230 CATALOGUE.— THEORY Ol" HYDBAULICS, HYDRAULIC PRESSURE. 



varying with the tangent of the angle of incidence, and a until the angle of incidence becomes greater than 80°. Thus, 

 -third portion proportionate to the square of the cosine, di- the direct resistance being unity, and a the angle of inci- 

 minished in the ratio of a power, or other function, of the dence.lhe oblique resistance will be.2 + .04t.a+288(cos.o)'; 

 angle of incidence. And it will appear upon inquiry, that (360+a°). A formula, somewhat more accurate than 

 if we take one fifth of the radius, increased by one twenty- this, deduced from experiment only, is r := (cos.o)' 

 fifth of the tangent, and add to it four fifths of the square of +.000C00!'217a'''''; the quantity added to the square of 

 the cosine, diminished in the ratio of the circumference of the cosine being a little less than the millionth of the cube 

 k circle Increased by the angle of incidence, to the simple of the angle of incidence, expressed in degrees. The re- 

 circumference, we may approach always within about one suits of these and other formulas are compared, in the 

 fiftieth, to the number expressing the oblique resistance, following table, with various experiments. 



Eytelwein's formula is (cos. a)'+.4v. s. a. Formula A is a comparison with those of Schober, which were made in 

 (cos. a)'-f . 1 t.fl. Formula B is the first, and C the second, a similar manner on air. The results of both these inves- 

 of those which have been mentioned. The experiments of ligations are here exhibited in a table, and compared with 

 the society for the encouragement of naval architecture a coarse approximation from this formula r;z:.4-f .6(cos a), 

 have been reduced by interpolation to the angles employed Dr. Hutton's experiments on air, when reduced, like the 

 by Bossut : but the society appears to have made some de- rest, to surfaces of given transverse projections, indicate at 

 ductions which cause apart of the apparent difference. first an increase of resistance as the surface becomes more 



M. Romme found, by numerous experiments, that when oblique. 

 the magnitude of the greatest section of a floating body, and 

 its distance from the angular points, were constant, the 

 form of the outline of any section of the body, whether 

 composed of right lines, or of curves of any kind, was either 

 wholly, or very nearly, indifferent to the magnitude of the 

 resistance : hence he infers, that in the construction of 

 ships, the curve of the sides ought to be determined from 

 considerations independent of the resistance. 



In experiments like those of Mr. Vince, the circumstances 

 are materially different: but the accuracy of Mr. Vince's 

 experiments on water is, in some measure, confirmed, by 



