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On the Rectification of the Hyperbola by Means of Two Ellipses; 

 proving that Method to be circuitous, and such as requires much more 

 Calculation than is requisite by an appropriate Theorem : in which 

 Process a new Theorem for the Rectification of that Curve is dis- 

 covered. 



To which are added some further Observations on the Rectification of 

 the Hyperbola : among which the great Advantage of descending 

 Series over ascending Series, in many cases, is clearly shown ; and 

 several Methods are given for computing the constant Quantity by 

 which those Series differ from each other. By the Rev. John Hel- 

 lins, B.D. F.R.S. and Vicar of Potter' s-Pury, in Northamptonshire. 



Being an Appendix to his fanner Paper on the Rectification of the 

 Hyperbola, inserted in the Philosophical Transactions for the Year 

 1802. Communicated by Nevil Maskelyne, D.D. F.R.S. Astro- 

 nomer Royal. Read January 10, 1811. [Phil. Trans. 1811, /j.110.] 



The present communication is designed by the author as an ap- 

 pendix to his former paper on the same subject, printed in our Trans- 

 actions for 1802. 



Although he acknowledges the ingenuity of Mr. John Landen, 

 who devised the rectification of the hyperbola by means of two ellipses, 

 and adds his tribute of applause to that which has been bestowed upon 

 it by the most eminent mathematicians of the Continent, as well as 

 of our own country, Mr. Hellins is nevertheless of opinion, that it is 

 more to be admired as curious than practically useful ; since it is 

 circuitous, and requires much more calculation than will be found 

 requisite by the theorem, which is the primary subject of this paper. 



Mr. Hellins also adds some further observations on the rectification 

 of the hyperbola, and shows the great advantage of descending series 

 over ascending series, in many cases, and gives several methods of 

 computing the constant quantity by which those series differ from 

 each other. 



On a Combination of Oxymuriatic Gas and Oxygen Gas. By Hum- 

 phry Davy, Esq. LL.D. Sec. R.S. Prof. Chem. R.I. Read Fe- 

 bruary 21, 1811. [Phil. Trans. 1811, p. 155.] 



The author, having observed the properties of oxymuriatic gas to 

 be different in consequence of its being prepared in different modes, 

 was endeavouring to determine the nature of these differences, and 

 the causes on which they depend, when he discovered the very sin- 

 gular compound which is the subject of the present paper. For the 

 formation of this compound, he pours a small quantity of dilute mu- 

 riatic acid upon a large quantity of hyperoxymuriate of potash. A 

 gas is then disengaged, which is capable of being absorbed by water, 

 but may be collected over mercury. It is of a bright yellow colour, 

 approaching to orange, and has nearly the specific gravity of oxy- 

 muriatic gas. 



It often explodes while collecting, in consequence of heat gene- 



