682 



SCIENCE 



[N. S. Vol. XL. No. 1036 



— Q.0000001684 cos 2X[Ki cos (Kt + arg„ K,) 

 + Oi cos (Oit + argo d) 



+ P, cos (Pit + argo P.) H ]. 



Here My Sj, K^, O^, Pj, denote abstract 

 numbers or coeflBcients of tidal constituents 

 bearing these names and are equal to 0.4543, 

 0.2114, 0.2652, 0.1886 and 0.0878, respectively. 

 The angles in the parentheses are the argu- 

 ments of the forces which give rise to the 

 various constituent tides. A denotes the lati- 

 tude of the place or station selected. 



The above expressions also denote the in- 

 stantaneous deviation of the vertical expressed 

 in radians (1 radian ^206265") • 



Let L denote the horizontal distance be- 

 tween the centers of the two tanks. Let 

 d denote the inside diameter of the small trans- 

 parent pipe used and I its length. Let O 

 denote the area of the water surface in either 

 tank. 



For convenience, consider here only the 

 principal periodic term of the lunar semi- 

 diurnal tide and let the two tanks be situated 

 upon the earth's equator. The foregoing ex- 

 pressions will enable one to make similar com- 

 putations for all terms given, for any latitude, 

 and for any orientation of the apparatus. 



At a time three lunar hours before the upper 

 or lower culmination of the mean moon, the 

 surface of the water in the eastern tank will 

 be L X 0.0000001684X0.4543 =.0.0000000765 L 

 units higher than the surface of the water in 

 the western tank. The reverse will be the case 

 three lunar hours after either meridian pas- 

 sage. 



The amount of water passing through any 

 cross section of the connecting pipe will be 



UL X 0.0000000765 



cubic units. 



If 2& denote the entire distance over which 

 the water in the glass section of the pipe 

 moves, we must have 



2b J X = flL X 0.0000000765; 



area tank 



. 26=LX0.0000000765X 



cross section small pipe ' 

 If this ratio be 10,000, then 



26 = 0.000765 L 



units, and if the length of L be 10,000 units 

 (say centimeters) then 



26 = 7.65 units (centimeters). 



Now the time required in making this trans- 

 fer of water is 6 lunar hours, or 22,357 seconds ; 

 .'. the average velocity in the small tube will 

 be 2&^ 22,357 = 0.00034 units per second, 

 and, because the disturbing force here used is 

 harmonic, the maximum velocity will be 

 26-^14,233 = 0.00054 units per second, and 



the maximum flux, 0.00054-(^^ cubic units per 



4 

 second. 



This small velocity in a pipe say 1 cm. in 

 diameter implies stream-line motion; and so 

 we can compute by Poiseuille's laws the flux, 

 or rate of discharge, under given or assumed 

 conditions as regards the diameter and lengti 

 of pipe and the difference of pressure at the 

 two ends of this pipe. The formula for this is 



cubic centimeters per second. In the first 

 place, assume that 



Pi — p, = X X 0.0000000765 gp. 

 Here p denotes the density of the water and is 

 about unity; 



^ 0.017 8 



^ l-f 0.3379 -1- 0.0002216/2 



denoting the temperature Centigrade; and 

 g = 981 centimeters per second. 



If 2 = 100 cm., and i = 10,000, the flux, 

 ignoring the resistance in the larger pipe, 

 would amount to 



_£ J_ 0.000765 

 8ii 16 100 ^ 



cubic centimeters per second, a quantity many 

 times greater than the maximum flux neces- 

 sitated by the water transference. 



For a pipe 100 meters long and of diameter 

 VIO centimeters, the flux will be the same as 

 for the small pipe one meter long just con- 

 sidered. 



From the above it can be seen that the 

 effect of all pipe resistance can be so reduced 

 by varying the diameters and lengths as to 



