coefficient, 694 as the second, 832 for the third, and 806 for the fourth, instead of 925, 1160, 1430, and 1580 as previously specified; while for such vessels as the Red Rover, Herne, Queen, and Prince of Wales, we shall have 962 instead of 2550.  These smaller coefficients, then, express the relative merits of the different vessels without reference to any difference of efficacy in the engines, and it appears preferable, with such a variable excess of the actual over the nominal power, to employ them instead of those first referred to.  From the circumstance of the third of the new coefficients being greater than the fourth, it appears that the superior result in the fourth set of experiments arose altogether from a greater excess of the actual over the nominal power.

548. Q.—­These experiments, you have already stated, were all made on paddle vessels.  Have similar coefficients of performance been obtained in the case of screw vessels?

A.—­The coefficients of a greater number of screw vessels have been obtained and recorded, but it would occupy too much time to enumerate them here.  The coefficient of performance of the Fairy is 464.8; of the Rattler 676.8; and of the Frankfort 792.3.  This coefficient, however, refers to nautical and not to statute miles.  If reduced to statute miles for the purpose of comparison with the previous experiments, the coefficients will respectively become 703, 1033, and 1212; which indicate that the performance of screw vessels is equal to the performance of paddle vessels, but some of the superiority of the result may be imputed to the superior size of the screw vessels.

INFLUENCE OF THE SIZE OF VESSELS UPON THEIR SPEED.

549. Q.—­Will large vessels attain a greater speed than small, supposing each to be furnished with the same proportionate power?

A.—­It is well known that large vessels furnished with the same proportionate power, will attain a greater speed than small vessels, as appears from the rule usual in yacht races of allowing a certain part of the distance to be run to vessels which are of inferior size.  The velocity attained by a large vessel will be greater than the velocity attained by a small vessel of the same mould and the same proportionate power, in the proportion of the square roots of the linear dimensions of the vessels.  A vessel therefore with four times the sectional area and four times the power of a smaller symmetrical vessel, and consequently of twice the length, will have its speed increased in the proportion of the square root of 1 to the square root of 2, or 1.4 times.

550. Q.—­Will you further illustrate this doctrine by an example?