52 



og som Control paa det benyttede Kviksolvs Renhed dettes 



0° 

 Egenvægt ved til 13.5963 



somt Søvandets Volumina ved forskjellige Temperaturer til 



'7-5 



Vt af I 



1.000308 



1.000794 



1. 001654 



1.002605 



1.003227 



Til Udjevning af den elter disse. Observationer op- 

 trukne Curve har jeg benyttet de mindste Kvadraters 

 Methode, idet jeg har sat Ligningen for Søvandets Volum 

 ved t" under Fonnen 



F ( =l + ai + 6i 2 + c* 3 . 

 Betingelsesligningerne blive 



a + 4 6 + 16 c— 0.000077 = 

 a-f- 8 6 + 64 c — 0.00009925 =0 

 a + 13 6 + 169 c — 0.00012723 = 

 a + 17.56 + 306.25c— 0.000148857 = 

 a 4- 20 + 400 c — 43.00016135 =0 



hvoraf Systemerne 



ort + 62.5 6 + 955.25c — 0.000613687 = 



62.5a 4- 955.255+ 16132.37c — 0.008588 =0 



955.25a-+ 16132.375 + 286702 c — 0.1392135 = 



som ved Elimination giver 



a = O.O0OO527328 

 5 = 0.00000617375 

 c = — 0.000000037516 



eller ved Afrunding 



V, - 1 + 0.000052733* + 0.1 II II N 1061738* - — 0.1 10000003752^. 



Etter denne Formel har jeg beregnet følgende Tabel, 

 hvori Søvandets Volum tindes opført for hver hel Grad 

 ogsaa for Temperaturerne under 0", uagtet Formelens Gyl- 

 dighed for dette Strøg ikke er støttet ved nogen Observa- 

 tion. 



and, as a test of pnrity, the specilic gravity of the mer- 



0° 

 curv at - was found to be 13.5963, and 



1 4° 



the volume of sea-water at different temperatures — 



t" o 



1 



r, of I 



i.ooooooj 1.000308 



1.000794 



i.001654 1 1.002605 



1.003227 



For smoothing the curve laid down from these obser- 

 vations, I adopted the method of the least squares, giving 

 the equation for the volume of the sea-water at t" the 

 form — 



V,- 1 -\- at + bf 2 -\- d 3 . 



The conditional equations will be 



ft+ 4 b+ 16 c 

 «+ 8 5+ 64 c- 

 a + 13 5+ 169 c- 

 «+17.55 + 306.25c 

 a + 20 5 + 400 c 



from which are deduced — 



0.000077 =0 

 (t.(i()O09925 =0 

 0.(10012723 =0 

 0.000148857 = 

 0.00016135 =0 



oa 4. G2.5 5+ 955.25c — 0.000613687=0 



62.5a + 955.255+ 16132.37c — 0.008588 •= 



955.25a + 16132.376 + 286702 c — 0.1392135 =0 



and these equations give by elimination — 



a = O.00OO527328 

 5= O.O0OOO617375 

 c = — 0.000000037516 



or. rounded off, 



- V t = 1 + 0.000052733* + 0.000006 1 738* 2 — 0.001 II I0CM I3752* 3 . 



By means of this formula I determined the results 

 set forth in the following Table, which shows the volume 

 of sea-water, computed for everv degree, including temper- 

 atures below 0°, although the applicability of the formula 

 to the latter has not been ascertained from observation. 



