[ •'^12 ] 



LIST OF PATENTS FOR NEW INVENTIONS. 



To Ilario Pcllafinet, of Earl's Couit, Middlesex, gentleman, for 

 certain new and improved machinery and methods for breaking, 

 bleaching, preparing, mannfacturing and spinning into thread or 

 yarn, flax, hemp, and other productions and substances of the like 

 nature ca])able of being manufactured into thread or yarn. — Dated 

 27th March 1821.' — 12 months allowed to enrol specification. 



To William Southwell, of Gresse-street, Rathbone-place, piano 

 forte manufacturer, for improvements on cabinet piano fortes. — 

 5th April. — 2 months. 



To James Goodman, of Northampton, sadler, for his improve- 

 ment on stirrup irons. — 5th April. — 2 months. 



To Lient.- Colonel Henry Goldfinch, of Hylhe, Kent, for his 

 improvement in the formation of horse shoes. — 5th April. — G 

 months. 



To William Annesley, of Belfast, architect, for certain improve- 

 ments in the construction of ships' boats and other vessels. — 

 .'ith April, — 2 montlis. 



To William Chapman, of Newcastle-upon-Tvne, civil engineer, 

 for his method of transferring the ladings of lighters and barges 

 into ships or vessels, or from ships or vessels into lighters and 

 barges. — April. — 2 months. 



To James Henry Marsh, of Chenies-strect, Tottenham Court 

 Road, for certain improvements on wheeled carriages. — l/lh 

 April. — 2 months. 



To James Smith, of Hackney, gentleman, for improvements 

 in the machinerv employed for shearing or cropping woollen 

 cloth. — ISth Apiil. — 2 months. 



MATHEMATICAL QUESTIONS. 



To Mr. Tilloch. 



Sir, — I. In contemplating the general figure of the curve 

 cilled thoLemvhcate, shown in the" Fhi!osoi)hical Transactions" 

 for 1820, by Mr. Herschel junior, to be traced by the Tints of 

 certain polarized Rays of Light, it appears that in one certain 

 proportion oi a io b (see his Equation) the Curve approaches the 

 nearest in form and dimensions to an Aj^nlonian Elli|)sis; it is re- 

 quired to assign this proportion ? ; and show in such case, how 

 far i\\cJocii and axes of tiie Lemniscate arc, from coinciding with 

 those of the Ellipsis? 



H. It also appears, that in one certain projiortion of the above 

 Elements, there is a straiglU part of the Curve ; it is required to 

 assign' these proportions?, and the length and |)osition of such 

 straight part ?. 



III. To show how'the method of investigation in the last ques- 

 tion. 



