Report of the U. & Coast Survey for 1883. "47 
that part of the Delaware river between Philadelphia and a 
point 53 miles below. In this stretch of water, 734 lines of 
Soundings have been run across the river, from which data the 
area of section and average depth have been calculated and 
tabulated. These results are presented in tables and in diagrams 
and strongly reinforce a conclusion based upon preliminary 
data and published in the C. & G. S. Report of 1879; this con- 
clusion is that, in the language of the Superintendent, “Jn the 
Estuary of the Delaware from League Island to the submerged 
delia, the mean depth is constant; the widths and sections vary 
with the square of the distance, and the retard of the tide can be 
exactly stated in terms of the mean depth and width,” 
Mathematically, then, these relations are expressed by equa- 
tions of parabolas in which the constants have been empirically 
determined. 
: et x be the distance of any section of the river from the 
Fort Mifflin section, down stream, measured along mid stream 
and in nautical miles; then we have 
Mean depth in feet =18°64 
Mean width of stream in feet =10'la?+5100; and 
Mean area of section in sq. ft. = 188a7+95000. 
The curves resulting from observation agree well with the 
curves resulting from these equations, particularly the latter, in 
Which the coefficient 188 results from multiplying the preced- 
Ing coefficient 10-1 by the average depth 18°64 fee. This 
_ depth, 18°64, is the mean of all the soundings in the river for 46 
miles below Fort Mifflin. alt 
he expression for high waterjis stated to be 
511 distance—0-0018 width + 92 minutes where “ each term 
has its distinet physical meaning,” but what that meaning is we 
are not told. 
A sketch of the estuary accompanies this appendix. 
Professor Wm. Ferrel, whose mathematical . researches in 
Practical directions have been so valuable, contributes two 
eyeers sa a topic peculiarly his own, viz: the tides. The 
I rief account of the results of the harmonic analysis of 
the tides at Sandy Hook, 1876-1881. It has special reference 
to determining the constants necessary to be used for this place 
In the tide-predicting machine. . 
Incidentally the mass of the moon is deduced from these 6 
years’ observations, and found to be between fy and yy, the 
Corresponding determination from the Penobscot Bay tides 
ng z's and from the Boston tides 74. | 
The second pa er, however,— Description of a maxima and 
Minima tide-predicting machine—is a much more important 
