A.—­The ratios of the pitches to the diameter being for each of the relative resistances enumerated above, 1.342, 1.425, 1.513, 1.607, 1.705, 1.810, 1.933, 2.080, and 2.243, the respective fractions of pitch or fractions of a whole convolution will be 0.455, 0.428, 0.402, 0.378, 0.355, 0.334, 0.313, 0.294, and 0.275.

608. Q.—­And what are the corresponding proportions proper for screws of six blades?

A.—­Beginning with the relative resistance of 5.5 as before, the proper ratio of pitch to diameter for that and each of the successive resistances in the case of screws with six blades, will be 1.677, 1.771, 1.891, 1.2009, 2.131, 2.262, 2.416, 2.600, 2.804; and the respective fractions of pitch will be 0.794, 0.749, 0.703, 0.661, 0.621, 0.585, 0.548, 0.515, and 0.481.  These are the proportions which will give a maximum performance in every case.[1]

[1] In my Treatise on the Screw Propeller I have gone into these various questions more fully than would consort with the limits of this publication.

SCREW VESSELS WITH FULL AND AUXILIARY POWER.

609. Q.—­Do you consider that the screw propeller is best adapted for vessels of full power, or for vessels with auxiliary power?

A.—­It is, in my opinion, best adapted for vessels with auxiliary power, and it is a worse propeller than paddle wheels for vessels which have habitually to encounter strong head winds.  Screw vessels are but ill calculated—­at least as constructed heretofore—­to encounter head winds, and the legitimate sphere of the screw is in propelling vessels with auxiliary power.

610. Q.—­Does the screw act well in conjunction with sails?

A.—­I cannot say it acts better than paddles, except in so far as it is less in the way and is less affected by the listing or heeling over of the ship.  A small steam power, however, acts very advantageously in aid of sails, for not only does the operation of the sails in reducing the resistance of the hull virtually increase the screw’s diameter, but the screw, by reducing the resistance which has to be overcome by the sails and by increasing the speed of the vessel, enables the sails to act with greater efficiency, as the wind will not rebound from them with as great a velocity as it would otherwise do, and a larger proportion of the power of the wind will also be used up.  In the case of beam winds, moreover, the action of the screw, by the larger advance it gives to the vessel will enable the sails to intercept a larger column of wind in a given time.  It appears, therefore, that the sails add to the efficiency of the screw, and that the screw also adds to the efficiency of the sails.

611. Q.—­What is the comparative cost of transporting merchandise in paddle steamers of full power, in screw steamers of auxiliary power, and in sailing ships?