HYDRODYNAMICS. 



563 





la vit Arcnimtde, Berl. 1767. Euler, ffm. Comment. 

 Petrop. torn. v. p. 259- Ferguson'* Lecturer, vol. ii. 

 p. 113. Pattu, Journal de* Mine*. Nov. 1815, vol. 

 xxxviii p S'Jl. Eytelwein's Handbuc/i tier Mechanik, 

 Berl. 1805, chap. xxi. Gregory 'i Mechanics, voL ii. 

 p. 348. 



S. On the Spiral Pump, or Zurich Machine. 



Thi machine, represented in Plate CCCXXIII. Fig. 

 1, was invented about 1746 by Andrew VVirtz, a 

 pewterer in Zurich, who erected it for a dye-houe 

 on the river Limmat. It consists of a spiral pipe 

 cccxzin. ABCDEF, either coiled round in one plane, a* shewn in 

 Ki. 1. ' t* Figure, or arranged round the cimimferenceofacone 

 or a cylinder. The interior end of the spiral G. or the re- 

 mote end of it, is connected by a watertight joint to an as- 

 cending pipe GH, in which the water is to be raised. 

 When this spiral, immersed in the water MN, which is 

 to be raised, is put in motion in the direction ABC I), the 

 coop BA, which begins to widen from C, takes in a 

 portion of water. As the scoop emerges, this water 

 passes along the spiral, driving the air before it into 

 the pipe GH. where it escapes. Air is again admitted 

 into the scoop after it emerges, and when the scoop has 

 performed one revolution, it again takes up another 

 portion of water, which is driven along the spiral as 

 before, and is separated from the first portion by a co- 

 lumn of air of nearly equal length. By continuing to 

 turn the spiral, a second column of water and another 

 of air will be introduced, and so on. Now, the water, 

 en every turn of the spiral, will hate both its ends ho- 

 rizontal, anil the included air will have its natural den 

 sity. But as the diameter of the spirals diminish to- 

 wards the centre, the column of water, which occupied 

 a semicircle in the outer spiral, will occupy more and 

 more of the inner spirals as they approach to the centre 

 ('. till there will be a certain spiral, of which it will oc- 

 cupy a complete turn. Hence it will occupy more than 

 the entire spiral within this spiral, and consequently 

 the water will run back over the top of the succeeding 

 spiral, as at No. 4. into the right hand side of spiral 

 ;. The water in spiral No. S. will consequently 

 be pushed upwards till it runs over at S into the right 

 hand aide of spiral I and so on till some of the 



water escapes at the scoop A into the cistern MN. 

 When the water enters the pipe GH at G, and rises a 

 little in it, the escape of the air is prevented when the 

 scoop AB takes in its next quantity of water. ' Here 

 then," as L)r Robison has remarked, " are two columns 

 of water acting against each other by hydrostati< 

 lure, and the intervening column of air. They must 

 cuiupiess the air between them, and the water and air 

 columns will now be unequal This will have a ge- 

 neral tendency to keep the whole water back, and cause 

 it to be higher on the left or rising side of each spire, 

 than on the right descending side. The excess of 

 height will be just such as produces the compression 

 of the air between that and the preceding column of 

 water. This will go on increasing as the water mounts 

 in the rising pipe ; for the air next to the rising pipe 

 is compressed at its inner end with the weight of the 

 whole column in the main. It must be as much com- 

 pressed at its outer end. This must be done by the 

 water column without it ; and this column exerts this 

 pressure, partly by reason that its outer end is higher 

 than its inner end, and partly by the transmission of 

 the pressure on its outer end by air, which U similarly 

 compressed from without. And thus it will happen, 

 that each column of water being higher at its outer 

 than at its inner end, compreues the air on the water 



column beyond or within it, which transmits this pres- Spin>! 

 sure to the air beyond it, adding to it the pressure ari- 

 sing from its own want of level at the ends. There- p^ AT C 

 fore, the greatest compression, viz. that of the air next cc< -xu i 

 the main, is produced by the sum of all the transmitted y, g- ^ 

 pressure*, and these are the sum of all the differences 

 between the elevation of the inner ends of the water 

 columns above their outer ends ; and the height to 

 which the water will rue in the main will be just equal 

 to this sum." 



