VOL. LXXIII.] PHILOSOPHICAL TRANSACTIONS. 367 



It comes therefore to be inquired, how far spots which, when near the middle 

 of the disk, appear equal and similar in all things, may yet differ from one 

 another considered as excavations, or as possessing the third dimension of depth, 

 and how far the peculiar circumstances by which they may disagree, can contri- 

 bute to make some resist this change of the umbra, when near the limb, much 

 more than others. In order to this, Dr. W. supposes two spots which occupy a 

 space on the sun corresponding to equal arches, but of different depths, and 

 inclinations of their sloping sides, and different distances from the sun's limb ; and 

 he shows geometrically how, according as the angle of inclination is less, the re- 

 spective spot will go nearer to the limb than the other, before the side of the 

 umbra vanishes. But those very exceptions to the general phenomena which we 

 are at present examining are of this kind, and may perhaps proceed wholly from 

 the shallowness and the very gradual shelving of some few spots which break out 

 in certain tracts of the sun's body over which the luminous matter lies very thinly 

 mantled. If therefore, on such principles it can be shown, he says, that spots, 

 similar to the rest, may sometimes go to the limb without the one umbra con- 

 tracting sensibly more than the other, the objection at present considered will be 

 entirely removed, and it will be allowable to conclude, that even these few spots 

 are excavations like all the rest, though shallower, as it would be quite unphilo- 

 sophical to multiply distinctions concerning their nature, where there is found no 

 necessity for so doing. 



Farthest umbra supposed Depth of nucleus in Apparent breadth 



to vanish when distant English miles and of nearest umbra, 



from the limb. seconds. 



1 1' 0" 4.54" 2118 8.58 



II 30 3.09 1442 6.02 



III 15 2.09 975 4.13 



IV 8 1.44 672 2.87 



Now, because in every aspect of a spot, the real breadth of either the farthest 

 or nearest umbra must be to the projected or apparent breadth, as radius to the 

 sine of the angle which this respective plane makes with the visual ray, it follows, 

 that at any time before the spot comes so near the limb as is expressed in the above 

 examples, the apparent breadth of the nearest and farthest umbra cannot differ 

 so much as by the quantity there set down for the apparent breadth of the 

 nearest, when the other is supposed to vanish. Regarding, therefore, the farthest 

 and nearest umbra of the spot in case 4, as two neighbouring visible objects 

 which turn narrower by degrees as the spot goes toward the limb, we should un- 

 doubtedly judge that they contract as to sense alike, since so long as the farthest 

 could be perceived, the other cannot appear to exceed it by a quantity that we 

 could distinguish ; and by the time the plane of the former coincides with the 



