319 



Let r be ratio of a geometric series. 



Jf be (= . 43494, &c.) modulus of common logarithms. 

 V be hypothetic distance between stations, upon suppo- 

 sition that the atmosphere be perfectly free from 

 aqueous vapour. 

 v be actual distance between stations, taking, of course, 

 into consideration the hygrometric state of the^at- 

 mosphere. 

 Now let us suppose the actual distance between the stations 

 (= v) to be divided into an extremely great number of equally 

 thin parts or strata, then -= actual thickness of each equal stra- 

 tum of air; also, — x is the general expression for the hv- 



n IT 



pothetic thickness of any stratum, upon supposition that the at- 

 mosphere be perfectly free from aqueous vapour.* 



" Now, adopting a notation (similar to that employed for 

 the upper station), relative to the pressure and force of va- 

 pour, for the successive strata of air, descending from the 

 upper to the lower station, we have for expression of the hy- 

 pothetic thicknesses of the various strata, upon supposition that 

 the air be perfectly dry, 



""'J-f. t^TLzJl. i^iLzIl. ^\. p""-f" '. g.^ 



n p n p n p n p 



Now, the whole being equal to the sum of its parts, 



. v' p - f 



V (- the hypothetic distance between the stations) = - x - — ^- 



v' p'-f , v\_p"-/" 



+ 



n p n p 

 that is, 



+ - X - — ^^ ; + &c. &c. 



„ = !i.(i_< + i_4 + i-4 + i-4,+ &c.| 



nip p p p J 



But p, p", p", p"", &c., form a geometric series, according to 



• Vide paper by Dr. Apjohn, Proceedings Royal Irish Academy, vol. ii. 

 p. 5G3 ; or p. 105, same volume. 



