Kii2oa) J 
LIX. Remarks on Lieutenant Lecount’s Treatise on Iron 
Rails. By Peter Bartow, Esq., F.R.S.* 
N amusing but not a very accurate critique of my Reports 
to the Directors of the London and Birmingham Railway 
Company having been recently published by Lieutenant Le- 
count, R.N., which must, I suppose, be considered as the last 
expiring groans of the fish-bellied rails, in which critique 
many of my formule are made to suffer woful transforma- 
tions, allow me in their defence to make a few observations, 
and they shall be very few. The author commences his in- 
quiry at page 20, and as an earnest of what is to follow, his 
very first step is to correct a simple trigonometrical expression 
Ihave given, (which is perfectly right as it stands,) and by his 
correction to render it ambiguous. With this corrected for- 
mula, however, after another forty pages, he contrives to prove 
what I have stated at page 19 of my Report, viz. that by taking 
a most injudicious form of parallel rail, we may get one inferior 
to the fish-bellied rail of the same weight. Now my object has 
been to prove, on the other hand, that by choosing a judicious 
section we may get one as decidedly superior; and I have 
no doubt that thus far both conclusions are just, notwith- 
standing the ambiguity of his formula. 
As it stands in my Report, the expression is 
V(r? + d® —2drcos 2); 
and Mr. Lecount, not recollecting that the cosines in the se- 
cond quadrant are negative and that “ minus into minus pro-~ 
duces plus,” has thought it necessary to make the alteration 
in question :—any student in trigonometry will judge with what 
propriety. 
The next 47 pages are employed to prove that all my rules 
for the neutral axis are unfounded; which of course they 
ought to be, if all Mr. Lecount says about them be correct. 
I will not even suspect that he has designedly misrepresented 
and misapplied my investigations, but I must say that the re- 
sult he conceives he has arrived at, page 107, is very far from 
a correct statement. It would seem from what he says, that 
I give the ratio of 1 to 9 for all cases. Now, if he had pro- 
perly understood what I had done, and if he had wished to 
have properly represented it, he would have informed the 
reader, that I had given a rule which was general for all bars; 
and that as an approximate rule only, sufficiently exact for 
all practical purposes, I had stated that taking the neutral axis 
in the middle of the head was nearly correct for all the usual 
forms of rails, and, as it happens, (the rail in question being 
* Communicated by the Author. 
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