VOL. II.] PHILOSOPHICAL TRANSACTIONS. 275 



such that 1 = A H G N a square if A be a right angle, or a rhombus if A be an 

 oblique angle. 



The same may also be accommodated both to the constructing of logarithms, 

 and to the finding the sum of the logarithms, which Mercator does in prop. 19. 

 Thus, putting AH= l,AI = IB = b, as before, and the plane BIHF =/>/; 

 it will he pi - b' + b' = BIps + BIqt + BIru, &c. till BIHF. 



If we begin, not at BI, but on either side of it, as suppose at ps; then 

 putting pH =a, and psFH = pi, it will be universally pstq-j-psur, &c. till 

 psFH = pi — ab^, where 1 = AH^. Which may be otherwise demonstrated, 

 if necessary. 



A Note relating to the former Narrative about Empty Tubes, serving 

 for a decayed Sight ; imparted by the same Author y in a Letter of 

 August 10, 1668.* N" 39, p. 765. 



I have now tried convex spectacles, which about three years ago (before 

 my sight fell into this decay) agreed very well for my use ; and putting these 

 glasses into the tapers, I found the smallest prints somewhat larger, but not 

 so clear, so distinct, nor so pleasing to the eye, as when I use the empty 

 tapers. Also I am confirmed that these empty tapers preserve, strengthen, 

 and in some small degree recover the sight. And I find myself best at ease 

 with those leathern tubes I first used, and rather without any fastening to the 

 bone of the spectacles : For as they hang in that slight manner, I can now with 

 a touch of my finger raise them up or bow them down, divide them or unite to 

 take in the same object. And I put them off and on as speedily and as easily as 

 any other spectacles. 



Extract of a Letter written from DantzicJc to the Hon. Mr. Boyle, 

 containing the Success of some Experiments of Infusing Medicines 

 into the Human Feins. N° 39, p- 766. 



Mons. Smith, physician in ordinary to this city, having liberty granted him 

 to try an experiment upon some persons desperately infected with the venereal 

 disease, then in the public hospital here, ventured the opening of a vein, and 

 infusing some medicines into the blood. This was tried upon two persons, one 

 of whom recovered, and the other died. Yet being since farther encouraged by 

 corresponding with some of the Royal Society in England, about a month since 

 the said physician, together with Mons. SchefFeler, another old practitioner in 



* See N° 37j p. 266 of this Abridgement. 

 MM2 



