Density of Water with the Temperature. 127 



be increased; and thus for —10°, I take it as +0*1, for +20° 



dv 

 and 100° as +0*05. By multiplying these values by -=- 



we get, for -10° +26, and for 20° ±10, and for 100° + 39 

 inillionths of the volume. 



(4) The foregoing examination of the points generally 

 taken as granted in determining the coefficient of expansion 

 of glass, leads to the conclusion that the error in the volume 

 of the vessel will attain at least +0*000001, which intro- 

 duces a possible error in the volumes of water of as much as 

 + (£—4) millionths of the volume, because the coefficient of 

 expansion of the vessel enters into the value of the volume of 

 water after being multiplied by the number of degrees. 



(5) Inasmuch as, up to the present, no corrections have been 

 made for an alteration in the volume of water due to a change 

 of atmospheric pressure, and since these differences of pressure 

 at various seasons of the year and in different localities may 

 amount to ^th of an atmosphere, I hold it necessary to add 

 a possible error of +4 millionths of the volume to the differ- 

 ences of individual observers, for the reason indicated, and 

 equal to ^0*1. 



(6) Judging from the description of the methods of in- 

 vestigation and from a comparison of individual observations, 

 we must recognize the existence of errors amounting to ten- 

 thousandths of a volume in the determination of volumes and 

 weights at different temperatures. But the greater portion 

 of possible errors of this category disappear in the majority 

 of cases, when the final results are calculated out (often by 

 the method of least squares). I therefore estimate such an 

 incidental error as not exceeding + 5 millionths of the volume 

 in the best extant determinations. 



(7) The sum of the errors enumerated above, which have 

 been taken at the lowest possible computation, is equal to 

 + 49 for -10°, +35 for +20°, and +144 for 100°, taking 

 the volume at 4° as equal to 10 6 . Supposing the errors pro- 

 portional to £ — 4, we have, in virtue of the above figures, the 

 following equation : 



Possible error = + (*-4) (3-0-0'0469£ + 0*00032 i 2 ). 



The values corresponding to this equation are given under 

 heading (d) in Table II. 



Since the constants A, B, and C, in formula No. 1 are 

 calculated from existing data, which contain, at the very least } 

 the above-mentioned errors, so these errors may also occur in 

 the values given by this formula. However, the best experi- 

 mental results differ from the numbers given by the formula 



