June, 1920
T H E JOURNAL OF I N D U S T R I A L A N D ENGINEERING CHEMISTRY
SOME NOTES ON THE BAUMg HYDROMETER By George H. Taber GULF REFININGCo.,PITTSBURGH, PENNSYLVANIA
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scales are now based on mathematical formulas, and t h a t t h e formula which has t h e most authority in this country for liquids heavier t h a n water is
Received December 10, 1919
After t h e name crude oil and t h e names of some of its products, t h e first thing likely t o come t o t h e attention of anybody engaging in t h e petroleum business, or studying i t theoretically or practically, is a reference t o what is called the “Baume gravity” of t h e oils; b u t i t is a conservative assertion t h a t a very large majority of the users of the Baume hydrometer a n d its readings are under some one or more misapprehensions in regard t o t h e instrument, its principles or their application. It is quite likely, as some readers may point out, t h a t t h e present writer shares in some of these misapprehensions, but, if so, they are self-inflicted and of long standing. Baume hydrometers are of the constant-weight, variable-volume type. As a n aid t o understanding what the Baume instrument is, and what i t is not, i t will be well first t o consider t h e constant-weight, variable-volume specific gravity hydrometer, which i t is precisely like except in its stem divisions and numbers. T h e basic principle of all hydrometers is t h a t a floating body displaces an amount of liquid equal t o its own weight. As the weight of the hydrometer under consideration is constant, t h e same weight of all liquids is displaced by i t when floating freely in them, a n d t h e specific gravities of t h e liquids vary inversely as the volumes displaced, these volumes being indicated by marks on t h e stem of t h e hydrometer, accompanied by numbers giving t h e corresponding specific gravities. Since t h e numbers marked on t h e stem delimit equal increments of specific gravity, and t h e volumes immersed vary as t h e reciprocals of these numbers, t h e successive volumes will necessarily form a harmonic series, t h e differences between t h e successive terms of which will increase as t h e specific gravities decrease; t h a t is, t h e spaces between t h e divisions showing equal increments of specific gravity increase in width from t h e bottom t o t h e t o p of t h e stem. T h e same thing may be stated in another way: namely, if t h e successive specific gravities marked on t h e stem be considered as abscissas of a rectangular hyperbola, t h e constant k of whose equation equals t h e volume immersed when t h e hydrometer is floating in water, t h e successive total volumes immersed will correspond t o t h e ordinates of t h e hyperbola. It will be seen from t h e preceding paragraph t h a t if, reversing t h e usual practice, t h e stem of t h e specific gravity hydrometer were graduated with equispaced divisions t o show t h e volume immersed, t h e corresponding specific gravities would not decrease by equal decrements, b u t these decrements would decrease in amount from t h e bottom t o the top of t h e stem. Disregarding t h e principles upon which the graduation a n d markings of t h e stems of Baume hydrometers were originally Eased, a n d t h e object of their adoption, and without going into details as t o t h e differences in scales which have prevailed in t h e past-some of which still persist-it suffices t o state here t h a t Baume
and for liquids lighter t h a n water-
145 being what is called t h e modulus of the former scale, and 140 t h a t of t h e latter. Examining the formula for liquids heavier t h a n water, we see t h a t Be.: = the reciprocal of the specific gravity multiplied by 145, and the product subtracted from 145; and t h a t t h e greater the specific gravity, t h e greater t h e equivalent Be., degrees. From t h e formula for liquids lighter t h a n water, we see t h a t Be.: = the reciprocal of the specific gravity multiplied by 140, and t h e product diminished by 140 less IO; and t h a t t h e greater t h e specific gravity, t h e smaller the equivalent Be., degrees. The deduction of I O from the modulus, which is in effect deducting t h e modulus and adding I O t o the result, shows t h a t water is 10’ by this scale, instead of o o as by t h e heavy scale. Since, as previously stated, t h e specific gravity varies inversely as t h e volume of liquid displaced, if the stem of a specific gravity hydrometer were divided t o show equal increments of immersion, t h e corresponding specific gravity numbers would form a harmonic series; and since t h e equivalent Baume degree numbers are reciprocals of a harmonic series of specific gravities, modified only by being multiplied by a constant and added t o another constant, they form a n arithmetic progression, a n d if these Baume degree numbers were applied t o such a scale, we should have an equispaced scale with equicrescent numbers, or in fact a Baume scale,-heavy or light according t o t h e conversion formula used. The following are some frequently misunderstood points: I-The name is Baume, not Beaume. 2-Specific gravity numbers are ratios, not degrees. Baume numbers are degrees, not ratios. 3-The Baume scale is not inaccurate, and i t is not unscientific. From its equispaced divisions, i t is likely t o be more correctly divided in t h e making, t h e correctness of its graduations can be more easily checked, a n d almost anyone can interpolate its markings readily by t h e eye, whereas correct, rapid interpolation between specific gravity graduations is practically impossible. Of course, in significance, Baume degrees are inferior t o specific gravity ratios, and i t requires one more step in calculation t o convert them into pounds per gallon or other absolute density standards; however, the Baume scale has become so fastened t o the petroleum business t h a t in all prob-
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T H E J O U R N A L OF I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y
Vol.
