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LVII. Notice on Barometrical, Thermometrical, and Hpgrometrical 

 Clocks. Bii Sir David Brewster, K.H., D.C.L., F.R.S., 

 V.P.R.S. Edin., and Associate of the Institute of France^. 



IN the Number of this Journal for December 1853, Mr- 

 Macquorn Rankine has described a Barometric Pendulum, 

 and has referred to the history of this class of instruments. 



About the year 1810 orl811, 1 proposed, in the articles 'Atmo- 

 spherical Clock and Barometer,^ published in the Edinburgh 

 Encyclopaedia t, the construction of barometrical, thermometrical, 

 and hygrometrical pendulums for registering the indications of 

 such instruments. As I was prevented by more interesting 

 pursuits from constructing any of these clocks, I should not 

 have thought of claiming any priority in proposing them ; but 

 I owe it to IMr. Babbage to state, that about 1820, without know- 

 ing of my suggestions, he actually constructed a barometrical 

 clock and sent to me a paper on the subject, which he declined 

 to have published, in consequence, I believe, of my having anti- 

 cipated him in the idea. If I recollect rightly, Mr. Babbage 

 not only made observations with his barometrical clock, but it 

 was proposed by some of the influential members of the Royal 

 Society to erect one of them in their apartments. 



LVITI. Poceedings of Learned Societies. 



ROYAL SOCIETY. 



[Contiuuecl from p. 2f)l.] 



Feb. 23, 1854.— The Rev. Baden Powell, V.P., in the Chair. 



7^HE folioM'ing communications were read : — 

 1. A paper entitled, " Continuation of the subject of a paper 

 read Dec. 22, 1 853, the supplement to which was read Jan. 1 2, 1854, 

 by Sir Frederick Pollock, &c. ; with a i)roof of Fermat's iirst and 

 second Theorems of the Polygonal Numbers, viz. that every odd 

 number is composedof four square numbers or less, and of three trian- 

 gular numbers or less." By Sir Frederick Pollock, M.A., F.R.S. &c. 

 The object of this paper is in the first instance to prove the 

 truth of a theorem stated in the supplement to a former paper, viz. 

 " that every odd number can be divided into foursquares (zero being 

 considered an even square) the algebraic sum of whose roots (in 

 some form or other) will equal 1, 3, 5, 7, &c. up to the greatest 

 possible sum of the roots." The paper also contains a proof, that if 

 every odd number 2« + 1 can be divided into four square numbers, 

 the algebraic sum of whose roots is equal to 1, then any number ?J 

 is com])osed of not exceeding three triangular numbers. 



* Communicated by the Author, 

 t Vol. iii. pp. 57 and 2.94. 



