38 Improvement in Field Surveying. 



The same principles were likewise applied by Mr. Johnson to 

 other branches of mensuration, and the whole, as I am inrformed, in- 

 corporated in a work, which is soon to be presented to the public. 

 ■ The following are the general directions as given by Mr. J. for 

 calculating areas by the algebraic process. 



1st. Place in one column the courses and distances of the outlines 

 of the field whose area is to be calculated, in the order in which they 

 occur in traversing around it. 



2d. Put the differences of latitude and the departures of each line 

 opposite the course and distance of the same line, — the differences 

 of latitude in one column and the departures in another. 



3d. Distinguish the northings and the southings of the several dif- 

 ferences of latitude by the signs plus and minus,^ and do the same 

 with the eastings and westings of the departures ; or otherwise, call 

 the first difference of latitude, and all of the same name with it, af- 

 firmative, arid all of a contrary name, negative, and do the same with 

 the departures. 



4th. Take the first departure and place it opposite, as the first 

 quantity in a column of multipliers. For the second multiplier, add 

 together the first multiplier, the first departure, and the second de- 

 parture ; and universally, to find any multiplier add together these 

 three quantities, viz. the last preceding multiplier, the departure be- 

 longing to it, and the next succeeding departure ; the number of mul- 

 tipliers to be the same with the outlines of the field, a multiplier to 

 each outline. 



5th. Involve each multiplier into the difference of latitude slanding 

 against it, and the half sum of the several products thus obtained, will 

 be the area of the field in square measures of the same denomination 

 in which its sides are measured. 



The operations of adding and multiplying, are in every case to be 

 performed algebraically. If the additions for the multipliers are 

 made correctly, the last multiplier will be equal to the last departure 

 with its sign changed. 



