316 Mr. stokes, on THE FRICTION OF FLUIDS IN MOTION, 



If J be greater than 5 B, Et ought to be a little greater than E^. This appears to agree 

 with observation. Thus the following numbers are given by M. Lame*£, =8000, E.^ = 7500 for 

 iron; £, = 2510, E^ = 2250 for brass -f*. The difference between the values of JE, and E.^ is 

 attributed by M. Lame to the errors to which the observation of the small quantity e is liable. 

 If the above numbers may be trusted, we shall have 



A = 60000, B = 7500, =8 for iron ; 

 B 



A = 29724, B = 2250, — = 13-2] for brass. 

 B 



The cubical contraction k is almost too small to be made the subject of direct observation J, 



it is therefore usually deduced from the value of e, or from the coefficient of elasticity E 



k 

 found in some other way. On the supposition of a single coefficient E, we have - = ^ , but 



retaining the two, A and B, we have = — =9(1+—] — , which will differ greatly 



from # if — be much greater than 5. The whole subject therefore requires, I think, a careful 

 B 



examination, before we can set down the values of the coefficients of cubical contraction of 

 different substances in the list of well ascertained physical data The result, which is generally 

 admitted, that the ratio of the velocity of propagation of normal, to that of tangential vibrations 

 in a solid is equal to \/3, is another which depends entirely on the supposition that A - ^B. 

 The value of m, again, as deduced from observation, will depend upon the ratio of A to B; 

 and it would be highly desirable to have an accurate list of the values of m for different 

 substances, in hopes of thereby discovering in what manner the action of iieat on those substances 

 is related to the physical constants belonging to them, such as their densities, atomic weights, &c. 



The observations usually made on elastic solids are made on slender pieces, such as wires, 

 rods, and thin plates. In such pieces, all the particles being at no great distance from the 

 surface, it is easy to see that when any small portion is squeezed in one direction it has consider- 

 able liberty of expanding itself in a direction perpendicular to this, and consequently the 

 results must depend mainly on the value of B, being not very different from what thty 

 would be if A were infinite. This is not so much the case with thick, stout pieces. If 

 therefore such pieces could be put into a state of isochronous vibration, so that the musical 

 notes and nodal lines could be observed, they would probably be better adapted than slender 

 pieces for determining the value of mA. The value of m might be determined by comparing 

 the value of m A, deduced from the observation of vibrations, with the value of A, deduced 

 from observations made in cases of equilibrium, or, perhaps, of very slow motion. 



21. The equations (32) are the same as those which have betn obtained by different 

 authors as the equations of motion of the luminiferous ether in vacuum. Assuming for the present 

 that the equations of motion of this medium ought to be determined on the same principles as 

 the equations of motion of an elastic solid, it will be necessary to consider whether the equations 

 (32) are altered by introducing the consideration of a uniform pressure 11 existing in the medium 



• Ijani^ fours de Physiqur^ Tom. i. prcssibility of solids which would be obtained from I*oisson'» 



+ These numbera refer to the l''rench units of length and weight 1 theory is in sonte cases as much as 20 01 .^0 limes too ^reat. See 



■*■ I tind however that direct experiments have been made by the Repot t 0/ the British Association for 1H33. j). '.Vy\ or Arvhnei 



Prof. Oersted, According to tliese experiments the cubical com- 1 des decouverles, S^-c for 1U34, p. 94. 



