96s On Solids of greatest Attraction, or Repulsion. 



tend to lessen the consumption of flour, an object of con- 

 siderable national importance. 



*^* Persuaded that in domestic oeconomy Mr. Way's 

 communication mav prove useful to many families, we 

 have given it a place in our pages. We have only to add, 

 that so far as this mixed bread may be considered as pre- 

 ferable to that from flour, we have reason to believe that 

 many of the good inhabitants of London, and its vicmiiy, 

 have for a considerable time been enjoying the benefit— to 

 the great emolument of many honest bakers. 



If the absurd practice of regulating the price of bread 

 must be contiaued, would it not be equitable that the ma- 

 gistrates, in fixing the assize, should in future be directed, 

 by law, to take into their consideration not nitrely the 

 market price of flour, but also of potatoes? — Edit. 



XLIII. On Solids of greatest Attraction, or Repulsion. 

 To Mr. Tilloch. 



Sir, — Ouch cylindrical portions of a sphere as I treated 

 of in my former papers, lead to interesting results, re- 

 speclinf solids of greatest attraction ; as will be seen in the 

 third of the following propositions. I might have added that 

 proposition to my last letter, but ihoughTit would be better 

 to connect it with a general theory of solids of greatest 

 attraction. 1 am^ sir. 



Your obedient servant, 

 X. Y. 



Prop. I. 



Conceive a particle of matter, w, to be placed at the 

 origin of the three rectangular coordinates x, y, and z: — 

 What must be the nature of the solid (of given mass) 

 which shall exercise the greatest possible attraction on the 

 point m, in the direction of x: the force being as 4:{x, 

 y, z)* a function of x, y, and z ; and the density as some 

 other function A{x, y, z) of the same quantities. 



It is easy to see, that the force which the solid ex- 

 ercises, oo che point m, in the direction of x, is 



^^r f4(.v,y,r).A (.,y,,)iyz^^ j^^ ^^^^^ j^ /77j(x,y, *)xy i. 



J J J {¥1 + 1/2 + Z-i) 2 J J •J 



* This expression, for the force, need not be restricted to such functions 

 as are positive for all values of t, y and z ,• we may extend tlie inquiry to 

 those cases in which the particles exercl«e a repelling force; or an attract- 

 ing or repelling force according to their situation. 



Therefore, 



