230 Properties of the Cotenarian Cvrve 



h If vegetable or animal matter be contained in water, it gives 

 it a brown colour, especially when evaporated, It may be de- 

 stroyed in the dry residue by igniting it with a small addition of 

 nitrate of ammonia. 



The following analyses of mineral waters may be advanta- 

 geously consulted by the student, as containing a variety of 

 useful details, which are necessarily omitted in the above obser- 

 vations. 



1. Analysis of the Hot Springs at Bath, by Richard Phil- 

 lips, Esq. 



2. Analysis of the Brighton Chalybeate, by Dr. Marcet. 



3. Analysis of the Tunhridge Wells Waters, by Dr. Scuda- 

 inore. 



4. The sixth chapter of Mr. Children's Translation of 

 Thenard's Essay on Chemical Analysis. 



Art. II. On some Properties of the Catenarian Citrve 

 with reference to Bridges hy Suspension. In a Letter to the 

 "EinToiLfrom Davies Gilbert, Esq. F.R.S. and M.P. 



Dear Sir, 



Now that the properties of the Catenarian curve have ac- 

 quired real importance from the construction of bridges by 

 suspension, I flatter myself, that the following investigation will 

 not be considered as wholly undeserving of attention : — 



It is needless to remark, that almost every general principle 

 of mechanics requires to be modified in its reduction to prac- 

 tice. Thus inertia and friction are omitted in the abstract theory 

 of machines. The difference of form between the bridge and its 

 suspending chain, and still more, perhaps, the weight of the links 

 or bars connecting them together, must sensibly alter the mathe- 

 matical form of the curve : yet, from the catenary alone, can 

 the real principle for constructing these bridges be derived ; and 

 they will probably be found not more remote from practical 

 cases than other general principles, and equally capable of 

 receiving all necessary corrections. 



The elements of the Catenarian curve are given in most in- 

 troductory treatises on fluxions ; but to avoid the necessity of 



