TRANSACTIONS OF THE SECTIONS. 6 



are sufficiently general for functional symbols, and from particular forms of which 

 by mathematical processes other truths may be derived. Such are the subjects of 

 Light, Heat, Sound, Electricity, Magnetism ; we propose to take these subjects in 

 the latter days of this week, and the first day of next. We shall, of course, con- 

 sult the convenience of contributors ; but it will tend, we think, to the orderly 

 arrangement of our business if this order can be adopted. Vast indeed in their 

 subjects are these sciences; and as discoveries are being daily made in them, 

 we have a right to expect some interesting communications, either in the way 

 of mathematical deduction from received laws, or as mathematical explana- 

 tions of observed phenomena, or as simple experiments. I cannot help observing 

 here the advantage of combining these sciences in the same Section with pure 

 mathematics ; it seems to indicate that the laws of all are to be brought to the 

 same test, — to the never-failing, to the unerring accuracy of measurement and num- 

 ber ; we show hereby the character of the knowledge we are in search of; not for- 

 tuitous observation, but precise laws. The mind will wander in its imagination ; 

 there is, indeed, no boundary to it ; once, however, bring it back to the severe test 

 of number and weight and" measurement, and the discovery or the observation 

 becomes valuable for its precision ; it thus leads to general laws, and sound mathe- 

 matical reasoning derives from them the results they are pregnant with. 



And, finally, we come to the facts of meteorology and its kindred subjects, many 

 of which are scarcely yet brought within any law at all ; analogies have been traced, 

 and concurrent events have been indicated in many cases ; little, however, has been 

 done towards a satisfactory proof of a connexion between cause and effect. It is 

 true that curves are traced, which purport to exhibit these effects ; and they do so 

 most graphically ; but, as mathematicians say, these curves are traced only hyjmints, 

 and the law is not known, or, in other words, we do not know the equation of the 

 curve ; so long as this is the case, our knowledge lacks precision. These papers, 

 however, are frequently valuable, because they supply us with accurately observed 

 facts, which will doubtless hereafter be brought within a law. This, however, I 

 suppose at present to be the state of the case ; but we must not despise the lesser 

 light because we have not the greater. I cannot pass over this class of papers (papers 

 of observed facts) without alluding to the loss which we all feel in the death of the 

 late able Professor of Geometry, Professor Baden Powell. For some years past 

 has he continued his reports on the meteors or falling stars, or whatever you call 

 them ; this year we have his last report, which, indeed, he has not lived to finish, 

 but has been placed in the hands of Mr. Glaisher, and completed by him. In 

 some of these subjects we shall, I hope, obtain large accessions to our knowledge. 



Some few years ago I remember reading a complaint made by an eminent philo- 

 sopher on the decay of mathematical knowledge in Great Britain, and especially in 

 that of physico-mathematical knowledge. It is not my duty to make invidious 

 distinctions ; but I am sure I am repeating the now common opinion of foreigners 

 when I tell you that that complaint was made in quite the infancy of some of 

 our older philosophers, and before the days of Cayley, Sylvester,' Boole, Mac- 

 cullagh, Stokes, W. Thomson, and Adams. To this revival of science amongst 

 us, doubtless, many causes have contributed ; and I believe that the periodical nieet- 

 ings of this Association have done good service towards that revival ; we have 

 hereby become acquainted with others who are engaged in the same pursuits as our- 

 selves, and stores of knowledge are communicated. Let us, however, bear in mind 

 that our Association is formed for the advancement of science, and that we do not 

 meet to hear of old things again in the old form; our motto is "progress." Old 

 things we do not discard, for they may be put before us in new forms : but we meet 

 especially to promote the advance of the boundaries of natural knowledge, and we ask 

 our members and others to lay before us the results of their investigations. And not 

 only m the papers which shall be read, but also in the elucidation of any difficulties 

 which authors may favour us with, and in the discussions which it is my duty to 

 invite you to take upon these papers, will additions to our knowledge be made • 

 and many remarks will, I venture to think, be made pregnant with matter for 

 thoughtful meditation hereafter. In all these discussions difference of opinion 

 will doubtless arise ; but I am sure that a spirit of friendly and mutual concession 

 will prevail ; and that in our search after truth we shall gladly and readily attribute 

 to those who differ from us the same pure motives which we claim to ourselves. 



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