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No. 6
ability the world's supply of crude oil would be exhausted of the constituents into specific gravities (or weights before it could be pried loose. per volume, like lbs. per gallon), make the calculation 4-AS is well known, t h e specific gravity of a mixture on these. and convert the result by the formula into of equal volumes of two liquids when there is no the corresponding Baume degrees. contraction or expansion of volume from mixing, will As a concrete arithmetic example is more convincing be the arithmetic mean of t h a t of each of the two t o some, and t o give a n idea of the possible error i n constituents. If the reason for this is not obvious, averaging Baume degrees, consider a mixture of equal change the specific gravities of the constituents t o volumes of liquids of IO' and 70' BC.,. Averpounds per gallon by multiplying each by the number aging them by the BaumC degrees (which we have just of pounds in a gallon of water a t 60' F. Say t h e proved an incorrect method), we should get 40' BB., results are, respectively, 6 and 8 lbs. per gallon. It is for the mixture. Averaging them by their equivalent obvious t h a t if I gallon weighing 6 lbs. be mixed with I specific gravities 1.000 and 0.700 (the correct way), gallon weighing 8 lbs., the result will. be 2 gallons we get 0.850 specific gravity, equal t o 34.7' BC.L. weighing 14 lbs., I gallon of which mixture will weigh However, if weights are used instead of volumes, 7 lbs., 7 being the arithmetic mean of 6 and 8 ; and problems in alligation relating t o liquids can be perdividing 7 by t h e number of pounds in a gallon of water, formed directly with Baume degrees of either the heavy we shall get the specific gravity of the mixture, which or light scale, as seen from t h e following considerai t will be seen must be t h e arithmetic mean of the tions, while they cannot be performed directly with specific .gravities of t h e two constituents. By an specific gravities. Take t h e simplest case,-say equal extension of this reasoning it will be seen t h a t the weights of two liquids, respectively, 0 ' BC., and specific gravity of a mixture of any number of con- 95' BC.,. The arithmetic mean of the two is stituents in any proportions can be calculated in t h e 47.5' BC.,. The specific gravities of the two consame way; in other words, all problems of alligation stituents are, respectively, 1.000 and 2.900. As their medial and alligation alternate relating t o liquids weights are equal, the volumes may be taken, respeccan be calculated directly b y their volumes and specific tively, as 29 and IO. 29 vols. of 1.000 sp. gr. a n d gravities when there is no contraction or expansion 7 sp. gr. = I O vols. of 2.900 sp. gr. average 1.487of volume resulting from the mixing. 59 Contrary, however, t o a somewhat generally held exactly 47. j o BC.,, which proves the contention in opinion, such computations cannot be made by direct this simple case. By a laborious calculation, i t can be use of Baum6 degrees of either the light or heavy demonstrated perhaps more conclusively. Take a lbs. scale, although when the densities of the liquids are of I " Be., b lbs. of m o BC., c lbs. of n o Be. First, fairly close together the error may not be prohibitive, multiply each number of Baume degrees b y t h e numb u t the further apart the constituents are in density, ber of lbs.; divide the sum of the products b y the sum t h e greater the error. Let us test the simplest case as of t h e lbs., and t h e quotient will be the Baume degrees follows: of the mixture. Second, convert the Baume degrees Consider t h a t we have equal volumes of two liquids of each component into specific gravity. By use of t h e of, respectively, a" BC., and b o BC.,. Take the arith- respective specific gravities, convert each number of metic mean of the Baume degrees of the two con- pounds into gallons, perform the alligation in t h e stituents, convert this mean into specific gravity and usual way, and convert t h e resulting specific gravity equate i t t o the arithmetic mean of the equivalent into Baume degrees, when t h e result will be seen specific gravities of the two constituents; solve the t o be t h e same as t h a t of t h e first operation where t h e equation, and ascertain the relation necessary between Baume degrees were used directly. a and b t o make the equation possible. From the foregoing it will be seen t h a t while specijic gravities and weights per u n i t of volume are closely We have related t o each other (in the metric system they are I 4 0+--- 140 140 practically the same), B a u m b degrees, light or heavy, - 1 3 0 + a 130 b are related, although more remotely, t o volumes per a + b unit of weight. This fact and the deduction from i t 130 f 2 2 t h a t alligation problems dealing with the weights which after expansion and reduction results in of the component and resultant liquids can be worked a 2 - 2 ab b2 = o directly with Baumk degrees, may be well known, a-b=o b u t the writer has never heard or seen them referred a = b t o orally or in print. or in words, the only case in which the degrees Baume 5-Frequently a would-be purist in nomenclature, of a mixture of equal volumes of two liquids lighter who approaches the oil business from a scientific t h a n water are the arithmetic mean of the degrees viewpoint, condemns t h e oil man for using. t h e exB a u d of the constituents, is when both are the same. pression " B a u d gravity," and tries t o persuade him The same result ( a = b ) would have been obtained t o say "Baume specific gravity," which is more cumberif we had taken a" BC., and b o BC., and made t h e some and further from being correct. If time in conversions by the formula for t h e heavy scale. Conse- speaking and time and space in writing were of no quently, in order to calculate the BaumC degrees of a importance, we might be absolutely precise and say, mixture, i t is necessary to convert the Baume degrees for instance in using t h e light Baume scale: "The
