PHILOSOPHICAL TRANSACTIONS 
I. On the Tides of the Arctic Seas. 
By the Rev. Samuel Haughton, M.D. Dubl., D.C.L. Oxon, F.R.S. , 
Fellow of Trinity College, Dublin. 
Part YIT. Tides of Port Kennedy, in Bellot Strait. {Final Discussion .) 
Received February 17, — Read March 15, 1877. 
[Plate 1.] 
In Part YI. I Lave discussed McClintock’s observations on the Tides of Port 
Kennedy, using only the Heights and Times of High and Low Water, as I wished 
to follow the same method in comparing all the Tidal observations in the Arctic 
Seas. Although I adopted this method for the purpose of comparison, I was well 
aware that I had not exhausted all the information at my disposal, for McClintock’s 
observations were made hourly during 23 days, and I used of these observations 
only those in the neighbourhood of H.W. and L.W. of Diurnal and Semidiurnal 
Tides. I shall now discuss the observations, with the aid of Fourier’s Theorem, 
so that all the observations made at every hour of each day shall enter into the 
constants determined for' that day. If F denote the height of the tide, observed 
at every hour of the day, we have by Fourier’s Theorem 
F= A 0 + A x cos 5+ A 2 cos 2s+ A 3 cos 3 s-f&c- 
Bisins+Bosin 2s+B 3 sin 3s+&c (1) 
where s denotes the sun’s hour angle, and where the coefficients A 0 , A,, B 1? A 2 , B 2 , &c., 
are found from the foUowing equations, in which F 0 , F b F 2 , &c., denote the values of 
F at the hours 0, 1, 2, &c., 23. 
24A 0 =F 0 +F 1 . . . +F 23 (2) 
MDCCCLXXVIII. 
B 
