divided it proceeds to 12 pence a pound but if you conceive the inches to be doubled and the foot measure also you shall have it to 24 d. or 48 d. the pound or one in tale of any commodity As at 18 d. a piece or pound the price comes to 7l 10s the C. for then every ten strokes is 20s in the foot measure and every inch is 2 pence and every eighth one farthing 2. Secondly for the buying of Timber at 50 foot to a Load at any price the load how much a foot Here in resolving this the inches are to be doubled and the foot measure taken as it is As at 40 shillings the Load 40 in the foot measure stands right against 4 inches 3 quarters and better which being doubled is 9d 2 far 1 2 far near for the price of one foot and on the contrary at 5d a foot is 41s 8 d. a load c. 3. For the great Hundred of 112l to the Hundred let the space of 12 inches be divided into 112 parts then the like rule holds for that also For the inches being divided into quarters every quarter is a farthing and every eighth half a farthing and every division of the 112 is a shilling and every alteration of a farthing in the price of a pound makes a groat in the Hundred as thus At 3 pence a pound is 28s the C. At 3d. 1 q. a pound 30s and 4d the C. At 3d. 1 2 the pound 32s 8 d. the C. At 3 d. 3 farthings 35s the C. Thus you see that every fraction at a farthing advance is 4 pence in the Hundred but for any other account as 3 pence farthing half farthing then count the fraction as 1 12th part of a shilling and nearer you cannot come by a bare occular inspection but the price of the Hundred being given the price of the pound you have as near by this occular inspection as any usual Coin is reducable viz. to the 32 part of a peny or nigher if you please Again note here also you may double or quadruple the price as to 24d or 48d the pound or any price between As for example At 13d a pound is 6l 1s 4d the C. At 32d or 2s 8d the pound is 14l 19s the C. and the like by dupling and quadrupling the inches and the 112 parts that layeth by it 4. These lines of equal parts serve as Scales for the protracting of any Draught of house or field or the like also for addition or substraction of any small number 5. Note that the line of foot measure may be applied for the reducing of any odde fraction to a decimal fraction as you may fee it in page 64. of Mr. Windgats Arithmetick made easie 2. The use of the lines of decimal Timber and Board measure The lines of decimal Timber and Board measure are fitted to agree with the tenths or foot measure as those lines in the first chapter of the Carpenters Rule are fitted to the inches and the use of them is thus And first for the decimal Board measure Suppose a Board is 1 foot 50 broad I look for 150 on that line and from that place to the end of the Rule forwards toward 100 so much in length must you have to make a foot of superficial or board measure 2. Or else thus If you apply the end of the Rule next 100 to one edge of the breadth of a board or glass then right against the other edge of the board on that line of decimal board measure you shall finde the 10ths and 100s or feet 10ths 100 parts of a foot that you must have in length to make a foot superficial at that breadth Example I come to a board and applying the upper end next 100 even to one edge of the board the other reacheth to 0. 8 tenths then I say that 8 tenths of a foot length at that breadth makes a foot 3. The use of decimal Timber measure The use of this is much like the Board measure onely here you must have a respect to the squareness of the piece and not to the breadth onely for after you know how much the piece of timber or stone is square in feet and 100 parts then look that number on the line of decimal Timber measure and from thence to the end of the Rule is the length that goes to make a foot of timber Example At 14 or 1. 40. parts of a foot square look the same on the rule and from thence to the end where 40 is is the length of a foot of Timber at that squareness being about 51 parts of a foot divided into a 100 parts 5. The use of the line of decimal yard measure also running yard measure according to the inches or decimal parts of a foot The decimal yard measure is nothing else but a yard or 3 foot divided into a 100 parts and used in the same manner as the foot measure is for if you take the length and the breadth in that measure and multiply it together you shall have the content in yards and 100 parts of a yard Example Suppose a peece of plastering is 4 yards 78 parts one way and 7. 