Mr. Woolhouse on the Theory of Gradients on Railways. 243 
The law in question, then, being a function of so many va- 
riable quantities, must be one of extreme complexity, perhaps 
beyond the powers of the most refined analysis to unfold. 
XLVIII. On the Theory of Gradients on Railways. 
By Mr. W.S. B. Wootnouse. 
To the Editors of the Philosophical Magazine and Journal. 
GENTLEMEN, 
S Dr. Lardner and Mr. Barlow, in your Numbers for 
* January and February, hold out conflicting opinions on 
the theory of gradients on railways, and have left the subject 
in a state more calculated to create doubts in the minds of the 
less informed of your readers than to lead them towards the 
formation of settled conclusions, perhaps you will favour me 
with the insertion of a few words, by way of explanation, as 
far as the philosophy of the question presents itself to my 
mind. Mr. Barlow, without absolutely saying which of the 
two solutions is wrong, though probably quite conclusive in 
his own view of the matter, first states his objection to the 
arithmetical results of the formula employed by Dr. Lardner 
for the velocity, in certain cases, then gives an outline of his 
principle of investigation, and finally expresses himself “ quite 
content to leave the decision to those whose minds have not 
already received a bias from preconceived notions of the 
forces.” Whatever sentiments may prevail as to the compe- 
tency of my opinions on such a subject, it will at least be 
acknowledged that I possess the qualification of being free 
from the bias here alluded to, and I am induced to hope that 
your readers will, on this very ground, acquit me of any ima- 
ginable interference in thus undertaking, voluntarily, the ex- 
amination of a point that has already had the attention of such 
distinguished individuals. By close and continued application 
of particular opinions to particular subjects, it is indeed sur- 
prising how they fix themselves in the mind, and become ulti- 
mately, whether true or false, of almost a fundamental character, 
But I donotconsider thisobservation to be applicable to the pre- 
sent case. It is my wishto simplify and expose the truth as far as 
Ican perceive it. Ido not, however, intrude the presentremarks 
in elucidation of the subject without some degree of hesitation, 
although quite free from apprehension as to their theoretical 
soundness. ‘To many of your readers, who must be far from 
satisfied with the present situation of the question, I never- 
theless feel myself justified in submitting them. 
2C2 
