Roots of Equations. — Phenomena of Springs. 4 1 7 



Oxford, Nov. 1, 1833. 



LXV. On Mr. Murphy's Proof of the Existence "of a teat or 

 imaginary Root for any proposed Equation. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 

 HPHE demonstration which appears in the Number of your 

 A Magazine for March 1833, by Mr. Murphy, does not 

 seem to me to be conclusive. 



For P is a function of p and q: as also is Q : now a value 

 being assigned to p, a value is found for q, which makes 

 Q = 0: and the value of P in (1) depends upon these as- 

 signed values of p and q. 



Again : in the second substitution, for p is put p + h. 



cos — ; the first part of this being the value above given to p : a 



value is then found for q-\-h . sin — , and therefore for<7,which 



x n 



makes Q = : hut this value does not necessarily appear to be 

 the same value as before obtained for q, and therefore the value 

 of P (which is a function of p and q) in (2) is not the same 

 as the value in (1). J. Henry. 



Nov. 1, 1833. 



LXV I. Observations on the Rise and Fall of Water in some 

 Wells in Cornwall, with brief Notices of other Matters 

 bearing on the Phenomena of Springs ; in a Letter to Sir 

 Charles Lemon, Bart. M.P. F.R.S. By W.J. Hen wood, 

 F.G.S. Lond. and Paris, Hon. M. Y.P.S.* 

 Sir, 

 A T Dr. Buckland's desire, and with the assistance of gen- 

 ■*"*• tlemen in various parts of Cornwall, I have endeavoured 

 to follow up for one year the measurements first instituted in 

 this country by Mr. Blandf, and which I have now the ho- 

 nour to present to your notice. 



* Communicated by Sir Charles Lemon. 

 f Phil. Mag. and Annals, vol. xi. p. 88. 

 Third Series. Vol. 3. No. 18. Dec. 1833. 



3H 



