354 Dr. Ure’s new experimental researches 
n = o F = 30.00 inches 
n = 25 F25 — - 11.25 
n = 50 F S o = 3.50 
n = 75 F 7S = °- 9 10 
Substituting these conditions in the above general formula, 
and bearing in mind that the logarithm of a fraction is equal 
to the logarithm of the numerator minus the logarithm of 
the denominator, we have the three following equations of 
conditions. 
— 04259687 = 25. a + 625 b 15625 c. 
— 0.9330519 = 50. a 4. 2500 b + 1 25000 c. 
— 1-5180799 = 75. a + 5625 b + 421875 c. 
Doubling the first, and subtracting it from the second, a 
disappears ; trebling it, and subtracting it from the third, a 
also disappears. Then dividing each of the resulting equa- 
tions by the coefficient of b, we have 
— 0.00006489160 = b -j- 75 c. 
— 0.00006404635 = b -j- 100 c. 
Subtracting the one of these from the other, b will disap- 
pear ; and dividing it by the coefficient of r, we shall have c. 
Next, by substituting the value of c in one of these equations, 
we get b. Lastly, putting b and c in one of the two first equa- 
tions, we have a. Thus we find 
a = — - °-° 1 5374 1 955 ° 
b = — 0.00006742735 
c = -f- 0.00000003381 
Whence the whole formula Log. F„ = Log. 30 -}- an -F 
bn 2 4" cn3 i s completely determined, and may serve for cal- 
culating F n , relative to any proposed value of n. 
