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 informed, 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. 
Ist. Place in one column the courses and distances of she 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 lime 
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, and all of a contrary name, negative, and do the same ‘shes 
the departures. 
-. 4th. Take the first departure and place it opposite, as oe. 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 elope to 
each outline. 
5th. Involve each multiplier into the difference of latitude aaa 
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 nn will be equal to the last departure 
with its sign changed. ° : 
