C. GENERAL PHYSICS. I59 



which Hehnholtz adduces in support of his acoustical appli- 

 cations of Fourier's theorem is precisely in the condition of 

 the relations we have just described, viz., that in which the 

 chords of a piano are caused to vibrate sympathetically to the 

 elements which may exist in the note w^e sing over the strings 

 of the instrument. 



As the mathematician in his analysis decomposes seriatim 

 every point of the recurring curve into its elements, so the 

 physicist, in confirming the theorem of Fourier, should decom- 

 pose into its elementary harmonic vibrations the sonorous 

 motions which such curve represents and, indeed, reproduces 

 when it is drawn under a slit in a piece of paper which ex- 

 poses only a point of t*he curve at once. To do this it is re- 

 quired that only one vibrating point of the body should be 

 experimented on, and that the composite vibratory motion of 

 this point should be conveyed along lines to bodies vibrating 

 sympathetically to the elements of the composite vibration, 

 and that these sympathetically vibrating bodies should be 

 capable alone of giving simple or pendulous vibrations. 



To render assurance doubly sure. Professor Mayer, having 

 found two fibrils of the antennsG of a mosquito which vibrated 

 l)0\verfully to two different notes, measured these fibrils very 

 accurately under the microscope. He then constructed some 

 fibrils out of pine wood, which, though two or three feet 

 long and of the thickness of small picture-cord, had exactly 

 the same proportion of length to thickness as the fibrils of 

 the antennae of the mosquito. He found that these slender 

 pine rods or fibrils had to each other the same ratio of vibra- 

 tion as the fibrils of the mosquito. 



These experiments were also extended in a direction which 

 added new facts to the physiology of the senses. If a sono- 

 rous impulse strike a fibre so that the direction of the im- 

 pulse is in the direction of the fibre,, then the fibre remains 

 stationary. But if the direction of the sound is at risrht an- 

 gles to the fibre, the fibre vibrates with its maximum inten- 

 sity. Thus, when a sound strikes the fibrils of an insect, 

 those on one antenna? are vibrated more powerfully than the 

 fibrils on the other, and the insect naturally turns in the di- 

 rection of that antenna? which is most strongly shaken. The 

 fibrils on the other antennae are now shaken with more and 

 more intensity, until, having turned his body so that both 



