TIDAL AND LEVELLING OBSERVATIONS. 199 



mean of all the successive heights, and in the figure is represented 

 by J D. 



If now it is required to calculate the height of the tide for any 

 port for which the tidal values have been obtained, it will be 

 necessary to find the value of the heights due to the mean sun 

 and the mean moon, and also each of the smaller constituents due 

 to the ellipticity of their orbits, &c. The algebraical sum of these 

 added to the mean height will give the height desired. 



It will be readily seen that if the number of ports be considerable 

 heights calculated in this manner for, say, each hour of the day for 

 a whole year would involve very great labour and require a con- 

 siderable staff of calculators. Recourse has consequently been had 

 to mechanical means to effect the desired object. It will be readily 

 understood that if, say, the hand of a clock represented propor- 

 tionally the value of any one tidal constituent, and it is made to 

 revolve in its proper time, then the successive heights clue to the 

 component will be traced by the end of the hand. Similar move- 

 ments would represent the other tidal constituents, and all that 

 would remain to be effected would be to combine all the heights 

 thus traced out. The tide-predicting machine, made by Mr. A. Lege 

 from the designs of Mr. Edward Roberts for the Indian Govern- 

 ment, embodies a beautiful and simple means of combination, the 

 suggestion of Mr. Beauchamp Tower, and consists of a very fine 

 and flexible wire fixed at one end and carrying a tracing point at 

 the other. This wire passes successively over and under 20 pullies 

 arranged in two rows of movements above and under each other. 

 Each pulley is made to revolve relatively to the others in its own 

 proper time, and is capable of being 

 thrown out from its centre to the range 

 of the constituent it represents. 



The free or tracing end of the wire will 



thus represent the height due to the whole 



of the pullies. To avoid the error due to 



the wire being thrown out of the vertical 



by the revolution of the pulley it is 



carried on a parallel slide (designed by 



Sir William Thomson), whereby the wire 



is kept strictly vertical under all the varying positions of the pullies. 



In the machine designed for the Indian Government Mr. Roberts 



has included no less than 24 tidal constituents, which, for most 



