MEMOIR OF EATON HODGKINSON. 213 



The result was the discovory of the cclebmted '' Ilodg'kinson's Beam," that 

 is, the strongest beam which can be made from a given weight of material 

 and a given length and depth of beam. George Stephenson, who was at this 

 time chief engineer to the Manchester and Liverpool Railway Company, took 

 great interest in these experiments, and he was frequently present when they 

 were made. Several pages are devoted again to tlie suWject of the neutral 

 line, indicating, from tlie manner of its discussion, that the subject was not at 

 this time clearly fixed in the minds of the foremost investigators ; and no one can 

 read these pages, and the views of Professor Barlow, without feeling convinced 

 that the learned professor has scarcely done full justice to Mr. Hodgkinson in 

 reference to the fixing of the neutral line in the section of fracture. The state- 

 ment of Professor Barlow, in his report to the British Association, and in his 

 essay " On the Strength of Materials," would lead to the conclusion that Mr. 

 Hodgkinson had only rectified a small error into which he. Barlow, had inad- 

 vertently fallen. This is not a complete statement. Mr. Hodgkinson did much 

 more than correct a slight error in an adopted theory ; he showed the fallacy of 

 the theory which it aj)i)ears Professor Barlow had olitained from M. Duleau, 

 a distinguished French writer. There can be no doubt that Mr. Hodgkinson 

 was the first to give the correct theory of fixing mathematically the jjosition of 

 the neutral line. ]\Ir. Ilodgkinson's paper was published in 1822, and we find, 

 in 1824, Dr. Whewell, in his '' j\[echauics," stating, " I woidd gladly have given 

 a section on the strength and fracture of beams had there l»een any mode of 

 considering the sul>ject which combined simplicity with a correspondence to facts. 

 The common theory, which supposes the material incapable of com])ression, is 

 manifestly and completely false ; and though Mr. Barlow's experiments and 

 investigations give us much information, thej' do not appear to lead to any con- 

 clusions sufficiently general and simple to authorize us to present the subject as 

 an elementary one." (See Preface, page xii, Whewell's " JNlechanics," 1824.) 

 It is obvious that the learned professor had not seen Mr. Hodgkinson's paper at 

 this time, or he would have given, without doubt, in this place the same chapter 

 which he published in his " Analytical Statics" in 1833.* 



The first series of experiments in this paper show that in cast iron the exten- 

 sions and compressions from equal forces are nearly equal. Tredgold asserted 

 that the same force which destroyed the elasticity of a body by tension would 

 destroy it bj' compression. The next two experiments disprove this assertion, 

 and show that the resistance to compression in cast iron is greater than to exten- 

 sion. '^J'his discovery is important, and modified considerably the best con- 

 structed cast-iron beams of this period. The succeeding experiments, which are 

 many and carefully recorded, were devised for the purpose of extending the con- 

 sequences of this practical discovery. And I shall liere avail myself of the 

 Ptev. Canon Moseley's concise and able exposition of the experiments and reason- 

 ings of Mr. Hodgkinson by which he established the best form of cast-iron beam: 

 " Since the extension and the compression of the material are the greatest at 

 those points which are most distant from the neutral axis of the section, it is evi- 

 dent that the material cannot be in the state bordering upon rupture at every 

 point of the section at the same instant, unless all the material of the com- 

 pressed side be collected at the same distance from the neutral axis, and like- 

 wise all the material of the extended side, or unless the material of the extended 

 side and the material of the conq)ressed side be respectively collected into two 

 geometrical lines parallel to the neutral axis — a distribution manifestly impossi- 

 ble, since it would ])roduce an entire separation of the two sides of the beam. 



''The nearest i)racticable ai)i)roach to this form of s((ction is that represented 

 in the acconi[)anying figure, where the material is shown c(dlected in two thin 



* I have Dr. Whewell's authority, in a letter which I received from him a few days ago, 

 in stating that he had not scon Mr. Ilodgkiusoa's paper when ho wrote his " Mechauics" of 

 1624. 



