1819.] Col. Beaitjui; cit the Const ruction of 'Sails. 187 



Column 1 contains the number of cloths which compose the 

 sail; 2. The radii of the concentric circles : 3. The circumfer- 

 ences of the circles ; -1. The length of the chords of the circular 

 segment; 5. The angles subtended by the chords ; 6. The length 

 of the arcs ; and 7. The differences between the length of each 

 chord, and its respective arc, which is the quantity of canvass 

 to be gathered in at the seams. Column 2 is formed by conti- 

 nually subtracting the width of the canvass TO 15 from the 

 radius of the after-let ch, i)i-465 ; and column 3, by deducting 

 the constant quantity, 6-38, the diminution of the periSheiiesi 

 Such were the construction of the sails of my land-sailing 

 machine,* which, in an open and extensive meadow, with a 

 moderate breeze, and five points from the wind, required a 

 gallop to keep pace with it. 



The versed sine of the mainsail is 10° 2T, but in sails made 

 with canvass, No. 1 or No. 2, it is probable that the versed sine 

 might be increased to 12 degrees without danger of the after- 

 leech flapping ; for the larger the versed sine, the better the sail 

 will set, provided it be not so great as to produce the above- 

 mentioned disadvantage. 



The length of the chord and versed sine in degrees being 

 given, the length of the versed sine and radius may be calculated 

 from a table of natural sines, cosines, and versed sines, as fol- 

 lows : Suppose the chord of the after-leech to be 70 feet, and 

 the versed sine 12 degrees, the natural versed sine of 12 degrees 

 is -021862, the natural cosine -97815, the natural sine -20791, 



radius being unity : -20791 : 35 (™) :: -021852 : 3-6786 = 3 feet 



8-14 in. the versed sine ; 20791 : 35 :: 1-97815 : 333-01, then 



— ! — -— — is 168-34 feet the radius. To describe in the usual 



manner a circular segment whose semidiameter amounts to 168 

 feet, in confined places is impossible : some other means must, 

 therefore, be adopted, and it may be performed two ways : 

 first, mechanically ; and secondly, by finding a number of points 

 and uniting them together by means of a flexible piece of wood, 

 for which an eligible rule is given in Mr. Mungo Murray's book 

 on naval architecture. The former method is frequently used by 

 carpenters, joiners, and other artizans, and is as follows : An 

 isosceles triangle is made of wood, whose base contains the num- 

 ber of feet and inches as the chord of the arc to be described, 

 and whose altitude is equal to the versed sine of the arc ; three 

 pins are then put on the board, or paper, on which the segment 

 is to be traced, one pin at each end of the chord, the third on 

 the extremity of the radius; a pencil is next applied to the vertex 

 of the triangle, and the whole made to slide on the three pins, 

 and the segment is traced. It is evident that it would be an 



* The quantity of canvass in the three sails measured .'312 superficial feet. 



