+ 0.1 



8 21 



H-0.3 



+ 0.8 



4-0.7 



—0.4 



9 SO 



—0.15 



—0.23 



—0.12 



0.0 



9 30 



0.0 



+ 0.1 



+ 0.1 



— 0.1 



10 29 



+ 0.35 



+ 0.38 



+ 0.46 



—0.1 



10 29 



—0.2 



—0.6 



—0.5 



+ 0.3 



11 28 



+ 0.65 



+ 0.89 



+ 0.89 



—0.2 



11 25 



—0.9 



—1.0 



—1.0 



+ 0.1 



The low waters are not as well represented as the high waters. 



