a Test of the Chronometers at Greemioich. 13 



time of the same place. It is submitted whether the followino- 

 quantity derived for each chronometer from the daily com- 

 parison with mean time will be a good criterion of this uni- 

 formity. Let the first differences of the daily differences of 

 each chronometer from Greenwich mean time (in fact, the 

 numbers piinted in the Greenwich reports for each day) be 

 d', d", d'", &c., and let the mean of all for the whole period 

 embraced by the trial be d; and then let the sum of the squares 

 of the differences of the number for each day, and the mean 

 of all, be calculated ; viz. {d' — d)- + {d" — df + {d"' — df + hc. 

 It appears to me that this number would be fit to judge by of 

 the quality of a chronometer, and every alteration in any one 

 number would produce a change in it. Without contending 

 that the reciprocal of this number would express the exact 

 weight of the different results obtained by these chronometers 

 during a subsequent period, it may be affirmed that the order of 

 the chronometers, with regard to quality, would be the reverse 

 of the order of those quantities as to magnitude. As the ob- 

 ject of these remarks is only to submit a proposal to the ex- 

 amination of those who are competent and willing to judge of 

 its propriety, I shall only add an example of the manner in 

 which this trial number of a chronometer is to be calculated. 

 The calculation would in most cases require litde accuracy, as 

 the numbers will vary greatly for the different chronometers ; 

 and only in cases where they would, for the best ones, be nearly 

 the same, would it be necessary, by a more accurate repetition 

 of the calculation, to decide the uncertainty left in the previous 

 approximate calculations. 



V. Re- 



