It must be owned, the art of masting ships is quite as imperfect as that of forming the bodies, for they bear no manner of proportion to any of the other dimensions of the ships and seem to be wholly regulated by the judgement and experience of the commanders. ThIs will appear very plain by examining the dimensions of the masts and yards of the following ships, and comparing them with the breadths and lengths of those ships, and yet their commanders were all allowed to be expert seamen.
|Bowsprit||36||16½||Crossjack and spritsail||32 feet long|
|Extreme breadth||23||Spritsail topsail-yard||24|
|Length on the lower deck from the aft side of the stem to the fore side of the stern-post||f. |
As to the form of masts and yards, the general method is to quarter the masts from the partners to the hounds, and the yards from the slings to the yard arms; so that both yard arms are exactly the same, except the mizen yard. The diameters at the quarters are in proportion to that at the partners or slings; whether this curve will be an arch of a circle or of an ellipse, or only a fair curve, we shall not at present examine, only give our readers the proportions; but as the beams are allowed to be arches of circles, we shall here shew a ready way of making a beam mould.
Let A B, Fig. 73, be the length of the beam, CD the round in the middle, so it is only describing a circle thro' the three points ADB; but as the circle in some cases will be so large that we cannot come at the center we may use the following method.
1st. Draw the lines AD and DB.
2d. From the center D, and with the radius DC, describe a circle; make the arch ae equal to the arch Ca, and the arch bf equal to the arch Cb, so the arches ae, and bf, will be equal, and of consequence, the angles ADC, ADe, BDC, BDf, will all be equal.
3d. Divide the lines DC, De, and Df into as many equal parts as you propose to find points in the curve; it is indifferent whether these parts be equal or unequal; only observing to begin the divisions from the point D, and that the divisions of the lines De, and Df, be the same distance from the point D that their corresponding divisions in the line DC are from the same point.
4th. Draw the line Bx to the first division of the line Df, and a line from A, thro' z (the first division of the line DC), to intersect the line Bx in g, which will be one point in the curve.
In like manner the other points are found, by drawing lines from B to the several divisions of the line Df, and lines from A thro' the corresponding divisions of the line DC, to intersect those drawn from B, which will all be in the circumference of the circle. In the figure we have only drawn the lines Bx, and Ag; but, in practice, we may take two chalk lines and fasten one at A and the other at B, and stretching the one thro' the points on the line DC, and the other thro' the corresponding points in the lines Df, and De, the intersections of the chalk lines will give the several points in the circumference.
The triangles BDx, and ADz are equal, for the sides AD, and DB are equal, the sides Dx, and Dz are likewise equal, and the angle BDx included by the sides BD and Dx, equal to the angle ADz, included by the sides AD and Dz; therefore the angle DBx is equal to the angle DAz.
The angles DAB, and DBA, are equal, and subtracting their sum from 180 we have the angle ADB; but the sum of the angles xBA, and zAB, is equal to the sum of the angles DAB, and DBA, for the angle DBx is added to the angle DBA, and the angle DAz (equal to the angle DBx) is subtracted from the angle DAB; therefore, the angle AbB is equal to the angle ADB, and of consequence the arch of the circle will pass thro' both; the line may be said of all the rest.
