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- 



n 



V TT- F . 



turn of air; also, - x is the general expression for the hy- 



n TT 



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, 



i.pz£., t^tzf, t^lzT. tjlir,^,. 



n p n p n p n p 



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

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



\ J r 7b J) 



+ 



^'y'-f\ij"-f-+^c.h.. 



n p n p 

 that is, 



nip p p P -> 



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



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

 p. 563 ; or p. 103, same volume. 



* 



