474 Mr. wales cn the Refolution 
differences. Find the numbers correfponding to thefe two 
films, and if the difference of thefe two numbers be equal to 
the difference of the co-tangents, the angle DCF was rightly 
aflumed ; but as that will feldom happen, take the difference, 
or error; affume the angle DCF again, repeat the operation, 
and find the error as before. Then, as the fum of the errors, 
if one of them was too great, and the other too little, or their 
difference, if both were too great, or both too little, is to the 
difference of thefe affumptions, fo is the lefs error to a number 
of minutes and feconds, which muff be added to that afiiimp- 
tion to which the leaf!: error belongs, if that aflumption w r as too 
fmall ; or fubtra£led from it, if the aflumption w T as too great : 
and, unlefs the firfl: aflumption was made very wide of the 
truth, which may always be avoided, the two angles will gene- 
rally be obtained within a few feconds of the truth, and, by 
repeating the operation once more, to the utmoft exa&nefs. 
SuppofeDC ( a ) be taken equal to 72, dC (^ = 48, and the 
radius Cl (r) = 40, the angle T)Cd being 82° 45': then the 
whole operation will ftand as follows : 
/• = 4©log. 11.6020600 - - 11.6020600 
/z = 72 log. l '^S 733 2 S ^ = 48 log. 1.6812412 
Conftant log. 9.7446275 Conftant log. 9.9208188 
Now, in the two triangles DCI, dCI , the angles DIC and 
dIC being equal, and Cl common, but dC confiderably lefs 
than DC, it is manifeft, that the angle dCI will be confiderably 
lefs than the angle DCI : let them be aflumed in the proportion 
that DC bears to its excefs above dC ; in which cafe the angle 
dCI will be 27 0 35' and DCI 55 0 io'. The co-tangent of the 
former will be 1.9141795, of the latter .6958813; and the 
difference of them 1,2182982, The log. co-fecants of thofe 
two 
