ANhLYTIChL EDITION
SEPTEMBER 15, 1940
T o demonstrate the accuracy of the quantitative method, representative results are given in Table 111 for both new and used oils, to which aqueous glycol solutions were added in the amounts indicated. This quantitative determination is possible only in the absence of high-boiling antifreezes other than ethylene glycol.
( 2 ) Feigl, F., "C2ualitative .$nalysis h y Spot Tests",
(3) (4)
(5) (6)
Literature Cited (1) Am. Soc Testing hfateiials, "Standards on Petroleum Products and Lubiicants", p 345, Philadelphia, .Imerican Society for Testing Materials, 1937.
527
(7)
1st ed., pp. 251-3, New l o r k , Sordemann Puhlishing Co., 1937. Fleury. P., and Marque, J.. J . pharm. c h i m . , (8) 10, 241-57 (19"). Leiin, H . , Uhrig. K., and Stehr, E.. ISD. Esu. CHEM.,Anal. Ed.. 1 1 , 134-6 (1939). Middleton, -1. W., Analyst, 59, 522 (1934). Morton. -1.A,. "Laboratory Technique in Organic Chemistry", 1st ed., pp. 50-1, 73, 74, Kew York, McGraw-Hill Book Co., 1938. Rosenthaler, L., "Der Nachxveis organischer Verbindungen", p. 104, Stuttgart, Ferdinand Enke, 1926.
Nomograph for Correction of Lactometer Readings and Calculation of Milk Solids LINCOLS RI. LAMPERT Dairy Service Laboratory, State Department of .4griculture, Sacramento, Calif.
I
S T H I S country the routine calculation of the solids-notfat or of total solids in a sample of milk usually is made by means of a formula based upon the Babcock fat test and a Quevenne lactometer reading. The simplified Babcock formula ( I O ) generally is used, in which
Solids-not-fat
=
lactometer reading at 60" F. 4
per cent fat $
5
A statistical study (6) of this formula showed that its accuracy increases as the number of cons contributing to the milk is increased. The estimation, however, is only approximate, and its use as such is understood by milk inspection departments and dairy officials. Variations from gravimetric results for the solids-not-fat may deviate b y 0.2 per cent or more. Investigations have shown that the physical state of the fat globules in the milk affects its density, and for the most accurate work this characteristic of the fat globules must be taken into consideration. Bakke and Honegger ( 1 ) made a thorough investigation of this problem and devised a method for securing a uniform basis for the comparison of lactometer readings. Their method, which has been overlooked by many American investigators, is to heat the milk to 40" C. (104" F,), cool to 15" C. (59" F.), and make the lactometer reading as usual. By this method consistent results are obtained on a sample of milk, whether it i. frebli, has been held a t room temperature or in a refrigerator, or has been subjected to various degrees of agitation. Kithout this preliminary treatment, the same milk gives widely different lactometer readings under these diverse conditions. Hoyt, Lampert, et 01. (4) corroborated these findings and pointed out other factors involved in the use of the lactometer. This and other work was recently reviewed by Lampert (6). Sharp and Hart (9) recommend that density readings be made when the fat globules are in the liquid state. According to their method, the milk is heated to 45" C.(110" F.) for 0.5 minute, and cooled to 30" C. (86" F,), and the tot;ll solids are estimated from the specific gravity according to the equation lactometer reading Total solids = 1.2537 fat 0.2680 sp. gr, of milk
+
It is generally conceded that the only reason for the use of the lactometer is the speed and conT-eniencewith which a very good approximation of the solids content may be obtained Long usage has established the Babcock formula, and pub-
lished data show that the results obtained with it are as satisfactory as those obtained with the other more complicated procedures, which, theoretically a t least, appear more valid. Sharp and Hart found that their calculated and gravimetric determinations may differ by 0.30 per cent and Hoyt, Lampert, et al. (4) found that the Bakke and Honegger method on mixed herd milk varied between +0.13 and -0.26 per cent from gravimetric results. Most textbooks and manuals ( 2 ) contain tables that serve to eliminate the calculation required b y the Babcock formula. Two sets of tables are needed, since the lactometer reading often is not made a t exactly 60" F. and therefore requires a correction, The second table gives the