18 Co-tidal lines of the Atlantic Coast of the United States. 
longitude of each group is taken, and the group is referred to this 
point as the origin of co-ordinates; the mean co-tidal hour is also 
taken. In the equation of the co-tidal line— 
r+Ny=<z 
x and y represent the known co-ordinates, the difference of lon- 
gitude being reduced to the same unit of the geographical mile 
as the difference of latitude. The co-efficients M and N are de- 
termined by the equations— 
M22? +N22y= 222 
M2ay+ Ny? == yz 
= is the tangent of the angle which the co-tidal line makes 
with the meridian, and “ M?+ N? gives the motion of the tides 
wave, or difference of co-tidal hour for one geographical mile per- 
pendicular to the co-tidal lines. : 
In this I have merely followed the admirable example given by 
Professor Lloyd, in the joint paper of himself and Colonel Sabin 
on the magnetic survey of the British Islands. 
aving investigated separate groups in this way, it is easy to. 
draw the co-tidal curves which represent the observations; the 
investigation tests the grouping in an interesting way, by the co- 
incidence or discrepancy of the computed and observed co-tidal 
ours. eo 
The first approximate indication from the discussion is the cor- 
rsa ice of the tides on our Atlantic coast to the supposition 
a tide-wave moving from 8. 53° E. to N. 53° W.; but this is 
baly a rude statement of the phenomen 
In scanning the co-tidal hours along the coast, we observe that 
they divide themselves into two groups, one south of Martha’s 
Vineyard, and the other north of Cape Cod, with a short anoma- 
lous group between them 
The co-tidal hours trols ‘Cape Florida to Quick’s Hole, Martha’s 
Viveyard sound, are not greater than 13h. 30m., nor less than 
11h. 38m. Hatteras i is decidedly, as was pointed out by the Mas- 
ter of Trinity, the Rev. Mr. Whewell, a point of divergence, the 
establishments on the north and east of it, and the south and west 
of it, being asa general rule, greater then the establishment of 
Hatteras. "Cae value for the co-tidal hour there differs from Mr. 
Whewell’s, and further observations now in progress, will decide 
between the two results. 
From Provincetown, Cape Cod, to A Sable Island, the co- 
tidal hours vary between 12h. 55m. a 43m. 
cinning at Tybee entrance, Fort Sey Savannah river, 
we have a good series of tidal stations to Hatteras, five in num- 
ber forming group a, Table No. 3. The mean co-tidal hour is 
11h. 52m., and the angle which the co-tidal line makes with the 
meridian is 50° 09, agreeing very nearly with the trend of the 
coast. 
