VOL. VII.] PHILOSOPHICAL TRANSACTIONS. 7 IS 



be more augmented by reflection from the convex than from the plane, because 

 of the inclination or deflection of the convex on all sides from the points, on 

 which every ray ought to be incident. — 5. For these reasons there is requisite 

 an extraordinary exactness in the figure of the little convex, whereas I find by 

 experience, that it is much more diflicult to communicate an exact figure 

 to such small pieces of metal, than to those that are greater. — 6. Because the 

 errors at the perimeter of the concave object metal, caused by the spherical ness 

 of its figure, are much augmented by the convex, it will not with distinctness 

 bear so large an aperture, as in the other constmction. — 7» By reason that the 

 little convex conduces very much to the magnifying virtue of the instrument, 

 which the oval plane does not, it will magnify much more in proportion to the 

 sphere, on which the great concave is ground, than in the other design; and 

 so magnifying objects much more than it ought to do in proportion to its aper- 

 ture, it must represent them very obscure and dark ; and not only so, but also 

 confused by reason of its being overcharged. Nor is there any convenient 

 remedy for this. For if the little convex be made of a larger sphere, that will 

 cause a greater inconvenience by intercepting too many of the best rays ; or, if 

 the charge of the eye-glass be made so much shallower as is necessary, the 

 angle of vision will thereby become so little, that it will be very difficult and 

 troublesome to find an object, and of that object when found_, there will be but 

 a very small part seen at once. 



By this you may perceive, that the three advantages which M. Cassegrain 

 proposes to himself, are rather disadvantages. For, according to his design, 

 the aperture of the instrument will be but small, the object dark and confused, 

 and also difficult to be found. Nor do I see why the reflection is more upon 

 the same axis, and so more natural, in one case than in the other : since the 

 axis itself is reflected towards the eye by the oval plain ; and the eye may be de- 

 fended from external light as well at the side, as at the bottom of the tube. 



You see therefore, that the advantages of this design are none, but the dis- 

 advantages so great and unavoidable, that I fear it will never be put in practice 

 with good effect. And when I consider, that by reason of its resemblance with 

 other telescopes, it is something more obvious than the other construction ; I 

 am apt to believe, that those, who have attempted any thing in catoptrics, 

 have ever tried it in the first place, and that their bad success in that attempt 

 has been the cause why nothing has been done in reflections. For Mr. Gregon", 

 speaking of these instruments in the aforesaid book, page Q5, says, De mechanica 

 horum speculorum et lentium, ab aliis frustra tentata, ego in mechanicis minus 

 versatus nihil dico. So that there have been trials made of these telescopes, 

 but yet in vain. And I am informed, that about 7 or 8 years since, Mr. 



VOL. I. 4 X 



