214' Mr. Uttiiig on a Planelari) Analogy. 



sin. A &c." the passage between the parentheses being the 

 correction. I am much obliged to the friend who informed 

 me of this omission ; for every departure from strict mathe- 

 matical truth ought to be announced ; at the same time such 

 deviations may often be made with great benefit. 



T. T. 



XLIV. Postscript to Mr. J. Utting's Paper on a Planetary 

 Analogy, page 119 of the present volume. 



TF the distances of the planets from the sun, and that of the 

 -*- satellites from their primaries, be estimated by the radii or 

 semiaxis major of the earth's orbit, equal to nniiy ,• and the 

 velocities of the planets and satellites be taken for one sidereal 

 year, the constant quantity thus obtained (viz. V x v^ D &c.) 

 will ahmys be equal to the circumference of the earth's orbit, 

 or equal to the circumference of a circle vohose radius is unity. 



It has been demonstrated by La Grange that, amid the 

 changes which arise fi-om the mutual actions of the planets, 

 there are two things which remain perpetually the same, namely, 

 the greater axis of the orbit which the planet describes, and 

 its periodic time ; so that the mear,, motion of a planet, and its 

 mean distance, are invariable quantities. 



Whence it appears that the velocity of a planet in its orbit, 

 multiplied by the square root of its mean tiistance from the 

 sun, is not only a quantity resultant for all the planets, but a 

 constant quantity, which Vi\SS.for ever remain invariably the same. 



The quantity produced by Vx V'D &c. as above, is equal 

 to the earth's sidereal motion in one year ; and if the radii of 

 the orbit and sidereal period of any other planet, be substi- 

 tuted for that of the earth, the constant quantity thus obtained 

 will always be equal to the circumference of a circle to radius 

 unity for each planet respectively. 



Lynn Regis, Sept. 1, 1823. J. U. 



Erratum. — Page 120 lines 21 & 2% for =0. read =unity. 



XLV. On the Construction of an Air Barometer. By Mr. 

 Henry Meikle. 



To the Editors of the Philosophical Magazine and Journal. 



TN your Number for January last, Mr. Murray has given 

 -■- the description of a barometer for measuring altitudes, 

 and which in his opinion possesses extraordinary advantages 

 over every other instrument employed for the same purpose. 

 But as these advantages are scarcely enumerated, much less 



minutely 



