t 166 ] 
fhall not appear. The fluxion of a logarithm is to 
the fluxion of its natural number, as the modulus of 
the fyftem to the natural number ; and 4343 is the 
modulus of the common logarithms, when the four 
places, next following the chara&eriftic, are taken as 
whole numbers, inftead of decimals, which is meant 
to be done in the ufe of the foregoing formula. 
D b 
Therefore being very fmall with refpedt to b , 
we (hall have, variation of log. b : variation of b 
(= — y) •• 4343 : ^ very nearly, and thence va- 
riation of log. 6 = + || x ^ = ± **£. 
Which (putting K= 178) — -f- 0,452 D. Hence 
log. {b 4- — log. b 4- 0,452 D; which 
being fubftituted in the formula above, will give 
the difference of height, of the two ftations, in 
Englilh fathom, in a more convenient expreflion. 
namely log. B — log. b + 0,452 D x 1 _ 4 4 g 4 * 
where the upper fign, — , is to be ufed, when the 
thermometer of the barometer is higheft at the 
lower ftation, and the lower fign, -f-> is to be ufed, 
when the faid thermometer is loweft at the lower 
ftation. The firft cafe will be moft common j efpe- 
cially where the difference of height of the two 
ftations is confiderable. It Ihould alfo be obferved, 
that when F, the height of Fahrenheit’s thermo- 
meter, is lefs than 40°, -f. 
-40 
449 
becoming nega- 
tive or fubftra&ive, muff: be applied in the calcu- 
lation accordingly. 
It 
