the above book has two usages of scientific notation before 1890.
1) pages 494-497 i9s a translation of a paper by Hermann Walther
Nernst ("Z. Physik. Chem. 4: 129-181 (1889)"). The equation
E = 0.860T ln (P/p) x 10^(-4) volt
(modified slightly for ASCII) appears on pages 495 and 496. The
translation apparently was made ca. 1952 for the book, so it is
possible that the use of scientific notation is an artifact of
the translation.
2) pages 354-360 is the text of an article by Robert Whillhelm
Bunsen that appeared in English in 1857 in _Philosophical
Transactions_. The following formulae appear on page 357 (again
modified slightly for ASCII):
I = I-sub-0 10^(-h alpha)
I = I-sub-1 10^(-h alpha) + I-sub-2 10^(-h alpha) + ...
Here the objection is that Bunsen was measuring the intensity of
light before and after going through a tube of chlorine, and the
alpha above is defined as "The value of 1/alpha, which
signifies...the depth of chlorine to which the chemical rays must
penetrate in order to be reduced to one-tenth of their original
amount..." Therefore the 10 is not necessarily part of
scientific notation but comes from the fact that Bunsen elected
to measure a reduction of light to one-tenth of the original.
James A Landau