35 parts another way being multiplied together makes 35 yards and 9954. of 10000 which is very neer 36 yards 5. But the decimal running yard measure is fitted to the foot measure and the use is thus Suppose a room is to be measured that is 7 foot 8 tenths high and I would know how much makes a yard at that breadth or height look foor 7f 8 10ths on the line of decimal running yard measure and the space on the rule from thence to the end next 100 is the true length that goeth to make up a yard of superficial measure at that breadth or height But if the peece be between 4 foot 5 10 broad and 2 foot then the table at the end of the line will supply the defect or you may change the terms and call the length the breadth and the contrary But if it be under 2 foot broad then if you do as you did with the board measure you shall have your desire Example At 1 foot 3 10th broad 6 foot 9 10ths make a yard 6. But if the running yard measure be made to agree with the inches then measure the height of the room in feet and inches and if you take a pair of compasses and measure from that place to the end of the rule then turn the compasses set at that distance as many times as you can about the room so many yards is there in the room 7. The use of the line of decimal round measure commonly called Girt-measure which is when the circumference of a round Cillender or piller given in inches or ten parts of a foot First for Girt-measure according to inches being the most usual measure now much the pillar is about then look for the same number on the line of Girt-measure and from thence to
the end of the rule is the length that goeth to make a foot of Timber But if it be under 30 inches about then you must have above two foot in length and then a table at the end of the line or a repetition in another line will supply the defect But if the line of Girt-measure be divided according to foot measure then use it as before seeking the decimal part on the line and from thence to the end is a foot 8. The use of a line of solid measure by having the Diameter of a round piece given in inches or foot measure Take the diameter with a rule or a pair of Callipers and learn the measure either in inches or foot measure according as your line of Diameter is divided Then look for the same number on the line of Diameter and from thence to the end of the rule forward is the length that makes a foot of timber at that diameter or measure cross the end of the round piece of Timber or stone The Tables of all the under measure for all these lines follow Decimal Superficiall under M.  10th F. 1000  10 F. 1000 p.  1 100. 00   3. 848  2 50. 000   3. 706  3 33. 300   3. 570  4 25. 000   3. 450  5 20. 000 3 3 3. 332  6 16. 600   3. 217  7 14. 300   3. 115  8 12. 500   3. 025  9 11. 120   2. 940 1 1 10. 000  5 2. 850  1 9. 100  6 2. 780  2 8. 340  7 2. 700  3 7. 720  8 2. 628  4 7. 150  9 2. 560  5 6. 670  4 2. 500  6 6. â—60   ◠440  7 5. 888   2. 382  8 5. 5â—5   2. 336  9 5. 260   2. 273 2 2 5. 000   2. 213   4. 760   2. 173   4. 5â—6   2. 127   4. 350   ◠083   4. 170   2. 042  5 4 000  5 2. 000 Decimall Superficiall M.  F. 1000. p. 01 F. 1000. p.  1. 962  1. 320  1. 923  1. 304  1. 816  1. 286  1. 850  1. 268  1. 820 8 1. 250  1. 785  1. 237  1. 756  1. 220  1. 726  1. 207  1. 697  1. 192 6 1. 669  1. 178  1. 640  1. 164  1. 615  1. 151  1. 589  1. 138  1. 563  1. 125  1. 538 9 1. 112  1. 516  1. 100  1. 493  1. 087  1. 472  1. 076  1. 450  1. 063 7 1. 430  1. 052  1. 409  1. 041  1. 391  1. 030  1. 373  1. 020  1. 353  1. 011  1. 337 10 1. 000 Decimal Solid under Measure  F. 1000. p. 10 F. 1000. p. 1 10000. 000  14. 805 2 2500. 000  13. 735 3 1100. 000  12. 780 4 630. 000  11. 916 5 400. 000 3 11. 125 6 277. 900  10. 415 7 200. 430  9. 760 8 150. 660  9. 125 9 120. 350  8. 625 1 100. 0000  8. 150  82. 800  7. 700  96. 500  7. 310  59. 390  6. 900  51. 100  6. 565  44. 500 4 6. 250  39. 150  5. 945  34. 650  5. 664  30. 850  5. 404  27. 750  5. 465 2 25. 000  4. 938  22. 700  4. 720  20. 675  4. 530  18. 920  4. 342  17. 400  4. 162  16. 000 5 4. 000 Decimall Solid under measure  F. 1000. p. 01. F. 100. p.  3. 825  1. 738  3. 7â—0  1. 694  3. 524  1. 651  3. 430  1. 608  3. 310 8 1. 568  3. 188  1. 528  3. 078  1. 493  2. 968  1. 458  2. 873  1. 420 6 2. 780  1. 390  2. 688  1. 356  2. 602  1. 323  2. 521  1. 297  2. 442  1. 266  2. 366 9 1. 236  2. 294  1. 208  2. 227  1. 185  2. 160  1. 160  2. 100  1. 131  2. 043  1. 109 7     1. 985  1. 084  1. 93â— Â 1 061  1. 878  1. 041  1. 830  1. 021  1. 781 10. 1. 000 Vnder Yard-measure for feet and inches from one inch'to four feet six inches F. F. 1000. F. F. 1000. In.  In.  1 108.000  3. 850 2 54. 000  3. 720 3 36. 000  3. 600 4 27. 000 6 3. 482 5 21. 