10 
HISTORY OF THE INVENTION. 
“ When a = 40°, the effective force is only 0*4368 Ihs. per foot, and the power to each 
foot must be *64 Tbs. The power therefore decreases nearly in the same ratio as the length. 
“ These calculations are sufficient to show that this method may be used with considerable 
advantage, the action being under water, and the projection from the side not so great 
as paddle wheels ; while the smoothness and the uniformity of the motion are circumstances 
much in its favour. On the other hand, the mode of communicating motion and the 
resistance the parts will offer that are applied for that purpose, are objections ; for the 
present I shall therefore content myself with recommending it to the notice of my readers.” 
We have quoted these remarks and calculations rather on account of their 
connexion with the history of the screw than from their practical utility. It 
appears probable that our author, not having attached much value to this system 
of propulsion, has not investigated its effect with his usual care. It is necessary 
to state this, since the errors of so high an authority as Mr. Tredgold are more 
injurious than those of less distinguished philosophers. His diagram and description 
evidently show he means a helix, although he speaks of a spiral. Without going 
through his formula it may be sufficient to show that some of his premises are 
erroneous. For example, he remarks that little more than one revolution of the spiral 
will produce the maximum of effect, by giving out to the water all the velocity the 
spiral could communicate. Now it must be clear that the power to communicate 
velocity does not alone depend upon the length to which the thread is extended, 
but upon the angle of the blade and its velocity, for we may conceive such a rapid 
rotation to be given that a very narrow blade will act upon as large a quantity 
of water as a broader one moving more slowly. Equally erroneous is the assump 
tion that there can be any case in which “ the power and effect are equal for 
as the water recedes at a right angle from every portion of the surface of a 
screw propeller, the power will always be exerted in a line forming a right angle 
to the thread, which we may call the hypothenuse, and the effect will be as the 
actual motion of the vessel in the line of the axis, which, under the best possible 
circumstances, can only be equal to the perpendicular ; and as the power and 
effect are to each other as the squares of their velocities, the power must be as 
the square of the hypothenuse, and the effect as the square of the perpendicular ; 
and hence the loss of power will be as the square of the base. 6 Hence, no decrease 
of pitch would make the power and effect equal; for if we decrease the pitch 
until it be equal to nothing, then the rotation of the screw would be incapable 
of communicating any motion to the vessel. 
6 It is not the least interesting feature in this investigation that we should owe the discovery of 
the screw, and the method of investigating its power as a propeller, to two of the most celebrated 
of our ancient philosophers, Archimedes and Pythagoras ; by the latter of whom, it is well known, the 
theorem given in Euclid as the forty-seventh proposition was discovered.