The spiral pumps seem to have remained long un- History -" 

 noticed. They were erected, however, at Florence in h spir.il 

 1778, with the improvement suggested by Bernoulli, of P um P- 

 having the spiral coiled on the circumference of a cy- 

 linder, as represented in Fig. 2. In 178t, a spiral pump Pig. t. 

 was erected at Archangelsky, near Moscow, which raised 

 a hogshead of water in a minute to the height of 74 feet, 

 and through a pipe 760 feet long. It has not yet been 

 ascertained whither the plane, the cylindrical, or the co- 

 nical spiral is best. The only p.actical difficulty consists 

 in making the joint perfectly water-tight. The ma- 

 chine erected at Florence had its spiral cylindrical. Its 

 diameter was 10 feet, and that of the pipe 6 inches. 

 The enlarged part occupied f of the circumference, and 

 was 7-fy inches wide at the outer end. The enlarged 

 part contained (>844 English cubic inches. The spiral 

 revolved six times in a minute, and raised 2-J cubic feet 

 of water 10 feet high in a minute. Eytelwein considers 

 this as a very powerful machine, and well deserv-ng 

 the attention ot the engineer. The length of the pipe 

 becomes extremely cumbersome when the water is to be 

 raised through great height. l)r Young found that 

 100 feet oi pipe J of an inch in diameter was necessary 

 for a height of 140 feet; and he considers that the 

 machine would succeed better if the pipes were entirely 

 of wood, or of tinned copper, or even of earthen- ware. 

 See Sutler's Samnlungm t'crmuchlcn Schri/'ten, 1754; 

 Daniel Bernoulli, N<*>. Comment. Pdrop.' \111, torn. 

 xvii. p. 249 ; Bail.) ' Muchinit ap^rnvra oj by the So- 

 ciety <>J A It, vol. i. p. Ijl ; Dr lloldson's Suttem o/' Afc- 

 c/ianic'ii I'ttUotovhy ; F.ytelwein IJiindbiicn tier .'/ c'ta- 

 nik, tec ; and I )r Thomas Young's Natural Phi/atO* 

 pliy, vol. i. p. S3O, &C. 



4. Dttcription of Piioft Bent Tube JOT measuring the 

 ' oj Water. 



One of the most ingenious instruments for measuring Pitoi'- LC..I 

 the velocity of water, is the tub' recum-be", or bent tube. 

 tube, invented by M. Pilot, and described in the Me- 

 moirs of the Academy of Sciences for 1732. It is re- 

 presented in Plate CCCXXIII. Fig 3, and consists of a F 'B- ' 

 prism of wood ABCDEF, one of the angles of which 

 U prevented to the current On the hinder face BCFE 

 are fixed two tubes of glass parallel to each other, and 

 having graduated scale between them ; one of them, 

 vis. M NO. being bent into a right angle at O, so that 

 the part M N may pass through the prism horizontally. 

 When tins instrument is plunged in a running stream, 

 the general level of the current is shewn by the rise of 

 the water in the straight tube I'Q, while the height of 

 the water in the bent tube MNO Incomes a measure of 

 the force of the stream. The difference between these 

 heights will therefore be the height due to the veloci- 

 ty. In the practical use of this instrument, it is how- 

 ever difficult to fix it sufficiently steady, to prevent the 

 water from oscillating in the tubes. 



M. Uu Buat having examined the instrument experi- improved 

 mentally, touiul that it could be trusted no farther than to by Du 

 give the ratio of different velocities. He therefore sup- Bu> ~ 

 pressed the tube PQ altogether, and substituted, in place 



