Formulae. 



346 HYDROGRAPHICAL SURVF.YING [chap. xiv. 



The intervals between the sets of observations for rates 

 should be between ten and thirty days. 

 Hartnup's Mr. Hartnup's formuhe are somewhat different, and do not 

 give exactly the same results with the same data. 



He observes the rate at tliree different temperatures not 

 less than 15° apart, but there must be an equal number of 

 degrees between them. 



The same remark already made as to M. Lieussou's method 

 will apply here — viz., that in service afloat it will be difficult to 

 fulfil the conditions of observation. His formulae are as 

 follows : 



C: 



f 



d + d^ 

 2Cp 



d + d^ 

 2 p 



Where C is the coefficient of change of rate, 

 T is temperature of maximum rate, 

 R is rate at that temperature, 

 ti is the middle temperature, 

 rj is observed rate at temperature t^, 

 d is difference of rate betv/een that at lowest tempera- 

 * ture and t^, 



di is difference of rate between t^ and that at highest 



temperature, 

 p is difference between highest and lowest tempera- 

 tures observed at. 



Then to find the rate in any required temperature. 



If N = any number of degrees from T, 



Rateat T±N-R + CN2. 

 Epochs of In using the rates of departure and arrival in calculating a 

 tion^^^' meridian distance, the Errors at the last observation at de- 

 parture and first at arrival should not be taken for the epochs 

 of calculation, but the mean of the two should be used for 

 the purpose, for it is at the mean date between the two obser- 

 vations for each rate at which the latter is actually fixed. 

 Thus, if we observe at a place A on the 2nd and 8th, and again 



