348 



HYDROGRAPHICAL SURVEYING [chap. xiv. 



The same formula, when intending to correct for tempcra- 



Tiarks' 



witT?em ^^r«^' ^vill Stand thus : 



perature 

 Correc- 

 tion. 



M = X^- A+^ 



a+.^+t(^- 



^2)2/]- 



Algebraic 

 Signs. 



['^ ' y 2/ ' \ 2 



Where, the other letters signifying as before, 



h is mean temperature during rating at departure, 

 6^ „ „ „ ,, arrival, 



02 ,, ,, during the passage, 



y is the coefficient for temperature found from previous 

 observations. 



In all cases of correction for temperature the algebraic sign 

 of y must be remembered ; that is, it must be applied according 

 to the observed effect in altering the rate. 



The same remark applies to the algebraic signs of all quan- 

 tities in the formulae. 



Thus in the formula 



Tiarks' 

 Formula 

 for Inter- 

 polation 

 with Har- 

 bour 

 Rates. 



the signs which are here given, as throughout, for chrono- 

 meters slow of mean time and losing rates, will only be true 

 under those circumstances with increasing losing rates and 

 when moving eastward. A consideration of the facts, and 

 obvious effects of the corrections, is perhaps the best course 

 to take to determine these signs. 



A meridian distance, founded only upon rates obtained at 

 one end, without any further correction, caimot be considered 

 as of any value M'hatever, unless the voyage be very short. 



When using the combination of harbour rates at each end 

 of a voyage, A to K, to determine the position of some inter- 

 mediate place, B, Ave must, to be consistent, remember that 

 we are assuming that the rate has gradually and uniformly 

 changed from that of departure to that of arrival, and that 

 the rate to be used for a portion of the voyage will not therefore 

 be the same as that for the whole of it. 



Tiarks, interpreted by Captain Shadwell, gives us the follow- 

 ing formula : 



Mi = Ai- A + 



('-;»} 



