364 Hydrostatics. 



h = JL (i + 0,00223 r^-^) - 32^) log. ^. 

 m # \ \ 2 x / => t' 



It will be pprceived that - - may require some modification, 



in order that the formula in this state should adapt itself to ob- 

 served heights or known values of h ; and indeed the observa- 

 tions of M. Ramond give, for the value of the co-efficient to be 



employed in this formula, = 18393 metres or 10031 fath- 



mg 



oms, exceeding the former by 6 fathoms. Accordingly the de- 

 pression of the temperature below 32, required in order to 

 change this to the more convenient form of 10000, will be found 

 to be 1,45 ; retaining the co-efficient 10000, therefore, we have 

 only to suppose the temperature 32 l,45 or 30,55. As 

 this differs less than half a degree from 31, and as we can sel- 

 dom be certain of the temperature of the air to a greater degree 

 of accuracy, we may still use the same formula without any oth- 

 er change than the omission of the term depending on -. We 



li. 



have hence a very simple, convenient, and for common cases, 

 sufficiently exact formula, namely, 



h = 10000 (1 -f 0,00223 ( T "^ T ) 31) (log. w log. w/.) 



This being adapted to the latitude of 45, when the barome- 

 terical observations relate to a place on a parallel considerably 

 distant either north or south, it will be seen directly by the fore- 

 going table when it is necessary to apply a correction for differ- 

 ence of latitude, and what this correction is. It will be recol- 

 lected that the lengths of the barometric columns w, w', which 

 represent the weights of the atmosphere respectively at the two 

 stations, are supposed to be reduced to the same temperature. 

 The upper column w' is usually the coldest, and consequently 

 too short. Now, according to the rate of expansion or contrac- 

 tion already mentioned, as 1 inch is shortened 0,0001 for each 

 degree, a column of 25 inches will be shortened 0,0025 of an 

 inch for each degree of depression, and consequently 0,01 for 

 ever y 4 and each portion of 2,5 inches will be shortened 

 one tenth part of this, or 0,001 for the same amount of depress- 



