336 Mr. R.'S. Brough on the proper Relative Sectional 



mass of similar calculations, came into the possession of Dr. 

 Olinthus Gregory, and were purchased by the Eoyal bociety 

 at the sale of his books in 1842." Nothing is known of them, 

 however, at the Eoyal Society. The Cambridge University 

 Library contains two copies of each of Mr. Goodwyn s publi- 

 cations of 1818 and 1823 *, but no copy of the specimen ot 

 1816. There is an account of Mr. Goodwyn s works in the 

 British Association Report on Tables (Bradford, 1873, pp. 

 31-33), where I have erroneously attributed the property 

 enunciated by Mr. Farey to Cauchy. A more complete de- 

 scription of Mr. Goodwyn's works is contained m a paper 

 " On Circulating Decimals, with special reference to Henry 

 Goodwyn's ' Table of Circles ' and < Tabular Series of Decimal 

 Quotients' (London, 1818-1823)," printed in the /Proceed- 

 ings of the Cambridge Philosophical Society, vol. m. (1*M) 

 pp. 185-206. 



Trinity College, Cambridge. 

 February 15th, 1879. 



LII. On the proper Relative Sectional Areas for Copper and 

 Iron Lightning-Rods. By K. S. BKOTJGHf. 



SO far as mere conductivity is concerned, a comparatively 

 thin wire of either copper or iron would suffice for the 

 loftiest conductor ; but such a thin conductor would be dan- 

 gerous, because it would be fused by a heavy discharge ot 

 lightning. Now the problem is to determine what relative 

 sectional areas should be given to copper and iron rods, in 

 order that neither should be more liable to fusion than the 



The usual answer given is, that an iron rod should have four 

 times the sectional area of a copper rod J. The result is, 1 

 suppose, arrived at in the following way. The conductivity 



* One of the copies of the < First Centenary' (1818) contains the fol- 

 lowino- letter, « September 16th, 1831. Mrs. Catherine Goodwyn presents 

 to the Library of the University of Cambridge a complete set of the works 

 of her late father, Henry Goodwyn, Esq., of Blacldieath Kent Koyai 

 Hill, Greenwich." Mr. Goodwyn also published a few folding sheets on 

 weights and measures &c. ; which are bound up at the end of this copy ot 

 the ' First Centenary.' K . ,. 



t Communicated by the Author, having been read before the Asiatic 

 Society of Bengal in November 1878. 



% War-Office Memorandum by General Sir Frederick Chapman, K.lS 

 G.C.B. 