|1000 : breadth in feet ::||748 :||main mast in yards||100|
|741 :||70||and 60|
|1000 : main mast ::||895 :||fore-mast||100 90 80|
|901 :||all the rest|
|1000 : main mast ::||870 :||mizen-mast||100 90 80|
|866 :||all the rest|
|1000 : main mast ::||640 :||bow-sprit||100 90 80|
|613 :||all the rest|
|1000 : main mast ::||600 :||main-top-mast||100 90 80|
|605 :||70 60 50 40|
|1000 : main-top-mast ::||900 :||fore-top-mast||100 90 80|
|910 :||all the rest|
|1000 : main-top-mast ::||710 :||mizen-top-mast||100 90 80|
|717 :||all the rest|
|1000 : main-top-mast ::||480 :||main-top gallant mast||100 90 80|
|508 :||all the rest|
|1000 : fore top-gallant-mast ::||480 :||fore-mast||100 90 80|
|505 :||all the rest|
|1000 : bow sprit ::||360 :||sprit-sail top-mast||100 90 80|
|1000 : gun deck ::||560 :||main yard||100|
|1000 : main yard ::||880 :||fore yard||100 90 80|
|874 :||all the rest|
|1000 : main yard ::||820 :||mizen yard||100 90 80 60 44|
|1000 : main yard ::||726 :||main top sail yard||24|
|720 :||all the rest|
|1000 : fore yard ::||719 :||fore top sail-yard||70|
|715 :||all the rest.|
|1000 : main top sail ya. ::||690 :||maintop gall.yard||all the rates|
|1000 : fore top-sail ya. ::||696 :||fore top gal. ya.||70|
|690 :||all the rest.|
|1000 : fore top-sail ya. ::||768 :||miz. top-sail ya.||70|
|750 :||all the rest.|
Having now found the length of the masts and yards; our next business is to determine their diameters at the partners and slings.
For 50 and 40 guns, twenty-seven twenty-eights of an inch diameter, to one yard in length.
For 24 guns, twelve thirteens of an inch diameter to one yard in length.
All top masts are nine tenths of an inch diameter to one yard in length.
The fore top-mast as big as the main top-mast.
The top gallant mast, one inch to a yard.
The mizen-mast 15/22 of an inch to 1 yard in length.
The mizen top-mast five sixths of an inch to one yard in length.
The bow-sprit an inch and half to one yard.
The flying gibb-boom seven eights of a ship to a yard.
The main and fore yard five sevenths of an inch to a yard.
The top-sail, cross-jack, and sprit-sail yards nine fourteenths of an inch to one yard.
The top-gallant, mizen top-sail, and sprit-sail top-sail yards eight thirteenths of an inch to one yard.
The mizen yard five ninths of an inch to one yard.
All steering sail booms and yards half an inch to one yard in length.
For the mizen mast, and sloops masts that head themselves, first quarter 60/61; for the second quarter 11/12; for the third quarter, a strait line from the second to the hounds; hounds three quarters; for the head two thirds.
For top and top gallant masts, first quarter 40/41 parts; second quarter 14/15 parts; third quarter 5/6 parts; hounds 9/13 parts; head 5/9 parts.
For the bow-sprit, first quarter 30/31 parts; second quarter 9/10 parts; third quarter 3 quarters; at the cap one half; at the heel 3 quarters.
For yards in general; first quarter 27/28 parts; second quarter nine tenths; third quarter seven tenths; yard arm two fifths.
For the lower arm of the mizen yard, first quarter 40/42 parts; second quarter 12/13 parts; third quarter 5/6 parts; yard arm two thirds.
The upper arm of the mizen yard the same as yards in general.
As some of our readers may not be acquainted with the way of notation in these proportions, we refer them to what is said on that head in the first part, where the principles of the rule of proportion, and the construction of the line of numbers is explained, and the use of the sliding-rule illustrated by a great variety of examples in the rule of three.
Those that are but the least acquainted with the rule of three, know that there are three numbers given; and, that if the second be multiplied by the third, and that product divided by the first, the quotient will give the fourth term, which will have the same proportion to the third, that the second term has to the first.
The proportion for the main mast of a ship of 50 guns, is thus expressed; 1000 : 740 :: breadth : length, that is to say, (supposing the breadth be 41 feet,): If 1000 give 740, what will 41 give?
Now, in order to give a solution to this by the sliding-rule, draw out the slider till 1000 is right against 740, and right against 41, you'll find 30 1/3 nearly, which is the length of the main-mast in yards: It is indifferent whether 1000 be on the slider or on the rule; but if 1000 be on the slider, 41 the breadth must likewise be on the slider, so 740 and 30 1/3, will be on the rule, and the contrary; or universally, the first and second terms will be on the same line of numbers, and the third and fourth on the other line of numbers, and it is indifferent whether 740, or the breadth, be the second term, but 1000 must be the first; and the length the fourth term; the one upon the slider and the other on the rule.