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June, 1920
T H E J O U R N A L O F I N D U S T R I A L A N D E A’ GIN E E R I N G C H E M I S X R Y
oil is of a specific gravity equivalent t o 5 0 degrees Baum6.” However, this is entirely unnecessary, and t h e expression, “The oil is 50 Baume gravity,” cannot be misunderstood and is entirely justifiable. I n speaking of t h e “degrees gravity’’ of an oil, t h e refiner follows t h e practice of t h e brewer who speaks of t h e “degrees of gravity in a wort,” b u t happily for t h e brewer his gravity degrees are much more easily converted into specific gravities t h a n those of t h e refiner. One meaning of t h e word gravity is “weight.” Some refiners speak of ‘(weighing” an oil, where most, meaning t h e same thing, call it “taking t h e gravity.” The word gravity has done d u t y since t h e early days for both specific gravities and for Baume degrees, a n d its use in this way is convenient. When t h e figures are attached there is little chance of misunderstanding which one is meant; b u t in t h e case of oil, t h e common expressions “higher gravity” and “lower gravity” have directly opposite meanings, depending upon whether t h e specific gravity or light Baume gravity is referred to. The first time this came t o t h e writer’s attention was when some thirty-seven years ago he heard two oil manufacturers spend much of a n afternoon talking at cross purposes, because when one spoke of a certain equipment’s giving a higher or lower gravity in t h e product, t h e speaker had in mind specific gravity, while t h e other, who was unable t o agree with t h e views expressed, understood Baume gravity t o be meant. The writer then determined t h a t t o afford himself t h e convenience of using t h e word gravity without. being misunderstood, he would say in making comparisons, “hemiei” or “lighter gravity,” which would convey t h e same meaning whether applied t o specific gravity or t o Baume degrees, and he has been trying ever since t o persuade others t o use in such cases t h e words “heavier” and “lighter” instead of “higher” and “lower,” or “lower” and “higher,” b u t with more or less lack of success. A reprehensible expression often used in oil contracts is “The oil shall be (say) 30’ gravity or better.” T h e meaning of t h e word “better” is obscure, as it depends on t h e opinion of t h e customer or a knowledge of t h e use t o which t h e oil is t o be put, t o decide whether i t would be better if i t were heavier, or better if it were lighter. T o return t o t h e subject in t h e beginning of this subhead, i t is probable t h a t if our theoretic friends wish t o do away with t h e use in t h e oil business of t h e convenient and time-honored word “gravity” as applied both t o specific gravities and Baum6 degrees, a n d t h e convenient and time-honored combination “Baumi: gravity” as applied t o t h e latter, they will have t o first kill off all t h e old-timers and then at least t h e second and third generations. A MODIFIED FORM OB THE SMITH FERMENTATION TUBE By Aubrey Vail Fuller SERVICE BIJREA_U, AMERICAN SUGAR REFINING COMPANY, NEWYORK,N. Y . Received February 16, 1920
It is frequently t h e case, especially in dealing with commercial problems, t h a t t h e analyst desires early
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information as t o t h e presence of organisms capable of causing t h e active fermentation of certain sugars. T o this end i t is t h e practice t o inoculate a fermentation tube, of either t h e Smith or Durham type, with a portion of t h e sample under examination, incubate and await developments. While, of course, this method yields satisfactory results when proper precautions regarding inoculation and incubation are observed, i t is believed t h a t , for rapidity and certainty, t h e modified construction of t h e t u b e pictured here offers certain advantages over t h e forms commonly used.
The bulb, instead of being symmetrical, is made trough shaped on its under side in order t o facilitate t h e falling of t h e growth t o t h e lowermost portion of t h e gas tube proper, with t h e results t h a t as t h e gas is liberated i t rises vertically and is trapped without an occurrence of appreciable loss through t h e bulb, as is t h e case when the Smith type is used. A very small quantity of fairly coarse acid-washed sand introduced into t h e depression aids materially in t h e disengagement of the gas as i t is formed. It has been found t h a t within a given time t h e volume of gas collected in a tube of this type is about three times as great as is t h e case when t h e Smith t y p e is used, t h e inoculum being t h e same both qualitatively and quantitatively. From this fact it follows t h a t this form of t u b e presents t h e additional advantages of enabling t h e bacteriologist t o secure evidence more quickly as t o t h e identity of t h e organism concerned by t h e customary “analysis” of t h e gas formed b y t h e soda absorption method; and, further, t h a t t h e results so obtained will be more accurate for a given period of incubation.
