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LXII. Abstract of an Essay by M. Girard " On the Resistance 

 of Cast-iron in relation to its Use for Conduit Pipes and the 

 Boilers of Steam-Engines." Communicated by Mr. Thomas 

 Tredgold. 



A PAPER with the above title forms the second article of 

 the Annates dc Chimied dc Physique for December last, an 

 Abstract of which will be interesting to our mechanical readers; 

 and pei'haps that interest will be somewhat increased if we 

 contrast the state of our knowledge of the subject in this country 

 with that which is exhibited in the paper before us. 



Mr. Girard commences the paper by stating that the shaft of 

 the water-wheel of the machine at the bridge of Notre Dame, 

 having failed from age ; it appeared to him that it would be 

 an advantage to replace it by a shaft of cast-iron, wliich would 

 render the chances of needing repairs much less frequent; yet 

 giving the assurance of long dui'ation. 



The shaft which it was proposed to replace was of oak 7*80 

 metres in length (25^ feet), and 70 centimetres square (27^ 

 inches), being one of those pieces of timber which it is rather 

 diflicult to pi-ocure free of defects on account of its magni- 

 tude ; and on that account a shaft of cast-iron could be more 

 expeditiously procured. This led Mr. Girard to inquire what 

 dimensions and what form should be given to the new shaft, 

 so that it might be capable of resisting, with a given excess of 

 strength, the different forces which would act upon it; at the 

 same time that it should be as light as possible *. 



Galileo, he remarks, was the first who pointed out that hol- 

 low cylinders, such as the bones of animals, and the stems of 

 certain 'plants, were capable of much greater resistance to 

 fracture than solid cylinders of the same substance, when 

 formed of the same quantity of matter and of the same weight. 

 It was cleai', consequently, that the shaft of cast-iron ought to 

 be a hollow cylinder f. 



But, says Mr. Girard, among all the hollow cylinders of the 

 same length, and same quantity of matter, there is one which 

 when su))ported horizontally, at its extremities, presents the 

 greatest jiossible degree of resistance to a force acting at the 

 middle of its length to cause fracture. And the hollow cylin- 

 der endowed with this property may be easily found, by ap- 

 jjlying the known formula of the resistance of solids in the 

 hypotheses of Mariotte and Leibnilz, and the ordinary me- 



* Shafts arc usually calculated by the resistance to flexure. (See Trecl- 

 golil on Cast-iron, art. 219 and 221.) 



f Hollow cylinders have often been employed for shafts in tills coiinfr_v, 

 and have been described m practical works which have been long before 

 the British public. 



thods 



