262 Journal of Agricultural Research voi. iii, No. 3 



It was found that the calculation of volumes could be most con- 

 veniently accomplished by changing the basis of the calculation from 

 35° to 20° C. The equation 



D,='D,,° + a(t-35)+P(t-35y i 



was accordingly transfonned to 



A=-D20° + «'(^-2o)+/?'(/-2o)2 2 



and the values of a' and ^' determined. It can be shown that a^ = a — 30^8 

 and that /3' = i9. As a further convenience in calculation, the equation 

 was changed to the form 



Vt=V,,' [i + A{t-2o)+B{t-2o)-] 3 



in which A and B may be found in terms of «' and /?•. 



It would, of course, be possible to calculate the volumes directly by 



means of equation 2, since c? = — or V = -z, but the calculation is much 



V a 



more easily done by means of equation 3. 



The volum.es thus calculated are given in Table V.^ 



SOURCES OF ERROR 



It has already been pointed out that one source of error is the gradual 

 separation of the sample under investigation into its constituent parts, 

 the fat rising to the top and the heavier portions settling toward the 

 bottom. The greatest source of error, however, is probably in the 

 assumed percentage of fat in the sample at the time the density deter- 

 minations are made. This will be explained somewhat in detail. The 

 samples of milk and cream were generally prepared at the Bureau of 

 Animal Industry in the morning and brought to the Bureau of Standards 

 in the afternoon of the same day. The density determinations were 

 made on the following day. During this interval of time between the 

 preparation of the samples and the making of the density determina- 

 tions the samples could be kept sweet without difficulty, but there was 

 in many cases a considerable amount of separation and "churning" of 

 the fat, so that granules of butter were collected on the neck and the 

 cap of the bottle in which the sample had been kept. 



This change in the percentage of fat contained in the sample was, 

 of course, always in such a direction that the sample at the time its 

 density was determined contained a lower percentage of fat than that 

 reported by the Bureau of Animal Industry at the time the sample 

 was prepared. For that reason, since the density increases with decreas- 

 ing percentage of fat, the densities of the different samples will in most 

 cases be somewhat too large for the percentages of fat to which they 

 are intended to correspond; or, in other words, the tabulated percentage 

 of fat in a given sample is somewhat too high. In the tabulated values 

 of percentage of fat and corresponding density (Table II), the density 



' These daU also appear as Table n, U. S. Dept. Agr. Bui. 98, p. 6-9. 



