Dec. 15, 19'A Expansion of Milk and Cream 263 



is in each case given as corresponding to the percentage of fat in the 

 sample at the time it was prepared. In reaHty it corresponds, not to 

 that percentage of fat, but to the percentage in the sample at the time 

 the density was determined. No attempt will be made at the present 

 time to estimate how great this discrepancy may be; in some cases it 

 is quite appreciable. 



Other sources of error are the temperature observations and the 

 weighings of the sinker. The weighings were made to tenths of a milli- 

 gram and were probably correct in most cases to about half a mg. Errors 

 greater than i or 2 mg. would be unlikely to occur. The thermometers 

 were graduated to tenths of a degree centigrade and were read to hun- 

 dredths. The mean of the four readings taken at each temperature 

 was probably correct within one or two hundredths of a degree. Errors 

 of more than three hundredths would not be expected. If both of 

 these maximum errors should occur in the same set of observations 

 and both should be in the same direction, the resulting error in the 

 density would be about six units in the fifth decimal place. Even 

 such an error would not be serious in the present instance, as the density 

 values are used in the table only to the fourth place. Tlie density 

 determinations are almost certainly accurate to that degree. In the 

 calculation of the densities the results were carried to the fifth place, 

 and they are seen to be concordant in most cases to somewhat better 

 than one in the fourth place. 



CONCLUSION 



Examination of the results here presented (see Table III) shows 

 that for the individual samples examined the density determinations may 

 be depended upon to about one unit of the fourth decimal place. These 

 values, however, when plotted (see figs, i and 2), present certain irregu- 

 larities which are far too great to be accounted for by errors in the deter- 

 minations. For example, four different samples were examined, each 

 of which was supposed to contain 30 per cent of fat. The densities of 

 the four samples at 35° C. were found to be In satisfactory agreement, 

 and for each sample the agreement between the observed and calculated 

 densities at other temperatures was such as to throw no suspicion upon 

 the determinations; and yet the rate of expansion of the four samples 

 was widely different. Only one out of the four fitted reasonably well 

 into the series formed by the samples above and below 30 per cent. 

 This and similar anomalies for certain other samples make it appear 

 that the rate of expansion of any given sample depends upon some- 

 thing more than the density or the percentage of fat present. It undoubt- 

 edly depends upon the physical and chemical condition of the sample 

 at the time the observations are made. This condition is probably 

 largely dependent upon the time that has elapsed since the preparation 

 of the sample and upon the temperature at which it has been kept. 

 That being the case, it would probably be impossible to find any fixed 

 relation that would express accurately the rate of expansion of all per- 

 centages of butter fat under all conditions. Further investigation to 

 determine the effect of time and temperature upon the rate of expansion 

 would be of considerable interest, and such an investigation of these 

 and similar points will be necessary before the rate of expansion under 

 all ordinary conditions can be accurately known. 



