So, I am using this common formula https://en.wikipedia.org/wiki/Propagation_of_uncertainty#Simplification to compute the uncertainty of dl = l2-l1 with matlab.
l2 = 100*(-(5*log((R0 - R3)/(R0 - R1)))/38)^(4/11),
l1 = 100*(-(5*log((R0 - R2)/(R0 - R1)))/38)^(4/11),
Now the uncertainties of l2 and l1:
vpa(subs(sqrt((diff(l2,R0)*sqrt(0.197/600))^2 + (diff(l2,R1)*sqrt(8.9/60))^2 + (diff(l2,R2)*sqrt(1.197/600))^2 + (diff(l2,R3)*sqrt(0.808/600))^2), [R0 R1 R2 R3], [0.197 8.9 1.197 0.808])),
ans = 0.74291424121955415578181189321097
vpa(subs(sqrt((diff(l1,R0)*sqrt(0.197/600))^2 + (diff(l1,R1)*sqrt(8.9/60))^2 + (diff(l1,R2)*sqrt(1.197/600))^2 + (diff(l1,R3)*sqrt(0.808/600))^2), [R0 R1 R2 R3], [0.197 8.9 1.197 0.808]))
ans = 0.69062293658353045325882186945072
and of l2 - l1:
vpa(subs(sqrt((diff(l2-l1,R0)*sqrt(0.197/600))^2 + (diff(l2-l1,R1)*sqrt(8.9/60))^2 + (diff(l2-l1,R2)*sqrt(1.197/600))^2 + (diff(l2-l1,R3)*sqrt(0.808/600))^2), [R0 R1 R2 R3], [0.197 8.9 1.197 0.808]))
ans = 0.74268061362923610313291669793113
It's smaller than both σ2 and σ1, why??? I was expecting sqrt(σ1^2 + σ2^2) = 1.01434.
First: As the Wiki article says: "Neglecting correlations or assuming independent variables yields...". But the variables are heavily correlated because the argument of the logarithm has to be positive.
Second: Even if you really had uncorrelated and independent variables, this is not necessarily a contradiction, because it may simply demonstrate the fact that a non-linear function cannot always be accurately approximated by the first order Taylor series.