and Strength of Materials. 241 
And finding the sums of the four preceding 
quantities, by the method used in article 4th, 
we have— 
x sba° sh DJ ov v 0 
Sum of the —— = — X (14 2’+ 3°&e. to @”) = 
sha sba : : : 
— = sum of the forces of tension = T in 
a (oI) 91 
T.D+T.A : 
con (article 13.) 
the foregoing rule, 
must he erroneous too, since they lead in a regular progres- 
sion to the last three. 
Now as Mr. Barlow has offered no reasons against the 
theory in the text (further than that it does not agree with 
his own, which we have just been examining,) we see no 
cause why it should be rejected, especially since it seems 
to us to be every where consistent and just. 
It may not be improper to mention that M. Coulomb, in 
his paper on this ‘subject (Memoires presentés a l’ Acadé- 
mie des Sciences, tom. 7) makes Lx W = the forces in 
Fx PF-+ the forces in f x Pf, and endeavours to shew 
that the forces in F and f, or those of tension and compres- 
sion are equal: The theory of Mr. Barlow then differs 
from that of the French philosopher in this last particular, 
but we conceive that the latter must be right ;--the results 
from it are the same as from that in the text, though it is 
much less convenient in its use. We particularly refer the 
reader to the above paper of M. Coulomb, as he has given 
a very minute analysis of the transverse strain: and the 
reason why this matter has been so long overlooked, seems 
to be that both M. Coulomb and Dr. Robison have contented 
themselves by giving a bare outline of it. 
Hh 
