. ** * 
■152 Dr. Wilson’s Anfwer to the 
and finally go oft the dilk, without that peculiar change of 
the umbra on one fide, which is fo obvious 011 common occa- 
lions, notw.ijthftanding it were an excavation, whole nucleus or 
bottom is : lo many miles below the level of the furrace. 
In the four-cafes above Hated, the diifance of the remotef! part 
of the nucleus from the fun’s limb when the vifual ray coming 
y « 
from it is julf interrupted by the lip of the excavation, or, in other 
words, the diftance of the nucleus from the limb when it is 
totally hid was ajfo computed. Thefe di dances are as follow : 
Cafe 1. - 16.93 Cafe 3. * 4-70 
2. - 8. 90 4. - 2.70 
and it is remarkable from the two laid, how very near the limb 
a lhallow fpot of not more than 40" in diameter may come 
before the nucleus wholly difappears. 
Computations of this kind are very eafily made, by fup- 
pofing 011 (fig. 2.) GDLS a lection of a fpot fo near to the limb 
A, that the vifual ray VB coincides with GS the plane of the 
excavation. JLet the ftraight line DF coincide with the other 
fide, and draw the radii CA, CQ^, fo as to be at right angles to 
GB, DF, and draw the radius CH through the point M. 
Now, becaufe the verled line AB, the apparent diifance 
from the limb, when the iide of the umbra GS vanilhes is 
given, the arch GA of the fun’s circumference is given, and 
from the known breadth of the fpot, the arch GD and its half 
GH are each of them given, and confequently the arches HA, 
DA, and QA, are all given. From thefe data the angles and 
Tides of the triangle GMD, fuppofed rectilineal, may be de- 
duced, alio HM the diifance of the point of interfedtion M 
from the furtace. When thefe particulars have been deter- 
mined for any aflumed diifance BA, and alfumed extent of the 
fpot 
