14 On the Prediction Tables for the Tides of the U. S. Coast. 
ee es he : 
+ ¢, cos ltsin 2. H+ t, cos lt cos 2H Baty perniinn, oprenettae, 
+@, sin 2ltsin2 H+ Q, sin 2/t cos 2H Son's dqctingsien coves 
+, cos2ltsin2 H+, cos 2ltcos2 H 
The grouping of the observations of one year at Boston, to 
apply this method, the formation of the equations and their solu- 
tion by the met od of indirect elimination has been the work of 
Mr. R. S. Avery, who has labored most assiduously and success- 
fully, ingeniously checking his work where the system of checks 
could be a pplied, at every step. He has determined the values 
of ) and of ee co-efficients for Boston, as follows :— 
A=438-:47, d=—3'17, d,=—35'62, p=—093, p,=—1°56 
s=— 19°49, s+ 11-97, pp=+ 131, py=—V21, pa=+7-23 
Ps=+060, 1,.= =-T11, g=+ 181, 7s= +291, ¢=—1-99 
‘37 
Q@,=-2) 25, Becace 39, Q5=+2710, Q,=+23'13 
There are propositions for facilitating this work, growing out 
of the experience acquired in the computations, but requiring 
more examination than they have yet received before pronounc- 
ing upon them. It is possible that by applyi ing Lubbock’s method 
of averages to some of the terms, approximate values pale ze 
found more readily than by the method we have employed. 
additional terms for the sun’s declination, D sin 2 lt, and D, cos 2 1, 
will be int 
I present to the Association the tables computed by Mr. Avery 
for applying this method to the prediction of the tides at Boston 
harbor. 
In order to test the co-efficients, igs i were made for 
different parts of the months of the year 1853, for which we 
have observations. Transit C was Ls as the transit of refer- 
ence. The differences between the predicted and observed results 
are shown in the annexed table, the* first column of which con- 
tains the dates, the second the computed, the third iis observed, 
and the fourth the observed lass the computed resul 
From the table it appears that in twenty pairs “of tides, the 
morning and afternoon results being grouped in the fifth column 
to get rid of the diurnal inequality, there are two differences of 
less than 2™, thirteen of more than 2™ and less than 4, three of 
more than 4™ and less than 10™, two of more than 10™. The 
probable error of, the Sen ang of a single pair of tides is 412. 
laborious researches are still in_ progress, but I have 
thought that. he ‘Noahs sisendy obtained, required 2 epotics of 
them, and a recognition of the labors of rey ee and 
Avery. 