600  3. 373 6 18. 000  3. 271 7 15. 420  3. 175 8 13. 520  3. 085 9 12. 000 3 3. 000 10 10. 300  2. 922 11 9. 820  2. 842 1. 9. 000  2. 769  8. 320  2. 710  7. 740  2. 633  7. 201 6 2. 572  6. 760  2. 512  6. 350  2. 455 6 6. 000  2. 400  5. 680  2. 345  5. 400  2. 298  5. 140 4 2. 250  4. 906 1 2. 203  4. 695 2 2. 160 2 5. 500 3 2. 119  4. 320 4 2. 073  4. 160 5 2. 037  4. 000 9 2. 000 Vnder yard measure according to Decimal or Foot measure F. 10. F. 1000. p.  F. 1000. p. 1 90. 000 4 3. 7â—0 2 45. 000 5 3. 600 3 30. 000 6 3. 461 4 22. 500 7 3. 332 5 18. 000 1 3. 211 6 15. 000 9 3. 104 7 12. 880 3 3. 000 8 11. 200 1 2. 903 9 10. 000 2 2. 812 1 9. 000 3 2. 728 1 8. 190 4 2. 648 2 7. 510 5 2. 572 3 6. 930 6 2. 502 4 6. 430 7 2. 435 5 6. 000 8 2. 370 6 5. 625 9 2. 310 7 5. 290 4 2. 250 8 5. 000 1 2. 195 9 4. 735 2 2. 142 1 4. 500 3 2. 093 1 4. 285 4 2. 046 2 4. 092 5 2. 000 3 3912   Vnder Girt-measure Inc. about F. in 100.  F. in 100 1 1809.6.81 24 3.1.87 2 452. 4. 74 25 2. 10. 74 3 201. 0. 77 26 2. 8. 12 4 113. 1. 18 27 2. 5. 87 5 72. 4. 60 28 2. 3. 70 6 50. 3. 19 29 2. 1. 83 7 39. 3. 22 30 2. 0. 13 8 28. 4. 00 31 1. 10. 60 9 22. 4. 09 32 1. 9. 21 10 18. 1. 15 33 1. 7 94 11 14. 11. 46 34 1. 6. 78 12 12. 6. 80 35 1.
1 2 then look for 17 3 4 on the first line where 15 1 2 was found and right against it on the second line is neer 42 the fractions are all decimal and you must reduce them to proper fractions accordingly To work the rule of 3 reverse 4. Set the first term sought out on the first line to the second being of the same denomination or kind to the second line or side Then seek the third term on the second side and on the first you shall have the answer required Example 5. If 300 masons build an edifice in 28 days how many men must I have to perform the same in six days the answer will be found to be 1400. 6. To work the double rule of 3 direct This is done by two workings As thus for Example If 112 l. or 1 C. weight cost 12 pence the carraiage for 20 miles what shall 6 C cost 100 miles Say first by the third rule last mentioned as 1 C. weight to 12 so is 6 C. weight to 72. pence secondly say if 6 C. cost 72 pence or rather 6s for 20 miles what shall 100 miles require the answer is 30 s. for if you set 20 against 6 then right against 100 is 30 the answer required The use of Mr. Whites rule in measuring Timber round or square the square or girt being given in inches and the length in feet and inches 1. The inches that a piece of Timber is square being given to finde how much in length makes a foot of Timber look the number of inches square on that side of the Timber line which is numbred with single figures from 1 to 12 and set it just against 100 on the other or second side then right against 12 at the lower or some times the upper end on the first line in the second you have the number of feet and inches required Example At 4 1 2 inches square you must have 7 foot 1 inch 1 3 to make a foot of Timber But if it be above 12 inches square then use the sixth Problem of the 5th chapter of the Carpenters Rule with the double figured side and Compasses 2. But if it be a round smooth stick of above 12 inches about and to it you would know how much in length makes a true foot then do thus Set the one at the beginning of the double figured side next your left hand to the feet and inches about counted in the other side numbred with single figures from 1 to 12 then right against three foot six 1 2 inches in the single figures side next the right hand you have in the first side the number of feet and inches required Example A piece of 12 inches about requires 11 f 7 in fere to make a foot Again a piece of 15 inches about must have 8 foot 1 2 an inch in length to make a foot of timber 3. But if you would have it to be equal to the square made by the 4th part of a line girt about the piece then instead of three foot 6 1 2 inches make use of four foot and you shall have your desire 4. The side of a square being given in inches and the length in feet to find the content of a piece of timber If it be under 12 inches square then work thus set 12 at the beginning or end of the right hand side to the length counted on the other side then right against the inches square on the right side is the content on the left side Example At 30 foot long 9 inches square you shall find 16 foot 11 inches for the working this question 12 at the end must be used But if it be above 12 inches square then ser one at the beginning or 10 at the end of the right hand side to the length counted on the other side then the number of inches or rather feet and inches counted on the first side shall shew on the second the feet and parts required Example At 1 f. 6 inch square and 30 foot long you shall finde 67 feet and about a 1 2. 