THE UNITED STATES OF AMERICA. 107 



This vessel was called the ' President ;' the particulars of her structure, &c. were as follow : 

 Breadth of beam .... 32^feet. 



Draught of water .... 9 feet. 



Diameter of water wheels . . . 22 feet. 



Length of bucket . . . .10 feet. 



Depth of ditto . . . . 3| feet. 



Engines, in number, ... 2 



Diameter of cylinders ... 4 feet. 



Length of stroke .... 7 feet. 



Number of revolutions . . . 21 per minute. 



The average velocity was 17'6 feet per second, or about 12 English miles per hour, and 

 the relative velocity of the circumference of the wheel was 6 1 feet per second. 



On one occasion it became necessary for the ( President' to make a passage with only one 

 of her wheels and engines in action. In this passage the velocity of the boat was diminished 

 to 13*8 feet per second, but the relative velocity of the wheel fell but little short of that 

 acquired when both wheels were used, being 6'3 feet per second. The constancy which thus 

 appeared to exist in the relative velocity of the circumference of the wheel, in two boats of 

 very different form and structure, and in the same boat, when propelled by forces, differing as 

 much as in the ratio of 2 : 1, is a remarkable fact, and appears wholly irreconcilable with the 

 ordinary mathematical expression of the relation between the two velocities of the wheel and 

 the vessel. It had been deduced by a course of reasoning, which has been received without 

 question, that the velocity of the vessel bears a constant proportion to that of the wheel, while 

 in the instances we have cited they differ by a constant quantity. 



Without attempting to question the skill in analysis of the distinguished mathematicians, 

 both French and English, who have investigated this problem, we may venture to state that 

 this appears to be a case in which the formula of Parent is applicable, and that the velocity of 

 the circumference of the paddle wheel through the water ought to be constant, and equal to 

 one-third of the greatest velocity at which a flat surface can be propelled through that fluid, 

 in a direction perpendicular to its plane. Assuming this to be twelve nautical, or 13'8 English 

 miles per hour, we have for the proper constant relative velocity of the circumference of a 

 paddle wheel 6J feet per second. On examination of the performance of a great number of 

 American steam boats, some of which we shall hereafter cite, it has been found that the 

 relative velocity of their paddle wheels has always been nearly this quantity. This fact is 

 thrown out for the present, for the purpose of drawing the attention of the scientific world to 

 it ; and should it be found to be universal, it will probably furnish a basis for the mathematical 

 theory of steam boats, whose results will be more applicable to the cases which occur in 

 practice, than those which are now set forth, but which are of little or no use to the engineer 

 or ship builder. 



As the speed which has been stated for one of the vessels, which, from their having been 

 long attentively observed by the writer, have been chosen as instances, is far beyond that 

 which has been attained in Europe, it may be well that we should cite the facts whence this 

 statement .has been derived. The distance from New York to Albany has been measured 

 by the late Surveyor-General of the State of New York, in straight lines joining the extreme 

 points of the several reaches of the river, and amounts to 145 miles. The average passages of 



