Wrights Mathematical Papers. 75 
verse table find the northings and southings, and the eastings and 
westings; placing the northings and southings in the first column, 
and the eastings and westings in the second column. When 
the northings are considered as affirmative quantities, the south- 
ings will be negative; and when eastings are affirmative, westings 
will be negative ; but when the southings are considered as affirm- 
ative quantities, the northings are negative, and when westings are 
affirmative, eastings will be negative. | 
In the second column put 0.00 for the factor corresponding to 
the first side. Suppose westings to be negative. When the depar- 
tures of the first and second sides are both eastings, or both westings, 
take their sum, placing the negative sign before it, when the depar- 
iures are westings ; but when one is an easting, and the other a west- 
ing, take their difference, placing the negative sign before it, when 
the greater number isa westing. ‘The number obtained by this ope- 
ration will be the factor to be multiplied into the northing or south- 
ing belonging to the second side. Following the same directions, 
take, again, the sum or difference, as the case may be, of this factor 
and the departure of the second side. 
‘When the number last found and the departure of the third side 
are both eastings or both westings, take their sum, placing the neg- 
ative sign before it, when they are westings; but if one is an easting 
and the other a westing, take their difference, placing the negative 
sign before it when the greater number is a westing. ‘The number 
thus obtained will be a factor to be multiplied into the northing or 
southing belonging to the third side. Observing the foregoing di- 
rections, take again, the sum or difference, as the case may be, of 
this last factor and the departure of the third side. In like manner 
proceed with all the remaining sides. Here it is obvious that accord- 
ing to the rule of adding affirmative and negative quantities in algebra, 
each departure is twice added, once before and once after multipli- 
cation. ‘This circumstance may assist in remembering the rule. 
At the bottom of the first column put the letters NE, SW, and 
at the bottom of the second column NW, SE. These letters de- 
note that the products, whose factors are northings and eastings, or 
southings and westings, are to be placed in the first column; while 
those whose factors are northings and westings, or southings and 
eastings are to be placed in the second column. Add the products 
in the first column together; and also those in the second ; take the 
difference of these sums, half of which will be the required area 
of the field. 
