now measuring on the Continent. 201 



the denominator of the fraction expressing the ellipticity. Nor 

 could the discordance, which the comparison of so erroneous a 

 result with other portions of the parallel would have manifested, 

 have insured a repetition ; since we observe the anomaly little 

 less in amount which exists in the portion of the parallel of 

 forty-five, between Isson and Geneva, has not been considered 

 to require a re-examination. 



The extension of the number of intermediate chronometrical 

 stations, as practised in France, has given rise to a question 

 of some nicety, of which the solution was not at first very 

 obvious, but which has been well and clearly discussed by Mr. 

 Herschel, in the account which he has given (Phil. Trans., 

 1826) of the operations in which he was engaged, for deter- 

 mining the difference of meridians between Greenwich and 

 Paris. The desideratum which he has there supplied is the 

 most advantageous way of employing a broken series of obser- 

 vations ; that is to say, a series made on a line, on which there 

 are two or more stations of transmission, and on which failures 

 in the complete transmission have taken place occasionally at 

 different parts of the line. To reject all but complete trans- 

 missions is obviously to reject a part of the evidence, when it 

 is most important to preserve all that the observations will 

 afford ; and it does, in fact, frequently happen, that the cases 

 in which a link fails, and which will give no result at all if 

 taken singly, form the principal part of tiie actual observations, 

 and being treated properly, are not less capable of yielding a 

 correct result than the complete transmissions. Did the chro- 

 nometers keep strict sidereal time, it is evident that the differ- 

 ence between any two of them would be constant ; and that it 

 would be indifferent whether the time at which they were com- 

 pared with each other was earlier or later than the comparisons 

 of each with the others next in succession in the line : that 

 all the comparisons, at all parts of the line, on the same night, 

 whensoever occurring, might, in fact, be regarded as simulta- 

 neous. The chronometers, however, do not keep strict time ; 

 which renders it necessarj^ particularly if the series be much 

 broken, to take into the account their rates, and the intervals 

 elapsing between the comparisons at different parts of the line. 

 We may perhaps render this clearer by an illustration : — Suppose 



