the direction of thM #ftdius, or t» VF; thenjjf we call R this 

 length, or the lra|^|^v#ct^ ^"^"ilii^^Q^^^lS^^^ 

 shall have ^ts ^, '^ s^ ' ^ su 



the values of R parallel to the axes are then ha^4>by the equa- 

 <^%ib tinobivo ei Ji rioiif// mo'ii j S bnc Y -fol vl miimia bnr. 



which we shall express simply as'«%A^, c% so that th^bqaq- 

 tion of the surface of elasticity will be, of the formt-uijqqB 3i 

 R2 = a^ cos^ X + ^'- cos2 Y i^^c^W^^f"^ sWuob 1o 

 'wiiere'TY Z now stand iox^^fi'AW'^^¥^^^^jWyi\i\i 

 ^^he axes or co-ordinates. . ,':... ' 



/ "Let us now imagine a molecule displaced and allowed to 

 vibrate in the direction of the radius 11, and retained in that 

 line, or at least let us neglect all that portion of its motion 

 which takes place at right angles to the radius vector. Then 

 the force of elasticity by which its vibrations are governed will 

 be proportional to R^, and the velocity of the luminous wave 

 propagated by means of them, in a direction transverse to 

 them (or at right angles to 11), will be proportional to R.^^^* 

 Of this extraordinary proposition the accomplished authBr 

 does not offer one syllable of proof or explanation. Whether 

 FresneFs writings are equally deficient, I am not aware; but 

 another eminent mathematical writer, the present Astronomer 

 Royal, after bestowing, as we may reasonably suppose, some 

 degree of diligence on the study of Fresnel's papers, appears 

 to have found nothing better in the way of a demonstration 

 than the following (vide Airy's Tracts, 2nd edition^ p. 341) : — 

 "To explain on mechanical principles the transmission of 

 a wave in which the vibrations are transverse to the direction 

 of its motion. '■. ,-, . ^ 



" In finjure adiomed let the lamt .. r. ? l u , ' 



dotsrepresenttheorigmal situations ,, ^^ K • .r 



of the particles ot a medium, arran- 

 ged regularly in square order, each » < » = ^ 8 a = X q. 

 line being at the distance h from the ' jy i = yv^S ^ != Y ! 

 next. Suppose all the particles in J -t^ = -^k So = S 

 each vertical line disturbed verti- , niavis Ikd^I laai an^ 

 cally by the same quantity, the dis- i^c^iJaM ciFjaqobvona 

 turbances of different vertical lines 93Blii/g & gsviaonoD Jxap 

 being different. Let s be the ho- rn^a^n h^iont^znoo \YlfpJl 

 rizontal abscissa of the second row, ,/Rcjij<!rJy lo eaxu srij 'to 

 X — h that of the first, and x + h .bt.nal c 9jlBl^8nojlD9ii| 

 tliat of the third ; let ti u^ and ii! be th^fqW^Bfifft^ 



