points from the direction of the real wind, which was at N.; but the course, if judged from the vane or flag, would probably be set down as only three points from the wind. The vessel would be said to turn in eight points" if there were only eight compass points in the arc she described in being put from one tack to the other.

From the table just given we learn that a yacht's speed increases as the angle of her course with the real wind increases, until she brings that wind a little abaft the beam (the vane would show the wind a little forward of the beam), and we have a difference of speed of nearly a knot an hour set down between the courses of 3 and 4 points. This seems a very important difference, and it will be well to inquire if by "squeezing" a vessel so close to the wind the loss of speed is compensated for. In beating to windward the proportion the real distance to be reached bears to the distance traversed is for 3 points as 1 is to 1·3; for 4 points, as 1 is to 1414; for 4 points, as 1 is to 16; and for 5 points, as 1 is to 1825. Thus, if a vessel had to beat twenty miles dead to windward, the distance sailed, according to the following courses (disregarding leeway) would be:

There unquestionably could be a great gain here in economising distance, but the matter for consideration is this: would the gain in distance compensate for the loss in speed? As we know what the speed per hour is on different points of sailing, this question can be answered by a very simple calculation. Thus:

Thus, say, two cutters of 75 tons each, equal in every respect as to speed, stability, and spread and effectiveness of canvas, set out to beat 20 miles to windward, and one lay 3 points from the wind and the other 44 points, there would be no loss or gain; but if one of them lay 4 points from the wind she would gain 7 minutes, and if she lay 5 points from the wind she would lose 11 minutes. Thus for a cutter beating to windward a course of 4 points from the wind would appear to be the most advantageous.

It must not be supposed, if of two vessels of 75 tons each one is a schooner, and the latter makes a course of 4 points from the wind, and

the cutter 4 points, that there will be, providing their general speed and area of canvas be equal, only seven minutes' difference between them at the end of a twenty miles' thrash to windward. The schooner will probably be the equal of the cutter with the wind abeam; but it is a very different matter when the wind and the sails make a very small angle, as in close-hauled sailing. For such sailing a great portion of the sails near the upper, lower, and after edges are ineffective; consequently, the greater the number of parts a vessel's sails are in, the more edges there will be, and the greater will be the loss of propelling power; and, further, the eddied wind thrown off by the sails greatly interferes with the direct or impelling currents of wind. Beyond this, a schooner suffers in stability, inasmuch as she has to carry the weight of two masts and two sets of rigging, instead of one mast and one set of rigging, and for any given area the heeling moment of the sails of a schooner will be greater as the centre of effort will be higher; for this reason (though otherwise she might have been equal), she would not carry her canvas so effectively, as the effectiveness of the canvas is practically reduced in proportion to the sine of the angle of heel.

This leads us up to the point that sails are not really planes, but surfaces which are more or less concave. There is no doubt that the

B

FIG. 12.

general pressure on a surface is equal whether that surface be a plane or a concave one, providing the areas are equal; but, on surfaces like those of sails, it is not the direct pressure (such as it would be when sailing dead before the wind) that drives a vessel ahead; but, as previously explained, a component of the wind force which strikes the sail at some angle. The exact value of this component for a concave surface is, so far as we know, undeterminable; but experience has taught us that it is vastly larger for flat surfaces. The oft-quoted example of the America's sails as against the wind-bags of British yachts in 1851, and the practice in consequence of the last quarter of a century, are sufficient evidence of the truth of this.

When the wind force applied to a sail comes obliquely from ahead, as in close hauled sailing, there is a plus pressure on the fore part of the sail, and Mr. Osborne Reynolds' illustration has very completely proved

that the centre of pressure is far ahead of the centre of area, as indicated by the letters a, b, c, d, Fig. 11, page 22. Let A (Fig. 12) be a projection of a plane moved obliquely through water or the air, in the direction of the arrow, by a line attached at p. So long as the line is kept attached at p the plane will keep in an oblique position, and the centre of pressure will be at p; but if the line were attached to the centre of the figure at æ, the plane would move square to the line of pull, as shown by B, and the centre of pressure would necessarily be at æ. If when the line were attached at p, the centre of pressure remained at æ, it is apparent that upon pulling the line the plane would be overbalanced, and would assume a horizontal position.

Mr. Wm. Froude has given this subject a great deal of attention, and, in speaking of sails, says:

A striking indication of a distribution of fluid pressure on a curved surface is supplied by the prima facie paradoxical curvatures into which sails often arrange themselves under the effect of wind, as is specially noticeable in jibs. In these sails especially many sailmakers, for reasons which it would be out of place to enter on here, cut the canvas with an extravagant roundness or convexity of outline on the anterior edge of the triangle (or "luff of the sail" as it is called) before roping it; and as the rope is made somewhat shorter than the rectilinear dimension of the side of the triangle, the prominent edge of the convexity becomes gathered in, so as to form, immediately behind the rope, a narrow tapered belt of slack canvas, which becomes conspicuously bagged out by the pressure of the wind. Now it is a most noticeable fact, familiar doubtless to all who have studied the "sit" of sails, that when the vessel which carries such a sail is "close-hauled," that is to say, when the wind strikes the sail obliquely from ahead, say at an angle of 45° with the line of the keel, the general wind pressure which the reaction of the rest of the sail produces swells out the "baggy" belt of canvas, not simply to leeward, but also so much forward that an observer viewing it in a direction at right angles to the vessel's course can see the convexity protruding itself ahead of the bolt rope, although, from the direction of the wind current as a whole, that part of the sail, when thus protruded by the internal pressure, must experience externally also a considerable direct pressure on its convex or (so to call it) leeward side. As the vessel is pressed closer to the wind, it is this part of the sail which will first begin to flap or "lift;" but this will not happen until the greater part of the windward surface of the sail is brought so nearly edgways to the wind, that the flatter, or less "baggy," portions of its surface are nearly relieved of pressure.

