Coppee.] 260 [March. 



for any practical astronomical purpose, the problem has been solved 

 in more than one way. 



'' The plan adopted in the Cincinnati Observatory may be described 

 as follows : The clock-work machinery employed to give to the great 

 equatorial telescope a uniform motion equal to that of the earth's 

 rotation on its axis, offered to me the first obvious approximate solu- 

 tion of the problem under consideration. This machinery was ac- 

 cordingly applied to the motion of the disk, or rather to regulate the 

 motion of revolution, this motion being produced by a descending 

 weight, after the fashion of an ordinary clock. It was soon discovered 

 that the ' Frauenhofer clock,' as this machine is called, was not com- 

 petent to produce a motion of such uniformity as was now required. 

 Several modifications were made with a positive gain ; but after long 

 study it was finally discovered that when the machinery was brought 

 into perfect adjustment, the dynamical equilibrium obtained was an 

 equilibrium of instability ; that is, if from a motion such as produced 

 a revolution in one exact minute, it began to lose, this loss or decre- 

 ment in velocity went on increasing, or if it commenced to gain, the 

 increment went on increasing at each revolution of the disk. Now 

 all these delicate changes could be watched with the most perfect 

 certainty; as in case the disk revolved uniformly once a minute, then 

 the seconds' dots would fall in such a manner (as we shall see di- 

 rectly), that the dots of the same recorded seconds would radiate 

 from the centre of the disk in a straight line. Any deviation from 

 this line would be marked with the utmost delicacy down to the 

 thousandth of a second. By long and careful study, it was at length 

 discovered, that to make any change in the velocity of ihe disk, to 

 increase or decrease quickly its motion, in short, to restore the dy- 

 namical equilibrium, the winding key of the ' Frauenhofer clock ' 

 was the point of the machinery where the extra helping force should 

 be applied; and it was found that a person of ordinary intelligence 

 stationed at the disk, and with his fingers on this key, could, when- 

 ever he noticed a slight deviation from uniformity, at once, by slight 

 assistauce, restore the equilibrium, when the machine would perhaps 

 continue its performance perfectly for several minutes, when again 

 some slight acceleration or retardation might be required from the 

 sentinel posted as an auxiliary. 



<' The mechanical problem now demanding solution was very 

 clearly announced. It was this : Required to construct an automaton 

 which should take the place of the intelligent sentinel, watch the 

 going of the disk, and instantly correct any acceleration or retarda- 



