VOL. VII.] PHILOSOPHICAL TRANSACTIONS. 6Q9 



conoid, which is, that all the sections parallel to the axis make the same para- 

 bola. 



Thus far M. Huygens's judicious letter, to the latter part of which, concerning 

 the grinding parabolical conoids, Mr. Newton says, in a letter of Feb. 20, 71, 

 that though he, with him, despairs of performing that work by geometrical rules, 

 yet he doubts not but that the thing may in some measure be accomplished by 

 mechanical devices. To all which I cannot but subjoin — 



An Extract of a Letter y received voy lately (March 19J, from the 



Inventor of this new Telescope y from Cambridge , viz. N" 81, 



p. 4009. 



In my last letter I gave you occasion to suspect, that the instrument which I 

 sent you is in some respect or other indisposed, or that the metals are tarnish- 

 ed. And, by your letter of March l6, I am fully confirmed in that opinion. 

 For while I had it, it represented the moon in some parts of it as distinctly as 

 other telescopes usually do which magnify as much as that. Yet I very well 

 know, that that instrument has its imperfections, both in the composition of 

 the metal, and in its being badly cast, as you may perceive by a scabrous place 

 near the middle of the metal of it on the polished side, and also in the figure of 

 that metal near that scabrous place. And in all those respects that instrument 

 is capable of further improvement. 



You seem to intimate, that the proportion of 38 to 1 holds only for its 

 magnifying objects at small distances. But if for such distances, suppose 500 

 feet, it magnify at that rate, by the rules of optics it must, for the greatest 

 distance imaginable, magnify more than 37|- to 1 ; which is so inconsiderable a 

 diminishing, that it may be even then as 38 to 1. 



Here is made another instrument like the former, which does very well. 

 Yesterday I compared it with a 6-foot telescope, and found it not only to mag- 

 nify more, but also more distinctly. And to day I found, that I could read in 

 one of the Philosophicj^l Transactions, placed in the sun's light, at 100 feet 

 distance, and that at 120 feet I could discern some of the words. When I 

 made this trial, its aperture (defined next the eye) was equivalent to more than 

 an inch and a third part of the object metal. This may be of some use to those 

 that shall endeavour any thing in reflections; for hereby they will in some 

 measure be enabled to judge of the goodness of their instruments, &c. 



Epitome Bines Methodi Tangentium Doctoris Johannis IFallisii Geom. 

 Prof. Saviliani OxonicSy &c. N" 81, p. 4010. 



These two methods of Dr. Wallis, for drawing tangents to cuives, may well 



