12 Dk. Arnott on the Measurement of Heights. 



divided by the difference of the approxi7na^e height, gives the co-efficient for 

 after use adapted to Omt thermometer and barometer." 



It is of no consequence whether the Centigrade or Fahrenheit's ther- 

 mometer be used, provided the same scale be adhered to. 



If in tropical countries the barometer usually stands at thirty inches at 

 the level of the sea, it becomes important to ascertain what is the boiling 

 point of the thermometer used, at that pressure ; and from what I have 

 already said, we obtain this simple rule : — 



" Observe the boiling 2'>oints under two as widely different barometric 

 jyi'essures as possible: divide the difference of these boiling points by the 

 difference of the logarithms of (lie barometer in inches, aiwl call this m ; 

 this midtijylied by the logarithm of one of the iwlications of the barometer, 

 and the jn-oduct subtraded from tlie elevation oftlie coire^ponding boiling 

 points above freezing, will give a number n : then m Log. 30 + n ^ 

 1 •4771213 X m -f- n gives tlie elevation of the boiling 2)oint above freezing 

 at the pressure of thirty inches; m and n being multiplied by 100, and 

 divided by this elevation, ivill adapt tlie formula to a tMrmometer graduated 

 at 100° Cent, under the pressitre of thirty inches, and temperature 0°." 



It is very desirable that thermometers, but particularly the boiling 

 point instruments, be all graduated to indicate 212 Fahr. or 100° Cent, at 

 thirty inches precisely, and when the external atmosphere is at freezing;* 

 and each instrument maker can easily accomplish this by keeping a 

 standard one whereby to gi-aduate those he sells. It is probable that in 

 this country most are now so graduated, and in that case it is necessary 

 to ascertain with some accuracy the boiling point for any particular 

 pressure, p. 



Mr. Forbes, in his Memoir, pp. 412, 414, gives eight observations on 



* In order to compare any other thermometer with this standard one, let a be 

 the boiUng point on the latter, (whether adapted to J&'ahrenheit or the Centigrade 

 scale,) and A the boiling point of the other thermometer at the same barometric 

 pressure and temperature of the atmosphere: and let c° be the point where the two 

 thermometers exactly coincide, whether that point be freezing, or above or below 

 it : then let h be any observed state of the thermometer, this will accord with 



c 4- -^-^ a — c\ or «^ — (" + ^ — -^)g on the standard one ; on the Centi- 



grade scale, if c ^ o, a =: 1 00 ; h becomes . Sometimes thermometers are 



made to coincide at 32oFahr., sometimes at Zero Fahr.: but in order to make the 

 degrees shown by the one correspond to those on the other, it is necessary to dis- 

 cover this point of coincidence, before we compare the boiling points. Usually, 32° is 



preferred for Fahrenheit's, in which case, the above becomes 32 -)- ^ — -^ — — - 



^j. 180 h + 32 A — 6784 ^j^^ common way is to call this 6 -f- 212 — A, which 



is too small by the quantity ^^ '^ ~ ~' : and if A — 212 amounts to U 



or 2", and if A — h, be 20» or 25", as in Saussure's observations, the error may 

 amount to 2 or 3 tenths of a degree. 



