Proceeding's (yf'ihe Society/ irf' Arts. 421 



Jan, 27. — Thomas Grainger, Esq. in the Chair. The following 

 communications were laid before tlie Society : — 



1. Part third of a paper, on the Construction of Oblique Arches. 

 By Edwai'd Sang, Esq. teacher of Mathematics, Vice-Pres. Soc. 

 Arts. Drawings were exhibited. 



In this part of the paper the f[)rms of the arch-stones were ex- 

 amined, and the methods of delineating and modelling them de- 

 scribed. The waste of material on account of the rhomboidal forms 

 of the stones was also discussed, and it was shewn, that the priu'- 

 cipal loss occurs on the ends of the stones, while scarcely any waste 

 is occasioned by the twist. It Was also mentioned, that any waste 

 occasioned by twist must have aiisen from the Use of improper 

 lines. Mr Sang stated, that he had revised and extended the former 

 parts of the paper ; and that, on investigating the appearances of 

 the joints when viewed from different sides, he had found the end 

 view to present the appearance of the Tractory, a curve well known 

 to students of the higher geometry ; while the side view of it is a 

 iiew curve, the companion to the tractory, closely allied to the trac- 

 tory and catenary, and capable of being described by a slight modi- 

 fication of Leslie's apparatus. 



2. Description aiid Drawing of a New Escapement. By Mr 

 Duncan Macgregor, Comrie A model was exhibited. 



3. Description of a New Construction of, and mode of propell- 

 ing Steam-Boats. By Dr A. Plantou, Philadelphia, United States, 

 the American patentee. Communicated by the Royal Society of 

 Edinburgh. 



4. A large accurate model (about seven feet long) of the celebrat* 

 ed American Steam Raft-Boat, which plied for some time on the 

 River Hudson ; — the machinery of which was fitted up by Mr Nell 

 Snodgrass, now engineer, Glasgow ; — was exhibited through the 

 kindness of Mr Snodgrass. An explanatory letter from that gentle* 

 man was read. 



5. Donation. — Solution of Algebraic Equations of all orders, 

 whether involving one or more unknown Quantities. By Edward 

 Sang, Esq. Teacher of Mathematics, Edinburgh. Eldin. 1829. From 

 the Author. Laid on the table. 



6. The report of the Committee on Mr M*Pherson's New Pinion 

 Ball- Cock, was read and approved of. 



7. A letter from Arthur Aitken, Esq. Sec. of Arts, London, wag 

 read, acknowledging receipt of the Select Printed Papers of the 



VOL. XX. NO. XL. APRIL 1836. K C 



