VEGA-EXPEDITIONENS VETENSKAPLIGA Alir.ETEN. 



267 



•comes impossible, because the ice from sucJi water has no definite 

 ■volume at its melting point. ^ 



We may simplify the calculation without the least injury 

 to the exactness of the results, by assuming pi = p in the 



quotient 



Pit, — pt 

 q t.-t 

 for temperatiires not exceeding the limits — 10° and + 10° C. 

 The formnia (4) then becomes 



(5) ,,,_ Lg-Qq + qpi + i7 ^ 



w 



It is self-evident, that instead of the volumes L, Q, p, pi, W 

 we may as well substitute in the formula the weights of the 

 corresponding quantities of mercury. 



On page 261 I ha ve alluded to the grave inconvenience, 

 which the uncertainty of the real value of the coefficient of 

 expansion of mercury involves. I will now tr}^ to show, how 

 the errors arising from this deficiency in the present state of 

 science can be counterbalanced and for a great part eliminated 

 from the results by a special arrangement. 



The quantities dependent upon the value ascribed to q in 

 formula (5) are 



Lg— Qq. 

 and 



qpi- 



The latter quantity is almost devoid of influence upon the 

 result, on account of its smallness. We may also reduce the 

 influence of the former considerably by selecting the quanti- 

 ties of mercury and of water so, that 



Lg-Qq = 0. 

 In this case the quantity 



Pi — P 



which is independaut of q and can be determined by direct 

 observations with great exactness, will be predominating in 

 the result, and the influence of erroneous assumptions of the 

 values of q and g will be immaterial. - 



In the series of determinations of the volumes of the 

 frozen water I, A given in chapter 3 



1 This fact (hitherto unnoticed) is the reason, why I have referred the 

 coefficients of dilatation to the quantity of liquid (instead of solid) water 

 contained in 1 cc. at Q" C. 



- It must be reniembered, that the values of q and g are dependent on 

 each other and must varv in the same sense. 



