II. CALCULATING MACHINES. 11 



40. Tide Calculating Machine. 



Sir William Thomson, F.R.S. 



The object is to predict the tides for any port for which the tidal con- 

 stituents have heen found by the harmonic analysis from tide gauge obser- 

 vations : not merely to predict the times and heights of high water, but the 

 depth of water at any and every instant, showing it by a continuous curve, 

 for a year, or for any number of years in advance. 



This object requires the summation of the simple harmonic functions repre- 

 senting the several tidal constituents to be taken into account, which is per- 

 formed by the machine in the following manner : For each tidal constituent 

 to be taken into account the machine has a shaft with an overhanging crank, 

 which carries a pulley pivoted on a parallel axis adjustable to a greater or 

 less distance from the shaft's axis, according to the greater or less range of 

 the particular tidal constituent for the different ports for which the machine 

 is to be used. The several shafts, with their axes all parallel, are geared 

 together so that their periods are to a sufficient degree of approximation pro- 

 portional to the periods of the tidal constituents. The crank on each shaft 

 can be turned round on the shaft and clamped in any position : thus it is set 

 to the proper position for the epoch of the particular tide which it is to pro- 

 duce. The axes of the several shafts are horizontal, and their vertical planes 

 are at successive distances one from another, each equal to the diameter of one 

 of the pulleys (the diameters of these being equal). The shafts are in two 

 rows, an upper and a lower, and the grooves of the pulleys are all in one 

 plane perpendicular to their axes. Suppose, now, the axes of the pulleys to 

 be set each at zero distance from the axis of its shaft, and let a fine wire or 

 chain, with one end hanging down and carrying a weight, pass alternately 

 over and under the pulleys in order, and vertically upwards or downwards 

 (according as the number of pulleys is even or odd) from the last pulley to a 

 fixed point. The weight is to be properly guided for vertical motion by a 

 geometrical slide. Turn the machine now, and the wire will remain undis- 

 turbed, with all its free parts vertical and the hanging weight unmoved. But 

 uow set the axis of any one of the pulleys to a distance T from its shaft's 

 axis, and turn the machine. If the distance of this pulley from the two on 

 each side of it in the other row is a considerable multiple of T, the hanging 

 weight will now (if the machine is turned uniformly) move up and down with 

 a simple harmonic motion of amplitude (or semi-range) equal to T in the 

 period of its shaft. If, next, a second pulley is displaced to a distance T', a 

 third to a distance T", and so on, the hanging weight will now perform a 

 complex harmonic motion equal to the sum of the several harmonic motions, 

 each in its proper period, which would be produced separately by the displace- 

 ments T, T', T". Thus, if the machine was made on a large scale, with T, 

 T'... equal respectively to the actual semi-ranges of the several constituent 

 tides, and if it is turned round slowly (by clockwork, for example), so that 

 each shaft goes once round in the actual period of the tide which it represents, 

 the hanging weight would rise and fall exactly with the water level as affected 

 by the whole tidal action. This, of course, could be of no use, and is only 

 suggested by way of illustration. The actual machine is made of such mag- 

 nitude that it can be set to give a motion to the hanging weight equal to the 

 actual motion of the water level reduced to any convenient scale : and pro- 

 vided the whole range does not exceed about 30 centimetres, the geometrical 

 error due to the deviation from perfect parallelism in the successive free parts 

 of the wire is not so great as to be practically objectionable. The proper 

 order for the shafts is the order of magnitude of the constituent tides which 

 they produce, the greatest next the hanging weight, and the least next the 

 fixed end of the wire : this so that the greatest constituent may have only one 

 pulley to move, the second in magnitude only two pulleys, and so on. In the 



