452 PHILOSOl'HICAL TKANSACTICNS. [aNNO 16qQ. 



wrapped up, as high as the shoulder, in leather steeped in oil, by which the 

 air, when exhausted out of the glass, (should there happen to be any fissures 

 in the little valve) may be excluded. When the thumb is applied close to the 

 bore, the plate g Q, fig. 14, is raised by the handle to 10 10 ; now because at 

 first the air filled only the space Q O Q, it is now so rarefied and expanded, as to 

 occupy the space y 10 10, which is 300^ times greater than the former ; there- 

 fore the elasticity of the air included in the glass, exceeding both the elasticity 

 of the spring, and of the air contained in the cylinder, the valve or plate will 

 be pushed upwiirds, which will continue open till such a quantity of air get out 

 of the glass into the cylinder, as that the elasticity of the complement of air 

 contained in the glass shall be equal to the elasticities both of the spring and of 

 the air now contained in the cylinder ; and on opening the hole o the valve is 

 firmly shut by the pressure of the external air, casteris paribus, on 3 or 4 suc- 

 tions, more or less, -j^gW parts of air (according to the power of the spring, 

 and the ratio between the capacity of the cylinder and that of the cupping 

 glass) will be exhausted ; and if the elasticity of the air in the same space be as 

 its quantity, the resistance or pressure under the glass will be to the pressure 

 on the circumjacent parts, as 1 to 1000 ; because, before the air was exhausted 

 out of the glass, the resistance or pressure under the glass was the same with 

 that on the parts without the glass. It may be worth observing, that by how 

 much the cylinder is greater than the spring, so much greater will be the quan- 

 tity of air that is exhausted out of the glass, because the air 9 O Q is expanded 

 into a greater space, and consequently has a less elasticity ; therefore the elasti- 

 city of the air in the glass has a greater ratio to the elasticity of the air con- 

 tained in the cylinder and spring, and for that reason a greater quantity of air 

 will be exhausted out of the glass. 



On the Quadrature of the Parts of the Lunula of Hippocrates of Chios ; by Mr. 

 John Perks. Jfilh the further hnprovements of the same, by Dr. David Gre- 

 gory, and Mr. John Caswell, Comnnmicated by Dr. IVallis. N° 25y, p. 41 1. 



The squaring a certain lunula by Hippocrates of Chios long since has been 

 known as to the whole lunula for many ages. But as to its parts new discoveries 

 have been lately made, which had not been considered by any before this ])resent 

 age. I received in Nov. 1699, from Mr. John Perks, of Old Swynford in 

 Worcestershire, a brief account of his squaring the portions of Hippocrates's 

 lunula. For the better understanding of which, I shall premise as known, 

 because long since demonstrated, that, if on ab, fig. 1, pi. 11, the chord of 

 ADB, the quadrantal arc of a circle, whose centre is c, be described, as a dia- 

 meter, a semicircle abe' ; this semicircle will be equal to that quadrant. Because 



