4:6 HISTORY OF ACOUSTICS. 



tradiction between the earliest and the latest discoveries in acoustics? 

 And the answer must be, that these intermediate modes of vibration 

 are complex in their nature, and difficult to produce ; and that those 

 which were formerly believed to be the only possible vibrating con 

 ditions, are so eminent above all the rest by their features, their sim 

 plicity, and their facility, that we may still, for common purposes, con- 

 sider them as a class apart ; although for the sake of reaching a 

 general theorem, we may associate them with the general mass of cases 

 of molecular vibrations. And thus we have no exception here, as we 

 can have none in any case, to our maxim, that what formed part of 

 the early discoveries of science, forms part of its latest systems. 



We have thus surveyed the progress of the science of sound up to 

 recent times, with respect both to the discovery of laws of phenomena, 

 and the reduction of these to their mechanical causes. The former 

 branch of the science has necessarily been inductively pursued ; and 

 therefore has been more peculiarly the subject of our attention. And 

 this consideration will explain why we have not dwelt more upon 

 the deductive labors of the great analysts who have treated of this 

 problem. 



To those who are acquainted with the high and deserved fame 

 which the labors of D'Alembert, Euler, Lagrange, and others, upon 

 this subject, enjoy among mathematicians, it may seem as if we had 

 not given them their due prominence in our sketch. But it is to be 

 recollected here, as we have already observed in the case of hydro- 

 dynamics, that even when the general principles are uncontested, mere 

 mathematical deductions from them do not belong to the history of 

 physical science, except when they point out laws which are interme- 

 diate between the general principle and the individual facts, and which 

 observation may confirm. 



The business of constructing any science may be figured as the 

 task of forming a road on which our reason can travel through a cer- 

 tain province of the external world. We have to throw a bridge 

 which may lead from the chambers of our own thoughts, from our 

 speculative principles, to the distant shore of material facts. But in 

 all cases the abyss is too wide to be crossed, except we can find some 

 intermediate points on which the piers of our structure may rest. 

 Mere facts, without connexion or law, are only the rude stones hewn 

 from the opposite bank, of which our arches may, at some time, be 

 built. But mere hypothetical mathematical calculations are only plans 

 of projected structures ; and those plans which exhibit only one vast 



