208 PHILOSOPHICAL IBANSACTIONS.! [aNNQ 1705. 



the radiating object may have a given ratio to its image made by the speculum. 

 Let r to 9 be the given ratio ; also let o denote the object, i the image, d the 

 distance of the object from the speculum, and f that of the image. Now, as 

 Dr. Gregory has demonstrated, it will he o : i :: d :/, that is, the object and the 

 image are directly proportional to the distances from the vertex of the speculum ; 

 and because it is required that it may be o : i :: r : ^^ it must also be d ifiir nj, 



or (instead off taking its value) d: _ :: r : 9 ; hence idq — rg =z rr, and 



d = — - — -, Now because dr = — ~-^, and 2<i — r = -, it will be / or 



2j ^ J, = — 2~~^ "^ — = ~T^» which is the distance / of the image 

 from the speculum, answering to the distance of the object. Therefore if the 

 object be set at the distance "^ ^ ^ , its image made at the distance --^, be- 

 ing compared to it, will have the ratio of 9 to r : or it will he : i :: r : q ; 



for It is : I :: a '.fix — - — - : — — ^ :: r : o. 



•^ 29 2 ' 



We have here considered the radiating object and the image as if they were 

 lines : but, if they be surfaces, then it will be o ; » :: d^ :f^ :: r : q ; hence we 

 shall come to this equation 4dd — 4qdr =s 1^ — qr^, from whence the value of 

 d may be very easily found by the common methods. 



R, P. Georg. Jos. Catnelli, De Plantis Philippensibus scandentibiiSy Pars Quarto. 

 Ad D. Jacobum Petiver, S. R. S. nuper transmissa. N" 296, p. 18 id. 



A continuation of the catalogue of climbing plants growing in the Philippine 

 Isles. 



Concerning the Barks of Trees. By M. Leuxvenhoeck, F, R. S. N^ 296, p. ia43. 



Although I have been many years fully convinced myself, that the bark of 

 trees was produced from the wood, and not the wood from the bark, as many 

 have affirmed ; yet I find that some, and those persons of good learning, still 

 maintain the contrary. This induced me to make a nicer inquiry into the barks 

 of trees, in order, if possible, more fully to convince the world that the bark 

 of trees always proceeds from the wood. Mr. L. first tried a small piece of dry 

 dnnamon wood ; but found it unfit for his purpose, partly by the fibres runnings 

 lengthwise in the bark, and partly because he could not cut the piece across 

 without the bark separating from the wood. For which reason he turnetl his 

 thoughts to the bark of cherry, plum, beach, &c. which have the vessels of their 

 bark not extended lengthwise, but circularly around the wood. And hence 



