WITHDRAWN FROM THE ACTION OF GRAVITY. 681 



sidered has traversed the distance comprised between the con- 

 tracted section and the place which the middle of the line occu- 

 pies at the precise instant of rupture, is independent of the velo- 

 city of transference ; consequently, if the diameter of the orifice 

 does not change, this time will be constant whatever may be the 

 charge. Now when the movement is uniform, the space tra- 

 versed during a determinate time being in proportion to the 

 velocity, the above distance will be in proportion to V2gh, 

 consequently to \^h. As we shall frequently have occasion to 

 make use of this distance, we shall represent it, for the sake of 

 brevity, by D. 



Now it is easily understood that in our vein the length of 

 the continuous part does not differ sensibly from the distance D. 

 In fact, the continuous part terminates at the exact place at 

 which, in each line, the most elevated of the points of rupture of 

 the latter is produced ; for at the instant at which the rupture 

 takes place, the phases of transformation of all that portion which 

 is above the unit in question are less advanced (§ 69), and there- 

 fore it still possesses continuity, whilst all that below this point 

 is necessarily already discontinuous. Thus, on the one hand, the 

 continuous part of the vein commences at the orifice and termi- 

 nates at the place at which the most elevated point of rupture 

 of each filament is produced ; and, on the other hand, the distance 

 D commences at the contracted section, and terminates at the 

 point corresponding to the middle of the length of each of the 

 lines at the instant of their rupture. The continuous part then 

 takes its origin rather higher up, but also terminates a little 

 above the distance D ; the difference in the origins of these two 

 magnitudes and that of their terminations must consequently 

 partially compensate each other; and as these differences are both 

 very minute, the excess of one over the other will a fortiori be 

 very small, so that the two magnitudes to which they refer may, 

 as I have stated, be regarded, without any sensible error, as equal 

 to each other*. In virtue of this equality, the length of the con- 

 tinuous part of the vein which we ai-e considering will then ap- 

 parently follow the same law as the distance D, i. e. it will be 

 Very nearly proportional to \^h. 



Thus in the imaginary case of uniform velocity of transference, 

 we again recognise the first of the laws given by Savart, Now 

 it is clear that in a real vein the velocity will deviate from 



• We shall recur to this point, and shall then estahlisli it more clearly. 