solids-not-fat corresponding to a given lactometer reading a t GO" F. These tables take into consideration the fact that the corrections involved vary with the temperature a t which the lactometer reading is made as well as with the specific gravity of the milk. At least three different slide rules have been macle for this calculation, but they are not in common use. One of these, Richmond's "milk scale" (S),is based upon a formula not often used in the United States since it gives results 0.14 per cent higher than those obtained by Babcock's formula. I n general, slide rules and tables give corrections for temperatures ranging from about 35" to 80" F., but the preferred practice is to obtain a lactometer reading a t a temperature of between 55" and 65" F. As far as the writer has been able to learn, no nomograph has been devised to replace the use of tables. Such a nomograph would have decided advantages, especially when many calculations are to be macle. The nomograph is easier and quicker to read than tables and eliminates the interpolations needed to obtain the corrections if the lactometer is read t o parts of a whole degree or if the fat reading is made to less than 0.1 per cent, the limit in most tables. T o this end, the nomograph illustrated was constructed and has been found very satisfactory. Since the nomograph is constructed from data in the tables, it cannot give results more accurate than those in the tables or obtained by formulas vhich in themselves are based upon the average analysis of many samples of milk. The principal advantages in its use are facility and speed and the fact that it may be printed on a single page. I n using the nomograph, two readings must be made by means of a straightedge, or better, a transparent celluloid guide with a line drawn down its length. First the lactometer
INDUSTRIAL AND ENGIKEERING CHEMISTRY
VOL. 12, NO. 9
1940 L.M.LAMPERT
COPWIGHT
reading must be corrected from that of the temperature of observation to that at 60" F., and then the solids-not-fat are found, corresponding to the fat reading previously obtained. For example, to find the solids-not-fat in a sample of milk which showed a lactometer reading of 30 a t 67' and contained 4.2 per cent of fat, place the guide line so that it passes through 67" on line 5 and through 30 on line 3. The corrected lactometer reading is shown where the guide passes through line 1-namely, 30.9. Then with one end of the guide a t 30.9 let it pass through 4.2 on line 4; on line 2 the guide passes through 8.60-the per cent of solids-not-fat in the sample. The results obtained with the nomograph have been found to differ less than 0.02 from those given by the tables.
The Quevenne type of lactometer is almost universally used in the United States, but in a few localities, especially in New York State, the Kew York Board of Health or Spence's lactometer is still in use. This use appears so limited (7) that the writer did not consider it advisable to complicate the nomograph with another set of figures. The conversion of the nomograph for use with Spence's scale is very simply done by supplementing or substituting the equivalent Spence's degrees
for the Quevenne degrees shown on scales 1 and 3. Conversion figures are published in a number of texts ( 3 ) . Richmond's formula for obtaining the total solids appears to be generally accepted in British practice. The solids-notfat corresponding to this formula may be obtained by adding 0.14 to the result found with the nomograph, or the chart could be constructed with line 2 shifted a space corresponding to 0.14 per cent, thus eliminating further calculation.
Literature Cited (1) Bakke arid Honegger, Lait, 3,KO.1, 3 (1923). ( 2 ) Beattie, TT. R.. U. 6. Dept. Agr., Circ. 384 revised (1929).
(3) Farrington, E. H., and TToll, F. TV., "Testing Milk and Its Products", Madison, Wis., Mendota Book Co., 1929. (4) Hoyt, C. F., Smith, N . C., Lampert, L. AI., and Saywell, L. G., Calif State Dept. hgr., -Yo. Bull. 17 (Nov., 1928). (5) Lampert, M i l k Dealer, 28, S o . 3, 25, 50 (Dec., 1938) (6) Overman, Davidson, and Sanmann, Ill. Agr. Expt. Sta., Bull. 263 (1925). (7) Personal correspondence. (8) Richmond, H. D., "Dairy Chemistry", pp. 89, 90, 3rd ed., London, Charles Griffin & Co., 1920. (9) Sharp and Hart, J . Dairy Sci., 19, 683-95 (1936). (10) Wisconsin Agr. Expt. Sta., Annual Rept., 1891.
