212 MEMOIR OF EATON HODGKINSON. 



This differential equation, uuder given conditions of the constants, is treated 

 in thip pa]jer in a very able manner, showing great command over the resources 

 of modern analysis, and facility in the use of the varied artifices employed in 

 the integration of differential equations. The results arrived at have been referred 

 to by the ablest writers of the age, Dr. Whewell and the Rev. Canon Mose- 

 lev — by the former in his '^ Analytical Statics/' where the solution of equation 

 (A,) as given by Mr. Hodglvinson, occupies a distinguished place ; by the latter 

 in his " Engineering and Architecture," in which the labors of our late friend 

 are honorably mentioned : 



'' This problem ap]3ears first to have been investigated by Mr. Hodgkinson in 

 the fifth volume of the ' Manchester Memoirs ;'• his investigation extends to tho 

 case in which the influence of the weights of the suspending rods is included." 

 After such testimony it would be presumption on my part to enter more into detail 

 on thispaper. To a modern student, however, the notation and procedure adopted 

 mav possibly contrast unfavorably with the notation and procedure which charac- 

 terize the elementary works of the present day. To such student, if there be 

 any, I would suggest that in forming an opinion on a paper like this, written 

 more than 30 years ago, it would be inifair to exclude tlie comparison of the state 

 of mathematical and physical science at that period with the present. It must 

 be remembered that Lord Brougham and his coadjutors in a great work have 

 done much to popularize and spread amongst their countrymen a knowledge of 

 the arts and sciences. These interesting subjects can now be read as they have 

 come from the hands of Euler, Lagrange, and Laplace, by means of cheap pub- 

 lications, which are within the reach of the humblest artisan. In consequence 

 of this, it is not high praise to state that questions in mathematics which could 

 have been accomplished with difhculty 30 years ago can now be readily solved 

 liy the present methods, which are now extensively known amongst the youth 

 of all ranks in society through the warming stimulant of competitive examina- 

 tions. In this statement I am anxious not to be misunderstood, and to guard 

 against giving an opinion as to the question " Has mathematical power increased 

 in the degree commensurate with the increase of mathematical learning f This 

 will form a nice question for the future historian of the inductive sciences to 

 detennine. I may, however, express my views on this debatable question so 

 far as to say that 1 have but little confidence in the products of unnatural growth 

 of any kind. 



There is a very marked difference in the mathematics of this and his former 

 paper " On the Strength of Materials;" The great battle between the dots and 

 the cVs had l)een fought at Cambridge University wdtli earnestness on both sides, 

 and, chiefly through the invincible courage and inexhaustible armory of Wood- 

 house, Peacock, Babbage, and Herschel, the d'S of Leibnitz wrested the victory 

 from the dots of Newton. The effects of this victory, which has produced a 

 great change in the mathematical literature of this country, are clearly seen in 

 this paper, the principles investigated in which are applied to the numerical 

 computation of the strength and strains of the Menai and Broughton suspension 

 bridges. 



"Theoretical and Experimental Researches to ascertain the Strength and 

 best Fonns of Iron Beams," (read April 2, 1830.) 



Whether we consider the theoretical exposition of the section of fracture, or 

 the faithfully recorded experiments and their practical dbductions, we must 

 regard this paper as the most valuable and original contribution to the history 

 of the strengjih of materials which this century can boast. There is mo work in 

 our language on the same subject which contains sounder theoretical views, and 

 there is none which can be more practical than it has been to meet the demands 

 of the engineers and the architect. From the theoretical expositions here given 

 of the neutral line, the experiments to determine the strongest beam were devised 

 and successfully carried out. 