There is no doubt that, if the fore part of sails did not go into the bag" described by Mr. Froude, they would be much more effective; and, within certain limitations, the heavier the canvas, or the more rigid and unstretchable it can be made by narrowness of cloth or other means, the more wind will the sails usefully resolve. Sailing masters generally well understand the importance of having the fore part of a sail flat and unbaggable." Hence, during a match, we frequently see them wetting the luff of a main sail, to shrink the flax and so strain this part of the sail flatter. But in old-fashioned sails (and in some ill-cut modern ones), the after part of the sail also went into a bag, and the idea was that the wind should not be allowed to escape. But the real effect of a bag in

the after part is to make a "back sail;" and, of course, a back sail retards a vessel's progress, and, in the case of after sail, helps to turn the vessel's head towards the wind, by pressing her stern to leeward. This bagginess in the after part is more or less apparent in all sails, and in the case of one set on a gaff the mischief of the tendency to turn the vessel towards the wind is somewhat remedied as the peak goes off to leeward, so that actually only little more than half the sail remains at the angle the boom is trimmed to. The conclusion is that the general pressure on a baggy sail is the same as on a flat surface of equal area if that pressure be applied at right angles to the plane; but if applied obliquely the component of the pressure (represented by F a, Fig. 10) which drives the vessel ahead is smaller, with a baggy sail, whilst the pressure that drives her to leeward, and assists in heeling her, is much larger. Before the wind this is a matter of no consequence; but by the wind it is evidently of the utmost importance that the sails should be perfectly flat, and that they should be well cut, without folds or girts of any kind, and that they should never go into bags in consequence of the canvas being soft or elastic.

It has been said that the centre of lateral resistance represents the point through which the resistance of the water to the sideway motion of a vessel acts, and the centre of effort of the sails represent the point through which the force acts which endeavours to impart sideway or broadside motion to the vessel. It is therefore evident, if these two horizontal forces do not act in the same vertical line, that some disturbance must take place in the direction of the vessel's motion. In short, the horizontal distance represented by a q or CE s in Fig. 11 is a coupling lever tending to turn the vessel towards the wind. When such conditions exist, a vessel requires what is known as "weather helm; " that is, if the vessel's head has a tendency to fly up in the wind, the rudder is turned to leeward by bringing the helm or tiller to windward. (The distance k, x in Fig. 11 shows the length of the lever upon which the rudder acts to turn the vessel, but this part of the subject will be fully treated in the next chapter.) It is obvious that if C E were directly over a no such lever would exist, as the force accumulated in C E would have no tendency to turn the vessel, either on or off the wind, and the vessel would "steer herself." If on the other hand a were at q, and C E at s, it is clear that the effort of the sails would be striving to turn the vessel's head off the wind, and she would in fact require "lee helm." Thus, two bad faults in a vessel whilst sailing by the wind are dependent on the fact that the centre of effort of the sails does not act in the vertical line in which is the centre of lateral resistance. It would appear to be a very simple matter to so arrange a vessel's sails that the

centre of effort came over the centre of lateral resistance, presuming the latter to be determined; but, owing to the concavity of the sails, and the fact that the pressure varies considerably on them (there being always a plus pressure on the fore part or luff of the sail), the centre of effort cannot be accurately computed. That is, it is always some distance ahead of the calculated centre, as already shown; but as the centre of lateral resistance is likewise ahead of the calculated centre, it is found in practice both safe and useful to treat the calculated centres as if they had been correctly determined. In "Yacht Designing," in summing up this question we find the following: "Experience teaches us that, to obtain the largest average of advantages, the calculated centre of effort of the sails should be some distance forward of the calculated centre of lateral resistance, and this distance may vary from 01 to 03 of the length of the load line. With such a ratio as 03 the vessel may carry 'lee helm' in light winds and be slack in stays, and probably a ratio of 02 will be a safe one to adopt. Thus, if a vessel be 50ft. on the load line, then 50 ×·02=1ft., which is the distance the calculated centre of effort of the lower sails is to be ahead of the calculated centre of lateral pressure on the immersed surface of the hull."

This, it should be understood, refers to racing yachts with much rockered or very raking keels; for cruisers it will be better and safer to have the centre of effort and centre of lateral resistance in the same vertical line. In the case of yawls it is generally found that the calculated centre of effort requires (relatively to the centre of lateral resistance) to be a little further aft that in either cutters or schooners, as the mizen is not a very effective sail on a wind.

As the longitudinal component (F a, Fig. 10, page 19,) of the force of the wind acts through the centre of effort of the sails considerably above the centre of lateral resistance a couple is formed (C E, q, Fig. 11) tending to depress the bow; but as the longitudinal stability of a vessel is so great, but little depression will actually take place. Thus, take the case of Seabelle at a speed of 7 knots, her resistance in the water would be about half a ton and the distance (C E, q) is 50ft., and at such speed the moment would be (50 x 0.5) equal to 25 foot tons, which would only cause Seabelle to be depressed by the head 14in. Of course, as the resistance increased, as it would very rapidly in the case of vessels with full bows driven at high speed, the moment would increase and the bow would be further depressed. In small yachts and boats, which are made to carry sail areas (by aid of trimming ballast up to windward) out of all proportion to their size, the depression of the head is often very considerable, and has to be met by shifting some of the ballast or crew farther aft.