5. To measure a round piece by having the length and the number of inches about being a smooth piece and to measure true and just measure then proceed thus Set 3 f. 6 1 2 inches on the right side to the length on the other side then the feet and inches about on the first side shall shew on the second or left the content required As at 20 inches about and 20 foot long the content will be found to be about 4 foot 5 inches But if you give the usual allowance that is made by dupling the string 4 times that girts the piece then you must set 4 foot on the right side to the length on the other then at 1 foot 8 inches about the last example you shall finde but three foot 6 inches 6. â— astly if the rule be made fit for foot measure onely then the point of 12 is altogether neglected and one onely made use of as a standing number and the point at three foot 6 1 2 will be at three foot 54 parts and the four will be the same and the same directions in every respect serve the turn And because I call it Mr. Whites rule being the contriver thereof according to feet and inches I have therefore fitted these directions accordingly and there are sufficient to the ingenious practitioner CHAP. XIX Certain Propositions to finde the hour and the Azimuth by the lines on the Sector PROP. 1. HAving the latitude and complements of the declination and Suns altitude and the hour from noon to finde the Suns Azimuth 〈◊〉 that time Take the right sine of the complement of the Suns altitude and mak 〈◊〉 it a parallel sine in the sine of th 〈◊〉 hour from noon counting 15 degree 〈◊〉 for an hour and 1 degree for for minutes counted from the center The Sector so set take the right sine of the complement of the declination and carry it parallel till the compasses stay in like sines and the sine wherein they stay shall be the sine of the Azimuth required Or else thus Take the right sine of the declination make it a parallel in the cosine of the Suns altitude then take the parallel sine of the hour from noon and it shall be the latteral or right sine of the Azimuth from the south required If it be between six in the morning and 6 at night or from the north if it be before or after six and so likewise is the Azimuth PROP. 2. Having the Azimuth from south or north the complement of the Suns altitude and declination to finde the hour Take the latteral or right sine of the complement of the Suns altitude make it a gaâ—â—llel in the cosine of the declination the sector so sett ake out the parallel sine of the Azimuth and measure it from the center and it shall reach to the right sine of the hour from noon required Or
not the time in common hours but is thus found Adde the complement of the Suns Ascension and the stars right Ascension and the stars hour last found together and the Sun if less than 12 or the remain 12 being substracted shall be the time of his rising in common hours but for his setting adde the stars setting last found to the other numbers and the sum or difference shall be the setting Example For the Bulls-eye on the 23 of December it riseth at 2 in the afternoon and sets at 4. 46 in the morning 4. To finde the time of the southing of any star on the Rule or any other whose right ascension and declination is known Substract the Suns right ascension from the stars increased by 24 when you cannot do without and the remainder if less than 12 is the time required in the afternoon or night before 12 but if there remain more than 12 substract 12 and the residue is the time from mid-night to mid-day following Example Lyons-heart on the tenth of March the Suns Ascension is 0 2 ' Lyons-heart whole right asc is 9 50 ' Time of southing is 9 48 ' at night 5. To finde how long any Star will be above the Horizon Lay the thread to the star and in the hour-line it sheweth the ascensional difference counting from 90 then note if the star have North declination adde that to 6 hours and the sum is half the time if south substract it from 6 and the residue is half the time and the complement of each to 24 being doubled is the whole Nocturnal Arch under the Horizon Example For the Bulls-eye his Ascensional difference will be found to be one hour 23 minutes which added to 6 hours and doubled makes 14. 46 the Diurnal Ark of the Star and the residue from 24 is 9. 