Experiment t en the lateral Communication of Motion in Fluicli. , f^'j 



The ancients remarked, that a defcending tube applied to a refervorr increafer the expen- 

 diture*. Mariotte eftimated that the water iflTues through C Q_, fig. 7, with a velocity near- 

 ly the mean proportional^ between the velocities arifing from the two heights A B, A Cf . 

 Guillielmini fought for the caufe of this augmentation in the weight of the atmofphere, and 

 determined the velocity at C to be the fame as would arife from the whole height A C%. In 

 his reafoning he fuppofes that the prelTure at C is the fame for the ftate of motion as for that 

 of reft } which is not true. In the experiments he made upon this objedl, he paid no regard 

 either to the diminution of expenditure produced by the irregularity of the inner furface of~ 

 the tubes, nor the augmentation occafioned by the form of the tubes themfelves. By a 

 fihgular accidental concurrence, one of thefe errors compenfated for the other, I know of 

 no other decifive experiment on this head fince Guillielmini. I (hall, therefore, proceed to 

 eftablifh the propofition upon the principle of virtual afcenfion combined, with the preflure of 

 the atmofphere, and that in a manner which fhall be clear of every objeflion, of theory as well 

 as of experiment. 



Let B L K O reprefent a conical tube adapted to the form of the contrafled vein § ; the 

 cylindrical tube L C Q_K is of the fame diameter as the contracted part. The fluid ftratum, 

 L K, continuing to defcend through LC, tends to accelerate its motion, according to the 

 laws of gravitation ; and confequently when it paffes from L K to M N, it tends to detach 

 itlelf from the ftratum which follows, or in other words it tends to produce a vacuum 

 between L K and M N ; and the fame efFe£l takes place through the whole length of the 

 tube L C. The preflure of the atmofphere becomes a£live as far as is necefiary to prevent 

 the vacuum ; and its aiStion is alike both at the furface of the fluid at A, and at the inferior 

 extremity of the tube at C. At A it increafes the expenditure, and at C it deftroys the fum 

 of the accelerations which would be produced along L C, fo that the fluid remains con- 

 tinuous in the tube. 



Let T reprefent the time which the continuous column of fluid L C Q_K employs to pafs 

 tlirough the tube L C, whatever may be the velocity at L, and the fucceflive acceleration 

 from L to C. And if we fuppofe this fame column to return upwards from D to E, it 

 will pafs through the fpace D E = L C in the fame time T ; during which it will lofe all the 

 acceleration it acquired from L to C. The preflure of the column E D, continued for the time 

 T, is therefore the quantity required to deftroy the fucceffive acceleration from L to C, and 

 to prevent the fluid from ceafing to be continuous in the tube L C : confequently that part of 

 the preflure of the atmofphere which is exerted at C Q,to deftroy the fum of the accelerations 

 through L C, is equal to the prefllire of a column E D of a fluid, homogeneous to that of 

 the refervoir A B. And flnce the fame preflTure muft alfo be exerted on the furface A of the 

 refervoir, if we take F A = LC, the fluid at LK will poflefs the velocity which is proper 

 to the height FL = A Cj without confidering the retardation which the external inequali- 

 ties of the tube L C QJC muft produce. 



• Calix devexus amplius rapit. Frontin. de aquseduft. Art. 36, See alfo the Pneumatics of Hero, in tlie 

 mathcm. vet. cd. 1693, page 157. 



t Mouvemcfti des eaux, part. 3, difc. j. ' 



+ Epift. hydroftatic. Oper. torn. \. page iii. 



§ When I fpeak of the form of the contradted vein, I always mean to exprefs the conoid formed by the fluid 

 •iffuing from an orifice through a thin plate. 



Vol. n. — July 1798. A a Experiment 



