VOL. XLVIII.] PHILOSOPHICAL TRANSACTIONS. 463 



spherical glasses is explained and demonstrated by all the writers on optics, it 

 being the very foundation of the science, the bare mention of it is sufficient for 

 the present purpose. 



Obs. 3. — It will be necessary however to observe further, that the lines con- 

 necting every point in the object with its corresponding points in the image, do 

 all intersect in a certain point of the axis or line passing through the poles of the 

 glass, where its two surfaces are parallel, and may be properly called its centre. 

 Whence it appears, that the angles subtended by the object and its image, from 

 that point, must be equal : and therefore their diameters will be in the same 

 ratio as their distances from that point. 



Ohs. 4. — As the formation of the image by the glass depends entirely on the 

 property above mentioned, viz. its collecting all the light, incident on it from 

 the several points of the object, into as many other points at its focus ; it follows, 

 that any segment of such a glass will also form an image equal, and every way 

 similar, to that exhibited by the whole glass ; with this difference only, that it 

 will be so much darker, as the area of the segment is less than that of the 

 whole glass. 



Obs. 5. — ^The axis of a spherical glass, is a line connecting the centres of the 

 spheres, to which the two surfaces are ground ; and wherever this line passes 

 through the glass, there the surfaces are parallel. But if it happens that this 

 line does not go through the substance of the glass, such a glass is said to have 

 no internal centre ; but it is conceived to be in its plane produced till it meets the 

 axis : and this imaginary point, though external to the glass, is as truly its centre, 

 and is as fixed in its position to it, as if it were actually within its substance. 



Obs. 6. — If a spherical glass, having its centre or pole near its middle or centre 

 of its circumference, should be divided by a straight line through the middle ; 

 the centre will be in one of the segments only. For how exact soever a person 

 may be supposed to be in cutting it through the centre , yet it is hard to con- 

 ceive how a mathematical point should be divided in two : therefore the centre 

 will be internal to one of the segments, and external to the other. But if a small 

 matter be ground away from the straight edge of each segment, both tlieir 

 centres will become external ; and so they will more easily be brought to a cc 

 incidence. 



Obs. 7. — If these two segments should be held together, so as to make their 

 centres coincide ; the images, which they give of any object, will likewise coin- 

 cide, and become a single one. This will be the case when their straight edges 

 are joined to make the glass, as it were, whole again: but let the centres be 

 any-how separated, their images will also separate, and each segment will give a 

 separate and distinct image of any object to which they may be exposecl. 



