On Fractional Values for the Heptagon and Circle. 281 



the transference is made from the embrace of the oxygen to the 

 embrace of the metal without any appearance of the full equi- 

 valent of force that would be generated if the metallic molecule 

 had descended from the vaporous or separate-molecule form. 



An atom of metal seems almost as indisposed to exist in a 

 state of isolation as an atom or half-molecule of gaseous element. 



To attempt to express such conditions by modifying the nota- 

 tion, would probably only lead to confusion. But I submit that 

 the burnt or unburnt, the clasped or raised condition of atoms, 

 should be kept well in view while studying chemical reactions ; 

 otherwise we shall be apt to lose sight of their real potential 

 nature and wander into a maze of false analogy, barren of any 

 result but an unmeaning jargon of words. For the same reason 

 I submit that chemical notation should be founded on physical 

 relations only, now that the classical labours of modern physi- 

 cists have supplied nearly all that is necessary to do so. 



J. J. Waterston. 



Edinburgh, February 21, 1864. 



XL VIII. On Fractional Values for the Heptagon and Circle. 

 By Henry Norton, Esq. 



To the Editors of the Philosophical Magazine and Journal, 



Gentlemen, 



YOUR Magazine for November 1863, at page 408, contains 

 a note by Mr. Drach on an approximate construction 

 of the heptagon ; and the Number for last February, at page 

 124, contains a paper by Sir W. R. Hamilton " On Roberts 

 Construction : " I wish through you to point out to those gen- 

 tlemen a third construction of remarkable simplicity and accuracy, 



3x5 



s 7T 105 3x5x7 e L . 2 



— —= = tttt; = Ti — -r, — 7>j or lor construction = 



r L 7 242 11x11x2' 11x11 



7 

 This value of sine j is . . . -43388,42975 . . . 



The true value, according to Sir! .^ g 

 W. Hamilton, is ... J ' 



Error .... -00000,05584... 



Error of H. Rober's s Z . . '00000,01579 . . . 



In strictness the latter is the more correct ; but practically, 

 taking into account the much greater simplicity of the construe- 



