188 Mr. W. G. Horner's Considerations relative to 



but still filling up the interstices of the concentric layers, and 

 binding them together, according to the similitude of Grew 

 and Malpighi, as the woof of a web binds together the longi- 

 tudinal threads of the warp. 



[To be continued.] 



■ - - ■ ■ . - '.'■" •-- -sr 



XXVII. Considerations relative to an interesting Case in 



Equations, By W. G. Horner, Esq.* 

 "DERCEIVING that Professor Moseley has resumed the 

 -*• development of the principle of least pressure, I presume 

 that the discussion, which was introduced by Mr. Earnshaw, 

 respecting the validity of the ^principle, has terminated. 

 Without entering, therefore, upon the general question, in 

 the fate of which I have no other interest than every lover of 

 science must be supposed to have, I may be allowed to ex- 

 press my disappointment at the unsatisfactory result of that 

 portion of the argument which, if conclusively handled, was 

 likely to have proved the most impressive. I allude to that 

 passage in which the Rev. Professor's reasoning assumed the 

 tangible form of an equation. That this was regarded by 

 both the disputants as a critical point, is abundantly apparent; 

 and, in fact, if the general theory is " such, in its nature, as 

 cannot be submitted to the test of experiment t", it is doubly 

 requisite that the testimony of calculation should be clear. 

 For these reasons, the liberty which I use in recalling atten- 

 tion to that particular point will be the more readily excused 

 by the gentlemen who have already agitated the question. 



In page 200 of the Number of this Magazine already re- 

 ferred to, Mr. Moseley, in considering the case of " a pressure 

 equally divided between three points of support in the same 

 right line," gives the following as " the two equations of equi- 

 librium :" 



u — + T + s= M 



x x—b x—c 



= Ma." 



a:— b x—c 



The resultant of this pair of equations he finds, with the tacit 

 assent of Mr. Earnshaw, to be a mere quadratic, which, how- 

 ever, seems to have been regarded by each party as having but 

 one root; and in consequence of this complicated oversight, the 

 dispute settled down into a discussion of the point of legitimacy 



* Communicated by the Author. 



f See Phil. Mag. and Annals, March 1834, p. 194. 



