T R A 



T R A 



port failed from ; then from A fet off the hrft courle and 

 diftance, viz. N.N.W. 68, from A to B ; and for the 

 fecond courfe, wnth the chord of 6c, and one foot in B, 

 draw the arc T W, upon which to fet off the nest courfe 

 S.S.W. 70 : obferve the rule above dehvered ; viz. to take 

 the number of points between the point next to fail on. 

 The reafon of which rule is this ; if from A to B your 

 opurfe be N.N.W., then back from B to A muft needs be 

 S.S.E. the oppofite point ; and then if you were to fail S. 

 by E. it muft be one point to the louthward of that S.S.E. 

 line ; if S. it is two points ; and confequently the next 

 courfe being S.S.W., you are to fet off four points, upon 

 which fet off 70 miles, from B to C, and then is your (hip 

 at C : for the third courfe, if from B to C be S.S.W., ttien 

 from C to B is N.N.E. ; but the next courfe being E. |N. 

 the points between N.N.E. and E. i N. are five points 

 and a half ; and therefore, with the chord of 60, and one 

 foot in C, draw the arc X Y, upon which fet off five points 

 and a half from X to Y ; and through Y draw the line C D, 

 upon which fet off 90 miles from C D : then is your fhip 

 atD. 



After the fame manner lay down all the reft, as D E, 

 which is W.N.W. i N. 70 ; then E F, S. 25 ; then F G, 

 E. i S. 45 ; then laiUy G H, S. 30, which is the laft 

 courfe. 



Thus your fhip being at H, and the port failed from at 

 A, the line A H, 28 miles, is the diftance made good ; and 

 the angle at A is four points, viz. S.E. ; but the port in- 

 tended for being S.W. 55, fet it from A to K ; and the 

 ihip being at H, the hne H K, 62 miles, is the dillance from 

 the fhip to the port bound for ; and the courfe is found by 

 meafuring the angle at H 71° 48', or W.S.W. more than a 

 quarter wefterly, &c. 



To 'wori a Traverfe by the Tables of Difference ofLtUitude and 

 Departure This is the principal ufe thofe tables are in- 

 tended for ; and the way of working a traverfe by them is 

 equal to the beft for exaclnefs, and fuperior in point of 

 expedition. 



Make a little table with fix columns, the firft for die 

 courfe, the fecond for the diftance, the third for the northing, 

 the fourth for the fouthing, the fifth for the eafting, the 

 fixth for the wefting. Then find the difference of the lati- 

 tude and the departure to every courfe, and fet them in their 

 proper columns ; as, where the courfe is northerly, fet the 

 difference of the latitude under northing, or in the north 

 column ; and where the courfe is foutherly, fet the differ- 

 ence of latitude in the fouth column. 



Again, where the courfe is eafterly, fet the departure in 

 the ealt column, and when wefterly, fet it in the weft column : 

 then, adding up each coliunn by itfelf, fubtracl the north 

 and fouth columns, the lefs from the greater, the remainder 

 is the northing or fouthing made good. Alfo fubtraft the 

 eaft and well columns, the lefs from the greater, the re- 

 mainder is the eafting or wefting made good ; then you 

 have the difference of latitude and departure given to find 

 the courfe and diftance. 



In the firft example above fpecified, the firft courfe is 

 S.S.E. 30 miles, or two points 30 miles ; for which I find 

 the difference of latitude 27 : 7. Now the courfe being 

 between fouth and eaft, I place my difference of latitude in 

 the fouth column, and my departure, 11 : 5, in the eaft 

 column, leaving the north and weft columns blank. 



Then for the fecond courfe N.E. by N. or three points 

 40 miles, my difference of latitude, 33 : 3, is to be placed in 

 the north coliunn, and the departure, 22 : 2, in the eaft 

 column ; becaufe the courfe is between the north and 

 eaft. 



Then the third courfe being E. by N. or feven points 

 25 miles, I place my difference of latitude, 4:9, in 

 the north column ; and departure, 24 : 5, in the eaft 

 cohimn. 



And fo for the fourth courfe N.N.E. or two points 44 

 miles, I place my difference of latitude, 40 : 6, in the nortli 

 column; and my departure, 16 : 8, in the eaft column : 

 then adding up each column, the fum of the northing 

 column is 78:8, and the fum of the fouthing coliunn is 

 27:7; which fubtrafted from the northing, 78:8, the 

 remainder, 51 : i, is the difference of latitude made good, 

 which is northing, becaufe the northing was the greater 

 number. 



Again, the fum of the eafting colunm is 75 : o, which, 

 becaule there is no wefling to fubtraft from it, is the 

 eafling made good. Thus you have the northing 51:1, 

 and the eafting 75 : o given, to find courfe and diftance ; 

 and though you cannot find in the table the exaft number 

 of 51 : 1 and 75 : o together, yet find the nearefl you can, 

 which is 75 : 4, and 50 : 9, over which, at the top, you 

 find 34 degrees for the courfe, wliich is N.E. by N. 0° 15' 

 eafterly, and the diftance is 9 1 miles. 



To rejolve a Traverfe by the Scales on Gunter's Scale, in:- 

 proved by Mr. Robertfon. — E. g. A fhip in 40" N. lat. 

 and 5^ 14' W. long, fails the S.E. by S. 68 min. then S.W. 

 by W. 55 min. and then W.N.W. 75 min. What is hcv 

 difference of latitude and departure in Uiis general run I 



The proportions are, for the 



Firjl Courfe. 



Diff. lat. :: S. cov 

 57' S. :: S. 3 pts. 



S. 8 pts. : 55' :: S. 3 pts. : 3o'.6 S. :: S. 5 pts. : 46' W. 



Third Courfe. 

 S. 8 pts. : 75' :: S. 2 pts. : 28'.8N. :: S. 6 pts. : 69'.5 W. 



Traverfe Table. 



viz. departure made good in this day's run. 



To -work the above on the SUding Gunler Set fine of 



8 points on the fixed piece, by the help of the brafs index, 

 againft 68 num. on the Aide ; then draw the faid index to S. 

 5 points, you will find 57 num. on the fhde for the dif- 

 ference of latitude ; and (without any alteration) againft S. 

 3 points, on the fixed piece, you will have 38 num. on the 

 Aide for the departure. 



With the compaffes, take the extent from 8 points on 

 the fine rhumbs to 68 on the numbers ; the faid extent laid 

 the fame way from fine 5 points will reach to 57 on the 



n.um. 



