,^ 



192 On the Flow of Elastic Fluids through Orifices. 



wiiere they are respectively delineated by a curve. The upper 

 curve represents the densities or elastic forces in the chamber, as 

 found by experiment ; the next curve those due to the new the- 

 ory, and the lower curve those due to the old theory. 



Notwithstanding the near approximation of the experimental 

 results to those due to the new theoryj there is yet a small but 

 distinct deviation, which holds throughout. This deviation indi- 

 cates either that there is some cause affecting the flow which the 

 theory does not lake into the account, or that in the structure of 

 the apparatus or in trying the experiment, there was some failure 

 10 comply with the requisite conditions. 



Although the apparatus was rude in its structure, yet care had 

 been taken to secure a compliance with the conditions on which 

 the experiment was based; and in conducting the experiment I 

 was assisted by my friend^ Prof A, C. Twining^ a gentleman dis- 

 tinguished for his accuracy in such matters. The experiment, 

 moreover, was several times repeated, with no important differ- 

 ence in the results. For these reasons, in seeking the cause of the 

 deviation, my first inquiry was whether it might be attributed 

 to a change in the ratio of elastic force to density; the theory 

 being predicated on the assumption that this ratio is constant. It 

 has been ascertained by experiment, that when air is condensed 

 and then suffered to lose the heat evolved by condensation, the 

 ratio of its elastic force to its density will be diminished. Hence 

 it is certain that a part or the whole, or possibly even more than 

 the whole heat evolved by condensation will be required to pre- 

 vent that ratio from being diminished. Still, however, it has gene- 

 rally been assumed by philosophers (I know not on what grounds) 

 that if air is suddenly condensed, so as not to allow the heat 

 evolved by condensation to escape, the ratio of elastic force to 

 density will be increased. This assumption was made by Laplace 

 when he attributed to this cause, in part, the velocity of sound. 

 Let us suppose then, for the present, that in sudden condensation 

 the ratio of elastic force to density is increased. It will then fol- 

 low that in sudden expansion^ the ratio of elastic force to density 

 will be diminished. But if that ratio were diminished, then the 

 deviation in the table should be in the opposite direction ; that is, 

 the experimental results, instead of being greater than the theo- 

 retical, should be less. The deviation, therefore, is not accounted 

 for by this supposition ; on the contrary, the experiment seems to 

 prove that the ratio is not diminished by expansion, and therefore 

 cannot be increased by condensation, as Laplace supposed. 



Let us next take the contrary supposition, viz., that the ratio 

 of elastic force to density is increased by expansion. This would 

 cause a deviation in the same direction as we find in the table. 

 In order to ascertain whether the deviation in question is due to 

 this cause, we must next inquire whether a deviation arising from 



