323 



N. B. — The approximate expression given by Dr. Ap- 



john,* viz., 



v=v. V{(P-f)x(P-F")] 



V{{p-/lx(p-F")]-i{f"+F'y 



in which Dr. Apjohn employs the geometric mean of pres- 

 sures minus the forces of aqueous vapour, instead of P, the 

 more correct expression, will answer very well indeed for hills 

 only 1000 feet high, and under that height. In fact, for hills of 

 such height, Dr. Apjohn's formula is astonishingly close to 

 the more correct expression. But for hills 2000 feet high and 

 upwards, Dr. Apjohn's approximate formula fails, inasmuch as 

 the error varies from 10 to 20 per cent, of the correction due to 

 the hygrometric state of the air. Now, as Dr. Apjohn justly 

 observes! that the correction due to the hygrometric state of 

 the air amounts to at least 30 feet in hills 2000 feet high, the 

 error of his formula will vary from 3 to 6 feet, according to 

 the greater or smaller quantity of watery vapour in the at- 

 mosphere. Indeed in hills of 1000 feet high and less, instead 

 of the geometric mean of pressures minus the forces of aqueous 

 vapour, we may employ the arithmetic mean of pressures 

 with perfect practical safety, viz. : 



, i(P+P) ^... (P + P) 



i(p+p')-i(/+/) {p+p)~(/'+fy 



N. B. — The formula given by Mr. Renny to Dr. Apjohn, 

 viz., " 



V =V X 



P-F' 



^, . M ^ p' 



P being 



\p pj 

 is not rigidly or mathematically correct ; because Mr. Renny's 



* Proceedings Royal Irish Academy, vol. ii. p. 563. 

 t Ibid. vol. ii. p. 564. 