14. for the Nocturnal Ark or the time of its being under the Horizon CHAP. IX To perform the fore-going work in any latitude as rising amplitude ascensional difference latitude hour and azimuth wherein I shall give onely the rule and leave out the examples for brevity sake 1. FOr the rising and setting and ascensional difference being all one do thus Take the Suns declination out of the general Scale of Altitudes then set one foot of the Compasses in the colatitude on the same scale and with the other lay the thred to the nighest distance then the thred so laid take the nighest distance from the latitude to the thread with that distance set one foot in the Suns declination counted from 90 toward the center and the thread laid to the nearest distance shall in the degrees shew the ascensional difference required counting from 90 at the head toward the end of the Rule and if you reduce those degrees and minutes to time you have the rising and setting before and after 6 according to the declination and time of the year 2. To finde the Suns amplitude Take the Suns declination and setting one foot in the colatitude with the other lay the thread to the nearest distance and on the degrees it sheweth the Suns amplitude at rising or setting counting as beâ—ore from 90 to the left end of the Rule 3. Having amplitude and declination to finde the latitude Take the declination from the general scale and set one foot in the amplitude the thread laid to the nearest distance in the line of degrees it sheweth the complement of the latitude required or the converse 4. Having latitude Suns declination and altitude to find the height at 6 and then at any other time of the day and year Count the declination in the degrees from 90 toward the end thereto lay the thread the least distance from which to the latitude in the general Scale shall be the Suns height at 6 in the summer or his depression in the winter The Compasses standing at this distance take measure on the general Scale of altitudes from the beginning at the pin towards 90 keeping one point there open the other to the Suns altitude thus have you substracted the height at 6 out of the Suns altitude but in winter you must adde the depression at 6 which is all one at the same declination with his height at 6 in summer and that is done thus Put one point of the Compasses so set in the general Scale to the Suns Altitude then turn the other outwards toward 90 there keep it then open the Compasses to the beginning of the Scale then have you added it to the Suns altitude having this distance set one foot in the colatitude on the general Scale lay the thread to the nearest distance the thread so laid take the nearest distance from 90 to the thred then set one foot in the declination counted from 90 and on the degrees it sheweth the hour from 6 reckoning from the head or from 12 counting from the end of the Rule I shall make all more plain by making three Propositions of it thus Prop. 1. To finde the hour in the Aequinoctial Take the Altitude from the beginning of the general Scale of altitudes and set one foot in the colatitude the thread laid to the nearest distance with the other foot in the degrees shall shew the hour from 6 counting from 90 and allowing for every 15d 1 hour and 4 min for every degree Prop. 2. To finde it at just 6. Is before exprest by the converse of the first part of the fourth which I shall again repeat Prop. 3. To finde it at any time do thus Count the Suns declination in the degrees thereunto lay the thred the least distance to which from latitude in the general Scale shall be the Suns altitude at 6 which distance in summer you must substract from but in winter you must add to the Suns present altitude having that distance set one foot in the coaltitude with the other lay the thread to the neerest distance take again the neerest distance from 90 to the thread then set one foot in the Suns diclination counted from 90 and lay the thread to the neerest distance and in the degrees it shall shew the hour required Example At 10 declination north and 30 high latitude 51. 32 the hour is found to be 8. 25 counting 90 for 6 and so forward Again at 20 degrees of declination South and 10 degrees of altitude I finde the hour in the same latitude to be 17 minutes past 9. Having latitude delination and altitude to finde the Suns Azimuth Take the sine of the declination put one foot in the latitude the thread laid to the neerest distance in the degrees it sheweth the Suns height at due East or West which you must in summer substract from the Suns altitude as before on the general Scale of Altitudes with which distance put one foot in the colatitude and lay the thread to the neerest distance then take the neerest distance from the sine of the latitude fit that again in the colatitude and the thread laid to the heerest