148 MEMOIR OF THE LATE PROF. E. HODGKINSON, F.R.S. 



The most novel and important conclusions here given 

 are as follows : — 



The strengths of long pillars of cast iron, wi'ought iron^ 

 cast steel_, and Dantzic oak, of the same dimensions, are in 

 proportion to the numbers looo, 1745, 2518, 109. Cast 

 iron is not reduced in strength when its temperature is 

 raised to 600°. 



The sets, in cast-iron beams, vary nearly as the square 

 of the force of deflection ; hence any force, however small, 

 will injure the elasticity of cast iron. The strength in tons 

 of beams approaching the best form is measured by the 

 formula, 2'j66ad-^l, where «= area of section of bottom 

 flange in the middle, d= the depth in inches of the beam, 

 and /= the distance in feet. 



A general investigation of the position of the neutral 

 line is given on tlie principle that the forces of extension 

 and compression of a particle vary as any function of its 

 distance from the neutral line. This includes every hypo- 

 thesis which has been proposed in order to compute the 

 strength of material bodies subjected to strains. 



Birth and Education. 



As I have already stated, Mr. Hodgkinson was bom at 

 Anderton, Cheshire, in the year 1789. His father, a re- 

 spectable farmer, died of fever when his son Eaton was 

 about six years of age, leaving Mrs. Hodgkinson with two 

 daughters and a son. 



On his father^s decease, his mother determined to con- 

 tinue the farm ; and by industry, thriftiness, and business- 

 like habits she was enabled to educate her children re- 

 spectably, and to send her son to the Grammar School of 

 North wich. 



At this school he received the rudiments of a classical 

 education, as he studied the Latin, Greek, and Hebrew 



