Mr. Giravd o7i the Resistance of Cast-Iron^ 271 



thods of maxima and minima, to be that of which the exterior 

 diameter is to the interior diameter; nearly as 112 is to 51, or 

 a proportion more easily remembered, as 11 : 5.* 



While occupied by the above inquiiy, Mr. Girard says he 

 was naturally led to resume the question of the resistance of 

 conduit pipes to the pressure of the water in them, a question 

 which gave occasion for the researches which Mariotte made 

 on the resistance of solids and to the hypothesis he substituted 

 for that of Galileo f . 



Mariotte made some experiments on the resistance of pipes 

 of lead, and tinned iron, h'om which he deduced a practical 

 rule for determining the thickness: but, continues Mr. Girard, 

 that rule is not founded on strict demonstration ; and though 

 the occasion of applying theory usefully to this particular 

 case of the resistance of bodies, presents itself frequently, 

 no geometer, at least to his knowledge, has yet investigated it 

 with the necessary strictness. 



In assigning practical rules, he observes, we should always 

 calculate the resistance for the most unfavoiu'able circum- 

 stances ; since the excess of force which this mode leads us to 

 give to bodies, only causes small inconveniences when they are 

 not destined to form some of the moving parts of a machine. 



Hence he supposes the pipe to be cylindrical, in a hol'i- 

 zontal position, and closed at the ends by two plates adhering 

 to the perimeter of the pipe. 



He also supposes the pipe to be filled with a fluid which 

 presses on its sides with all the weight of a column of which 

 the height is given ; and the height of the column of fluid 

 sufficient to burst the pipe by its pressure. 



But the whole resistance to fracture will in this hypothesis 

 be composed of the resistance of the pipe and that of its ends: 

 consequently he supposes, in order to abstract the effect of the 

 ends, that the ends are inadherent to the sides, but in intimate 

 contact so as to perfectly close the cylinder, and yet offer no 



* This inaximum Iuls place only in the imaginary condition that the 

 axis of equilihriiiin or neutral axis is a tangent to one of the surfaces of 

 the cylinder: and that such a condition must be imaginary is evident ; fin- 

 it can only happen when the material is absolutely incomijrcssible at that 

 axis. In experience we find the neutral axis at the middle of the deplh 

 in a beam strained in this manner, and there is no maxiimnn in this case, 

 the expansion of the tni)e being limited only by the thickness necessary to 

 preserve the section of a circular form. 



f Whoever takes the trouble to examine what Mariotte has written on 

 the subject will find that his ex])eriments led him to the corrett theory of 

 resistance, viz. that which is founded on the compression as well as exten- 

 sion of the body. Mr. fiirard is therefore not correct in ascribing to him 

 the hypothesis whicii leads to the erroneous result we have previously 

 noticed. 



friction 



