190 REPORT—1840. 
miles an hour, with a saving of coals amounting to 40 tons out of 320; 
and when it is remembered that the voyage for which 18 days would be 
required as continual allowance in the one case might always be calcu- 
lated on as performed in 10 days in the other, the advantage is placed 
beyond all doubt. It appears, therefore, that for long voyages espe- 
cially, there are great advantages in point of ceconomy, certainty and 
speed, to be obtained by the use of vessels of a higher power than 
usual, and that in a given case the best proportion of power to tonnage 
may readily be determined from the rules already laid down. In 
regard to absolute or definite proportion, it may be stated as the result 
of the best vessels, that the proportion of power to tonnage should not 
be greater than one horse power to two tons, nor less than one horse 
to three tons; the greater proportion holding in the smaller, and the 
less proportion of power in the greater vessel.” 
Notice of Properties of the Catenary and Curves of Equilibration, 
with Tables for their Construction, contained in a Memoir entitled, 
“ The Parallelogram Forces and Curves of Equilibration; together 
with Tables for their Construction, deduced from a Funetional 
Equation. By Witt1am Waturact, LL.D., &c., Emeritus Pro- 
fessor of Mathematics in the University of Edinburgh.” 
The memoir in the Edinburgh Transactions here noticed, contains 
tables for the construction of the catenary, which are true to ten 
decimal places (the parameter being the unit); by these the co-ordi- 
nates of the curve, also its length, may be found to an extent of the 
curve and degree of accuracy beyond the wants of the civil engineer 
in actual practice. Tosecure accuracy, the tables have been stereotyped 
in an octavo size, and proofs of the plates carefully compared with the 
original calculations, which have been all preserved, and may be de- 
posited with some public body. 
It is intended in the course of the ensuing winter to re-publish the 
tables in an octavo form, accompanied with a Treatise on the Catenary 
and Curves of Equilibration ; and to these will be added some other 
matters connected with the practice of civil engineering. 
On a New Mode of Propelling Fluids, or an uniformly Propelling 
Wheel. By the Rev. J. Brovte. 
In this communication the author gave an account of a uniformly 
propelling wheel for steam-boats, and directed attention to the proper 
form of the leaves of a propeller on the Archimedean principle. The 
contrivance for uniform propulsion consists of a number of vanes or 
float-boards, placed on a revolving axle, so that the plane of the float- 
boards forms an acute angle with the axle to which they are applied. 
They may be either fastened to the axis spirally, forming a sort of 
screw, or affixed circularly, forming a wheel. 
This principle admits of various applications, and may be employed 
in propelling either with water or air. 
