of Professor Brlnldey, 163 



Chronological Catalogue of the Memoirs published by Brinkley, 



General demonstration of the Theorems for the Sines and Cosines of 

 Multiple Circular ArcSj and also of the Theorems for expressing the pow- 

 ers of Sines and Cosines gf Multiple Arcs ; to which is added a theorem, 

 by help whereof the same method may be applied to demonstrate the pro- 

 perties of Multiple Hyperbolic Arcs. Read to the Royal Irish Academy 

 May 6. 1797. — A general demonstration of the properties of the Circle, 

 discovered by Mr Cotes, deduced from the circle alone. Read to the 

 Royal Irish Academy November 4. 1797. — A method of expressing, when 

 possible, the value of one variable quality in integral powers of another 

 and constant quantities, having given equations expressing the relation of 

 these variable quantities ; in which is contained the general doctrine of 

 Reversion of Sines, of approximating to the roots of equations, and of the 

 solution of fluxional equations by sines. Read to the Royal Irish Aca- 

 demy November 3. 1798. — On the Orbits in which Bodies revolve, being 

 acted upon by a centripetal force, varying as any function of the dis- 

 tance, when thesp orbits have two apsides. Read to the Royal Irish 

 Academy March 9. 1801. — On determining the Innumerable Portions of 

 a Sphere, the solidities and spherical superficies of which portions are at 

 the same time algebraically assignable. Read to the Royal Irish Aca- 

 demy November 2. 1801. — An Examination of various Solutions of Kep- 

 ler's Problem, and a short practical solution of that problem pointed out. 

 Read to the Royal Irish Academy November 4. 1802. — A Theorem for 

 finding the surface of an Oblique Cylinder, with its demonstration. Read 

 to the Royal Irish Academy December 20. 1802. — An investigation of the 

 general term of an important Series in the inverse method of infinite dif- 

 ferences. Read to the Royal Society, London, February 26. 1807. — On 

 Sir Isaac Newton's first Solution of the problem for finding the relation 

 between Resistance and Gravity, that a body may be made to describe a 

 given curve, &c. Read to tlie Royal Irish Academy May 25. 1807. — In- 

 vestigations relative to the problem for clearing the apparent distance of 

 the Moon from the Moon or a Star from the efiects of Parallax and Re- 

 fraction, and an easy and concise method pointed out. Read to the Royal 

 Irish Academy March 7. 1808. — An account of Observations made at the 

 Observatory of Trinity College, Dublin, with an Astronomical Circle, eight 

 feet in diameter, which appear to point out an annual parallax in certain 

 fixed Stars : Also a Catalogue of North Polar Distances of forty-seven 

 principal Stars, from recent observations, and a comparison thereof with 

 those of the same stars obtained by other instruments, and by the same 

 instrument at a former period. Read to the Royal Irish Academy May 9. 

 1814. — Analytical Investigations respecting Astronomical Refractions, 

 and the application thereof to the formation of convenient tables, together 

 ■with the results of observations of Circumpolar Stars tending to illustratie 

 the theory of Refractions. Read to the Royal Irish Academy May^9. 



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