I 



TRANSACTIONS OF SECTION A. 439 



When an ixnexpected eifect is observed, the question ■will arise whether or not 

 an explanation can be found upon admitted principles. Sometimes the answer can 

 be quickly jjiven ; but more often it will happen that an assertion of what ought 

 to have been expected can only be made as the result of an elaborate discussion of 

 the circumstances of the case, and this discussion must generally be mathematical 

 in its spirit, if not in its ibrm. In repeating-, at the beginning of the century, the 

 well-known experiment of the inaudibility of a bell rung in vacuo, Leslie made the 

 interesting observation that the presence of hydrogen was inimical to the produc- 

 tion of sound, so that not merely was the sound less in hydrogen than in air of 

 equal pressure, but that the actual addition of hydrogen to rarefied air caused a 

 diminution in the intensity of soimd. How is this remarkable fact to be explained ? 

 Does it prove that, as Ilerschel was inclined to think, a mixture of gases of widely 

 diiferent densities difi'ers in its acoustical properties from a single gas ? These 

 questions could scarcely be answered satisfactorily but b}' a mathematical investi- 

 gation of the process by which -sibratious are communicated from a vibrating solid 

 body to the surrounding gas. Such an investigation, founded exclusively upon 

 principles well established before the date of Leslie's observation, was imdertaken 

 years afterwards by Stokes, who proved that what Leslie observed was exactly 

 what ought to have been expected. The addition of hydrogen to attenuated air 

 increases the wave-length of vibrations of given pitch, and consequently the 

 facility with which the gas can pass round the edge of the bell from the advancing 

 to the retreating face, and thus escape those rarefactions and condensations which 

 are essential to the formation of a complete sound-wave. There remains no reason 

 for supposing that the phenomenon depends upon any other elements than the 

 density and pressure of the gaseous atmosphere, and a direct trial, e.g. a compari- 

 son between air and a mLxture of carbonic aniiydride and hydrogen of like density, 

 is almost superfluous. 



Examples such as this, which might be multiplied ad libitum, show how diffi- 

 cult it often is for an experimenter rightly to interpret his results without the aid 

 of mathematics. It is eminently desirable that the experimenter himself shoidd be 

 in a position to make the calculations, to which his work gives occasion, and 

 from which in return he would often receive valuable hints for fiu'ther experiment. 

 I shoidd like to see a course of mathematical instruction arranged with especial 

 reference to physics, within which those whose bent was plainly towards experi- 

 ment might, more or less completely, confine themselves. Probably a year spent 

 judiciously on such a course woidd do more to qualify the student for actual work 

 than two or three years of the usual mathematical curricidum. On the other side, 

 it must be remembered that the human mind is limited, and that few can carry 

 the weight of a complete mathematical armament without some repression of their 

 energies in other directions. With many of us difficulty of remembering, if not 

 want of time for acquiring, would impose an early limit. Here, as elsewhere, the 

 natural advantages of a division of labour will assert themselves. Innate dexterity 

 and facility in contrivance, backed by unflinching perseverance, may often conduct 

 to successful discovery or invention a man who has little taste for specidation ; and 

 on the other hand the mathematician, endowed with genius and insight, may find a 

 sufficient field for his energies in interpreting and systematising the work of others. 



The difierent habits of mind of the two schools of physicists sometimes lead 

 them to the adoption of antagonistic views on doubtful and difficult questions. 

 The tendency of the purely experimental school is to rely almost exclusively upon 

 direct evidence, even when it is obviously imperfect, and to disregard arguments 

 which they stigmatise as theoretical. The tendency of the mathematician is to 

 overrate the solidity of his theoretical structures, nnd to forget the narrowness of 

 the experimental foundation upon which many of them rest. 



By direct observation, one of the most experienced and successful experimenters 

 of the last generation convinced himself that light of definite refrangibility was 

 capable of further analysis by absorption. It has happened to myself, in the course 

 of measurements of the absorbing power of various media for the different rays of 

 the spectrum, to come across appearances at fii-st sight strongly confirmatory of 

 Brewster's views, and I can therefore understand the persistency with which lie 



