172 Analysis of Scientific Books and Memoirs. 



Now, assuming the above reasoning, respecting the forces on each side 

 the neutral line, as true, we will examine the consequences ; and since 

 wXnt = w'Xnc, and wX nt + w'Xnc = W X riN, n must, from the last 

 equation, evidently act as a fulcrum or joint, on which the double lever 

 ~N?it, Nrae, would turn. Suppose, then, instead of the double lever, we had 

 two levers Nnt and N'/<c unconnected, except at the firm joint n, on 

 which they both turned, and at the ends N and N' of their equal arms, 

 we applied £ W ; it is evident, since w X nt = w' X nc, that each lever 

 would be in equilibrio with its load, and one have no tendency to deflec- 

 tion more than the other. If now we supposed the two arms cement- 

 ed together, the two levers must evidently have the same effect upon the 

 joint n as the compound lever Nn(, Nrcc, with W suspended at N, And 

 since W can only act in the direction of gravity, and consequently has no 

 effect on the levers (of which the beam is assumed to be composed) in 

 drawing them from, or pressing them toward the wall, we shall have in 

 the lever ~Hnt, the pressure on n, (in the direction Nn) equal the tension 

 in I, equal w ; and, in the lever N'«c, the joint n will have to resist an ef- 

 fort in the opposite direction 7^N', equal to the pressure in c, equal w'. 

 The imaginary joint n, which is in the neutral line, will then be affected 

 by a force equal to the difference of the weights w and w', viz. of the 

 forces of tension and compression, and have its fibres stretched or com- 

 pressed by the force; which, when the above forces are unequal, is con- 

 trary to the definition of the neutral line. The assumption w x « = 

 w' X nc, as a general equation, is therefore erroneous. 



It will further appear, that the foregoing deductions, while they tend 

 to refute the supposition of Mr Barlow, serve equally to establish that of 

 Coulomb, the deficiencies of whose effort I have endeavoured to supply in 

 the above mentioned Memoir. 



The next conclusion of Mr Barlow in the above paragraph is, wXnt + 

 w > X nc==W X mN=2m> X nt, andthelast equation,viz. W X »N=2u> X nt, 

 is that which he has used for estimating the strength of materials; but 

 this, like the former, must be incorrect, since w X nt is not generally equal 

 to w' X nc, their sum, therefore, cannot then be equal to 2 w X nt. 



The errors in the preceding theorems extend their influence through 

 a great number of the pages following the paragraph quoted above, entire- 

 ly destroying the ingenious deductions in the first 20 of them, and the 

 conclusions so unsatisfactory of the coincidence of the centres of tension 

 and compression with those of gravity : those conclusions having been 

 drawn from experiments conjoined with the theory we have just been ex- 

 amining. 



Mr Barlow will likewise have to correct (besides some errors of secon- 

 dary importance) the last column of the tables presented to the Honour- 

 able the Principal Officers and Commissioners of the Navy. 



As the mechanism of the transverse strain seems by no means to be 

 well understood, I possibly shall be excused for giving the following me- 

 chanical illustration of the matter. 



I took a board ABCD, Plate I. Fig. 10, 3 feet 6 inches long, and 1 

 foot broad ; and at about half the distance between its two ends, and near 



