Objections of M. de la lands. 
fpot GD, the depth of the nucleus HE, may be found by the 
following analogies. 
By limilar triangles MD : DO :: ML : LS. But LS being 
the breadth of the nucleus is, by hypothecs, equal to LD, the 
breadth of the umbra ; therefore MD : DG :: ML : LD, or as 
ME : EH on account of the parallels SL and GD. By eompo- 
fition, MD -f DG : DG :: MH : HE. Hence HE, the only 
unknown qu unity of thefe proportionals, is found, and is the 
depth of the nucleus fought. If DP, the apparent breadth 
of DL, the fide of the umbra next the limb be 'equired, cor- 
relponding to the prefent alpedt of the fpot, this may be de- 
rived from the data by the refolution of the triangle DLP, 
whole hypotheuufe DL and angle DLP, are known. Again, if 
the neared: apparent didance of the nucleus from the limb, 
when it wholly difappears, be fought, it will come out equal 
to the verfed line of the arch GA, when diminifhed by half 
the arch HA, which lad is by condruTion equal to half of 
either of the acute angles of the triangle DGM. In order to 
fee the reafon of this, it mud confidered, that the fegments 
ML, LD, of the bafe MD, are in the fame ratio with the 
Tides DG, GM ; on which account a ftraight line drawn from 
G to L, the lad: part of the nucleus which can be feen, muff 
bifedl the angle DGM. Therefore, before the vilual ray or 
line ZGL can fall perpendicularly upon the radius CA, this 
mud: be drawn didant from the point A towards D, by an arch 
correfponding to half the angle DGM, that is, by an arch 
equal to half of HA. 
Perhaps it may be urged, that very (hallow fpots ought al- 
ways to be known from the red, and to difeover themfelves, 
by a furrounding umbra very narrow compared to the extent 
of the nucleus ; but we know far too little of the qualities of 
the luminous matter, and of the proximate cauies of the fpots, 
Vol. LXXIII. X e* 
