[ 3^8 ] 



Lastly, it Hiould be noticed that the horizontal diftance be- 

 tween the places of obfervation fliould not exceed eight or ten 

 miles. 



Bv means of this progreflion feveral curious queftions may be 

 refolved, the latitudes being given. 



Let H denote the heat below, h the heat above, D the di- 

 minution, d the common difference or rate of the progreflion, 

 « the number of terms in the propofed or fought for height,, 

 whicli mnltiplicd by loo gives the height truly, to lefs than 

 20 feet. 



L the height of the upper line of congelation, in the given 

 Latitude. 



Then t° tf'^ — — ^. ado. Y)=d n. 3io. « = — 4°. H=;/5+D 

 L — r d 



5^ /& = H— D. 6° L = (!i:ZJ^_+ i) X 100. 



d 



Thus 1°. the heat below being given in latitude 56^,30 to 

 find the rate of its progreflion upwards ? Suppofe the heat below 



54°, then by the firft formula -^-T — ^^ — = n. — = ,408; then 



54,86—1 53,86 



it is diminiflied ,408 of a degree in every hundred feet of its 



progrefs upwards. 



Thus 



