12 SEC. 1. ARITHMETIC. 



actual machine there are 10 shafts, which, taken in order from the hanging 

 weight, give respectively the following tidal constituents : 



1. The mean lunar semi-diurnal. 



2. The mean solar semi-diurnal. 



3. The larger elliptic semi-diurnal. 



4. The luni-solar diurnal declinational. 



5. The lunar diurnal declinational. 



6. The luni-solar semi-diurnal declinational. 



7. The smaller elliptic semi-diurnal. 



8. The solar diurnal declinational. 



9. The lunar quarter-diurnal, or first shallow-water overtide of mean lunar 



semi-diurnal. 



10. The luni-solar quarter diurnal, shallow-water tide. 



The hanging weight consists of an ink bottle with a glass tubular pen 

 which marks the tide level in a continuous curve on a long band of paper moved 

 horizontally across the line of motion of the pen, by a vertical cylinder geared 

 to the revolving shafts of the machine. One of the five sliding points of the 

 geometrical slide is the point of the pen sliding on the paper stretched on the 

 cylinder, and the couple formed by the normal pressure on this point, and on 

 another of the five, which is about 4 centimetres above its level and ] centi- 

 metres from the paper, balances the couple due to gravity of the ink bottle 

 and the vertical component of the pull of the bearing wire, which is in a line 

 about a millimetre or two farther from the paper than that in which the centre 

 of gravity moves. Thus is ensured, notwithstanding small inequalities of the 

 paper, a pressure of the pen on the paper very approximately constant, and as 

 small as is desired. 



Hour marks are made on the curve by a small horizontal movement of the 

 ink bottle's lateral guides, made once an hour ; a somewhat greater move- 

 ment, giving a deeper notch, to mark the noon of every day. 



The machine may be turned so rapidly as to run off a year's tides for any 

 port in about four hours. 



It is intended that each crank shall carry an adjustable counterpoise, to be 

 adjusted so that when the crank is not vertical the pulls of the approximately 

 vertical portions of wire acting on it through the pulley which it carries shall, 

 as exactly as may be, balance on the axis of the shaft, and that the motion of 

 the shaft shall be resisted by a slight weight hanging on a thread wrapped 

 once round it and attached at its other end to a fixed point. This part of the 

 design, planned to secure against " lost time " or " back-lash " in the gearings 

 of the shafts, and to preserve uniformity of pressures between teeth and teeth, 

 teeth and screws, and ends of axles and " end-plates," was not carried out, 

 but can easily be applied to the machine now exhibited. 



The general plan of the screw gearing for the motions of the different 

 shafts is due to Mr. Lege, the maker of the machine. The construction has 

 been superintended throughout by Mr. Roberts, and to him is due the whole 

 arithmetical design of the gearing to give with sufficient approximation the 

 proper periods to the several shafts. 



4Oa. Sir William Thomson's Instrument for Harmonic 

 Analysis of Tidal Observations, and for other uses. 

 It includes a disc-ball and cylinder integrator of Professor James 

 Thomson. For explanations, reference may be made to proceed- 

 ings of the Royal Society for February 3, 1 876. 



Sir William Thomson. 

 41. Pascal's Calculating Machine (1642). 



Conservatoire des Arts et Metiers, Paris. 



