the Decrease of' Heat. 97 



4243, (Playfair's Outlines, art. 344,) therefore, 



'iT = *(£_») . . (B) 



which is the Professor's theorem. 



It is evident this theorem cannot be very correct, as it is 

 well known that theorem (A) does not accurately give the al- 

 titude, because no allowance is made for the expansion of the 

 air depending on the temperatures at the two places of observa- 

 tion, and other minor circumstances, which are indispensable 

 in the more accurate barometric formula. 



We are quite at a loss to discover how such a simple investi- 

 gation could have cost the Professor so much labour and re- 

 search as he seems to insinuate. 



From theorem (A) a simple rule may be derived for deter- 

 mining moderate heights without the aid of logarithmic tables, 

 thus : 



/B 3\ (B4-3)(B— jS) 



Example. Required the height of Arthur's Seat above the 

 Pier of Leith, from the following observations : 



Bar. 

 Leith Pier, 29-567 



Arthur Seat, 28.704 



28.704 X3.5 

 ] 0000 



And 28-704 -f 0.01 =28.714 = £ , 

 Whence B + jS = 29-567 + 28.714 a: 58.281 

 And B — /3- 29-567 — 28.714= 0.853 



But 0.00244 X 20| X 127-16 — 6. 293 



Height in fathoms, - - 133. 449 = 801 feet 



nearly, differing about two feet from the result by levelling. 



If the proper correction for aqueous vapour in the atmo- 

 sphere were made, it would almost agree with that determined 

 by levelling. 



Cor. h — 13000 x »i «> feet nearly, 



op 



which, in small heights, may be sufficiently correct. 



VOL. V. NO. I. JULY 1826. G 



