MEMOIR OF THE LATE PROF. E. HODGKINSON^ F.R.S. 165 



by Mr. Hodgkinson in the fifth volume of the ' Manchester 

 Memoirs -y his investigation extends to the 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 this paper. To a 

 modem student, however, the notation and procedure 

 adopted may possibly contrast unfavourably with the no- 

 tation and procedure which characterize 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 thirty years ago, it 

 would be unfair to exclude the 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, La- 

 grange, and Laplace, by means of cheap publications, 

 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 ac- 

 complished with difficulty thirty years ago can now be 

 readily solved by the present methods, which are now 

 extensively known amongst the youth of aU ranks in 

 society though the warming stimulant of competitive exa- 

 minations. 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 mathe- 

 matical learning V^ This will form a nice question for the 

 future historian of the inductive sciences to determine. I 

 may, however, express my views on this debatable question 

 so far as to say that I have but little confidence in the pro- 

 ducts of unnatural growth of any kind. 



