270 Mr DAVIES on the Equations of Loci 



sions of their equations, without the aid of expansions and dif- 

 ferential coefficients, I am compelled to omit many properties of 

 this curve which are exceedingly curious, not less curious than 

 those which belong to its stereographic projection, the logarith- 

 mic spiral, which induced JAMES BERNOULLI to designate it by 

 the name spiral mirabilis. Finally, I slightly examine a locus 

 which has considerable physical interest, especially arising out 

 of the elegant experiment of Mr BARLOW, to shew " the probable 

 electric origin of the phenomena of terrestrial magnetism," de- 

 tailed in the last fasciculus of the Philosophical Transactions. 



In pursuance of a plan like the present, it was impossible to 

 concentrate every thing I had to say in the text : and therefore, 

 I insert a few notes and illustrations, in the form of addenda to 

 the paper itself. It only remains for me to apologise for the 

 length of this explanatory and historical preface, and to express 

 my regret that it could not be compressed into smaUer space, 

 without ceasing to answer the purpose for which it was in- 

 tended. 



BATH, November 21. 1831. 



