upon the Antique Dials. 79 



experiment for the mathematical syllogism, which the subject 

 unquestionably both admitted and required. 



With these facts in view, it appeared to me the most satis- 

 factory, as in the end it proved to be the most simple, method 

 of proceeding, to revert to first principles, and obtain, if possible, 

 a general equation of these curves. As the result of my investi- 

 gation sets the question at rest, by shewing the exact character 

 of the curves ; and as it has the advantage of being effected by 

 principles which embrace all the circumstances of the inquiry, I 

 beg to offer it to the Royal Society of Edinburgh, and venture 

 to hope that it may be deemed worthy of a place in the Trans- 

 actions of that learned body. 



BATH, February 24. 1830. 



L 2 



