f 



k 



4 



On the Flora of Elastic Fluids through Orifices. 193 



this cause, would vary in the same manner throughout the table, 

 as does the observed deviation. Now if we go through the ta- 

 ble and assign for each observation severally, the manner in which 

 the ratio of elastic force to density must increase, in order to sat- 

 isfy that observation, we shall find very nearly one and the same 

 increment of the ratio demanded for all the observations. Hence 

 if we attribute the deviation to this cause we should be obliged 

 to conclude that one and the same change in the ratio takes place, 

 whether the expansion be greater or less. But such a conclusion 

 is obviously inadmissible. We cannot, therefore, attribute the 

 deviation in question to a change in that ratio, either by increase 

 or diminution. 



Nor can we ascribe the deviation to that which is the chief 

 cause of deviation from theory in the case of the flow of liquids^ 

 viz., the contraction of the stream in passing an orifice. For if 

 that cause operated, it would affect the flow in the same ratio in 

 both orifices, and therefore would not. in this case, affect the indi- 

 cations of the mercurial columns. Moreover, I think it can be 

 shown, from considerations a priori^ that the cause which produ- 

 ces the contraction of the stream in liquids, could not operate to 



affect the flow of expansible fluids. 



d 



causes above named, my next inquiry was, whether a difference 

 m the sizes of the orifices (hitherto assumed to be equal) would 

 cause a deviation corresponding to that in the table. In examin- 

 ing this point, 1 found that the experimental results would be 

 very nearly satisfied throughout the table, by the assumption that 

 the area of the second orifice was less than that of the first, in 

 about the ratio o( -933 to 1. As the two orifices had been made 

 as nearly equal as they could be by forcing the same steel plug 

 through both, I was confident that, as originally formed, they 

 could not differ to this extent. But it occurred to me that some 

 accidental circumstance might have occurred to diminish the in- 

 ner orifice, and I suspected that the workman, in handling the 

 brass plate after the orifice was made, had got dirt into it, and 

 had omitted to cleanse it before soldering on the outer plate. To 

 ascertain whether such was the case, I divided the tube near the 

 second orifice, and, upon examining it with a microscope, discov- 

 ered that there was dirt adhering around its inner periphery suffi- 

 cient, I think, to cause a diminution of its area to the extent 

 above named. Unfortunately this discovery was made after the 

 arrangements for trying the experiment had been removed; and 

 I have not since fi^und leisure to replace rhem and try the exper- 

 iment anew. But for this accidental circumstance no doubt there 

 ^ould have been a still nearer approximation of the experimen- 

 tal results to those derived from the formula. The coincidence, 

 however, is sufficiently near to establish the truth of the new 



Second Series, VoL XII, No. 35.— Sept., 1861. 25 