The diameter at the partners you will find in the proportions 27/28 parts of an inch to every yard in length; that is to say, if the mast were 28 yards long, the diameter at the partners would be 27 inches; and therefore by the rule of three 28 : 27 :: 30 1/3 : 29¼; therefore, draw out the slider till 28 is against 27, and right against 30 1/3 is 29¼.
The diameters at the quarters are given in what the ship-wrights call fractional parts of the diameter at the partners, or slings; that of the first quarter of the main mast is 42/43, that is to say, if the diameter at the partners be 43, that at the first quarter will be 42. Now the diameter at the partners, by the preceding operation, is 30 1/3, so we have three terms of the rule of three given, thus expressed, 43 : 42 : 30 1/3, and when the slider is drawn out till 43 is against 42, we shall find 29½ against 30 1/3, so 29½ inches is the diameter at the first quarter; hence we have this general rule; when the fractional part is given, draw out the slider till the denominator is right against the numerator, then look for the diameter at the partners, or slings, on the same line with the denominator; and right against the partners, or slings, you have the diameter for that quarter, and by using the same operation as for finding the first quarters, we shall find the second quarter 28¾; the third 25¼; the hound 20¾; and the head 17¼.
Now, to find the length and diameter of the main yard; the length of the gun deck is 144 feet, the proportion for the length is 1000 : 575 :: 144, therefore, draw out the slider till 1000 is right against 575, and right against 144 is 83 nearly, which is the length of the main yard in feet.
The diameter at the slings is 5/7 of an inch to every yard in length; 83 feet is 27 2/3 yards, therefore draw out the slider till 7 is against 5, and against 27 2/3 is 19¾.
It is presumed these examples may suffice to explain the manner of notation in the preceding proportions, and likewise the method of working by the sliding-rule, which may be applied to all questions in the rule of three, such as measuring plank, and timber, wainscoting, &c.
We shall now give our readers the proportions, for the heads, and hounds of masts, and likewise for the caps, tops, trussel-trees, and cross-trees.
The head of the main and fore masts, five inches to one yard of the length of the mast.
Mizen-mast head, if it steps on the hold, 4 1/8 of an inch to one yard in length.
All top and top-gallant mast heads, four inches to a yard in length.
The length of the hounds, two fifths of their respective heads.
All caps, except the flying gibb boom, to be in breadth twice the diameter of their top-masts; and their lengths to be twice their breadth. The thickness of the main and fore caps, half the diameter of their breadths; the mizen cap three sevenths, and the top-masts two fifths of their respective breadths.
The flying gibb boom cap, to be in length five times the diameter of the boom, and in breadth twice its diameter, and, in depth, nine tenths of the breadth.
The breadth of the top thwartships, to be one third of the length of the top-mast; the mizen-top thwartships, by some, is nine thirtieths of the length of the mizen top-mast; all tops, before and aft, three fourths of what they are thwartships; the square hole five inches to a foot.
In length, to reach within three inches of the outer edge of the top.
The depth of the main and fore trussel-trees, 25/26 of an inch to one foot in length: their breadth five sevenths of their depth.
The depth of the mizen trussel-trees, six sevenths of an inch to one foot in length; and their breadth eleven sixteenths of their depth.
The main and fore top-mast trussel-trees, to be in length the fifth part of the length of their top-gallant-masts; their depths 25/26 of an inch to one foot in length, and their breadth 18/25 of their depth.
The mizen-top-mast trussel-trees, half the length of the main-top-mast trussel-trees; their depth, one inch to a foot in length, and their breadth five sixths of their depth
The length of the cross-trees, for the main and fore cross-trees, to reach within three inches of the outer edge of the top.
The mizen cross-trees, the same length with the trussel-trees.
The cross-trees the same breadth with the trussel-trees, and half their depth.
|Sheet & bow.||23||22||21||22||18½||17½||16||14½||13|
|Length||Wt of |
|Wt. of |
|Length||Wt of |
|Wt. of |
F I N I S.
Transcribed by Lars Bruzelius
Sjöhistoriska Samfundet | The Maritime History Virtual Archives | Rigging & Masting.
Copyright © 1998 Lars Bruzelius.