CHAP. XIV.] CHRONOMETRIC MERIDIAN DISTANCES 345 



He ascertains by observations for rate at different tempera- 

 tures, undertaken by the officers when the chronometers are 

 embarked, the coefficient for temperature by simply dividing 

 the difference of rate by the difference of mean temperatures 

 during the intervals of rating. 



This coefficient of change will remain constant for some period, 

 though the actual rates themselves will alter from other causes ; 

 nevertheless, the more these observations are multiplied the 

 better, and the latest determinations wiU be used in practice. 



In determining the sea rate for a meridian distance, he 

 applies to the rate of departure the change of rate due to the 

 difference between the mean temperature during rating and 

 the mean temperature during the passage, which gives one value 

 for the sea rate. Doing the same for the rates of arrival, he 

 gets another value for sea rate. The mean of these two he 

 takes as the final mean sea rate to be used. One weak point 

 here is that the mean temperature, T, of the compensation 

 will not be indicated, unless many observations at different 

 temperatures are made. It will therefore add considerably 

 to the value of this method if we can find T. 



It will be more satisfactory if we can get this from the Lieussou's 

 Observatory ; but a formula for ascertaining it is given by fo°/™s^e^. 

 Captain Shadwell, from M. Lieussou, which we here append, taining T. 

 but we apprehend that in practice not many opportunities will 

 present themselves for making use of it. It depends on the 

 results of four observations for rates, at equal intervals of 

 time, and at different temperatures, a difficult condition to 

 satisfy except with artificial aid for the temperature. M. Lieus- 

 sou remarks, " that four rates and four temperatures, observed 

 at intervals of ten days, determine the constants for each 

 chronometer with a precision sufficiently remarkable." With 

 the other constants we do not propose to deal, but solely to give 

 his formula for ascertaining T, which is — 



(m^ - 2w., + mj {t,^ - 2t^ + tj — (m, - 2m^ + mj {t^ - 2«, + 1^) 



Here T = mean temperature of compensation required. 



mi m.2 m^ m^ are the four observed rates corresponding to 

 ^1 1^ ^3 ti, the four temperatures. 



