474 
Mr, WALES on 
the Re Mutton 
differences. Find the numbers correfpondins: to thefe two 
fums, and if the difference of thefe two numbers be equal to 
the. difference of the co tangents, the angle DCF was rightly 
affumed ; but as that will feidom 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 affump- 
tion to which the lead: error belongs, if that affumption w r as too 
fmall ; or fubtracled from it, if the affumption was too great : 
and, unlefs the firft affumption 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 exaftnefs. 
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 : 
r = 40 log. 11.6020600 - - 11.6020600 
a-j 2 log. t. 8573325 £ = 48 log. 1.6812412 
Conftant log. 9.7446275 Conftant log. 9.9208188 
Now, in the two triangles DC 1 , dCl, the angles DIG and 
dlC being equal, and Cl common, but dC conliderably lefs 
than DC, it is manifeft, that the angle dCl will be conliderably 
lefs than the angle DCI : let them be affumed in the proportion 
that DC bears to its excefs above dC ; in which cafe the angle 
dCl will be 27 0 35' and DCI 55 0 ioh The co- tan gent of the 
former will be 1.9x41795, of the latter .6958813; and the 
difference of them 1,2182982, The log. co-fecants of thofe 
two 
