HYDRODYNAMICS. 



437 



hei'.'- .- 



druv -' '. 

 FliTE 



Fig. 1. 



This formula differs from No. 4. only in the substitu- 

 tion of M S in place of L. 



CHAP. III. 



Ox THE THEORY AND CONSTRUCTION OF AREOMETERS, 

 OR HYDROMETERS, FOR MEASURING SPECIFIC GRAVID 



TIL-. 



SICT. IV. On the Cotulnctio* of different Hydrometer*. 



The names areometer, hydrometer, gravimefrr, have 

 been indiscriminately applied to those instruments 

 which are employed, when very great accuracy is not 

 required, for determining the specific gravities of spi- 

 rituous liquors, and other fluid*. 



Before we enter upon the description of these instru- 

 ments, we shall first explain the general principles of 

 their construction, as exhibited in the hydrometer of 

 Fahrenheit. 



1. Fahrenhdt't Hydrometer. 



This instrument is represented in Plate CCCXIV. 

 Fig. 1. It may be constructed either of glass or me- 

 tal, and consists of a cylindrical stem AB, Fig. 1. con- 

 nected with two hollow balls C, D. A small quantity of 

 mercury, or of leaden shot, is introduced into the lower 

 ball D, so as to prevent it from overturning, and to make 

 it float steadily when it is immersed in a fluid. In 

 using this iiistf uini nt, we may either load it with dif- 

 ferent weights, or have a scale of equal parts engraven 

 upon it* item. Fahrenheit adopted the first of the** 

 method*. He made a mark *> upon the stem A B, and 

 having- immersed it in the lightest liquor, (Fahrenheit 

 iissrl spirits or wine and spirits of turpentine,) such as 

 ether, he introduced mercury into the lull D. till the 

 surface of the light fluid stood at the mark ir. The 

 tube AB was then hermetically sealed, and the irutru- 

 ment weighed in a nice pair of Kales. This weight will 

 obviously be the weight of the quantity of fluid which 

 it displaces. When the instrument was placed in a 

 denser fluid, such a* water, he placed weight* in the 

 small box at A, till the hydrometer sunk to the same 

 mark -. By again weighing the hydrometer with the 

 additional weights, he obtained the weight of a quanti- 

 ty of the denser fluid which was displaced ; but as the 

 part immersed wa* the same in both casts, the two 

 weights which he had obtained werr the absolute 

 weights of equal quantities of two fluids, and were, 

 therft"nre, the ratio* of their specific gravities Thu* if 

 W be the weight of the loaded instrument in distilled 

 water at the temperature of 60* of Fahrenheit, when it 

 has sunk to any mark upon the stem, and tp the weight, 

 which roust either be taken from the box at A, or added 

 to it, in orli-r to make the instrument -.ink to the same 

 point in another fluid, ami B the volume or bulk of the 

 part immersed, then S, /, being the specific gravities, 

 we have W = S^B, and W=fc w= , x B. Hence 



B = s" and B= ~ T^'* T~ = ~' " nd by " 



S v W^^^M 

 duction/= ; or since S=1.00 in water, 



'= w - I" tJ>c thermometer of Fahrenheit which 



we have described, the stem AB is made wy short, and 

 is only one-third of the length of a tube which be places 

 between the balls C and I). 



The results obtained with this hydrometer, may be Hydromf- 

 reduced to the temperature of 32 of Fahrenheit, and ttn - 

 allowance made for the effects of heat, both upon the li- 

 quid and the hydrometer itself. The following formu- 

 la, given by M. Biot, includes these effects. 



. 



In this formula, () is the weipht in grammes of a 

 cubic centimetre of the liquid subjected to experiment, 

 A is the dilatation of this liquid from 3^ to the tempe- 

 rature *, P is the absolute weight of the hydrometer 

 when weighed in vacua, or its weight in air diminished 

 by the weight of the quantity of air which it displaces, 

 and it also expresses, in cubic centimetres, the value of 

 the part immersed in the liquid; (P) is the absolute 

 weight of the part immersed at 32 of Fahrenheit ; 

 and K the cubic dilatation of the substance of the areo- 



meter. 



8. Clarke 1 * Hydrometer. 



The hydrometer invented by Mr Clarke, and de ritrke'* 

 scribed in the Philosophical Transactions by Dr Desa- hydrometer 

 gu tiers, was made of metal instead of glass. The prin- for i P' r ' tTH 

 cipal ball wa* made hollow and of copper, and the brass <MU b<lu " r "' 

 wire of about Jth of an inch thick, was soldered into 

 it. I'pen the item a mark is made, to which the in- 

 strument sinks when it is placed in proof spirits, and 

 another mark is made above and below this, at which 

 it sinks when the spirit is Vs 1 " under proof, or ^th 

 above proof. The lower ball could be screwed off, 

 and other ball* of different weight* screwed on, for 

 liquors that differ more than T '. th from proof, so a* to 

 give the specific gravities of all the mixtures of spi. 

 rituous liquors that are used in trials. See the Phil. 

 Traru. 17*0, No. 413, p. 277. ; and Deiaguliers' Count 

 oj Experimental Plalotophy, edit 3d, vol. ii. p. 233. 



S. DetagtJicrt' Hydrometer. 



The object of this instrument was to ascertain the Dtngu. 

 specific gravities of different kind* of water; and in HeiVhy- 

 order to give it a high degree of sensibility, Dr De- ln Ur - 

 sagulien made the hollow glass ball less than three 

 inches in diameter, while the item to which it wa* at- 

 tached was a long slender wire, whose diameter wa* 

 only the 4Oth part of an inch, and whose length was 10 

 inches. Under the great ball is placed a small ball, 

 about one inch in diamHer, to contain shot for floating 

 the instrument in a vertical position. In river or sou 

 P*' B ll water, the hydrometer sinks to a fixed point in 

 the middle of it* *tem. If a *ingle grain weight i* 

 added, the item will descend a whole mch. Now, a* the 

 hydrometer weigh* 4OOO grains, nnd ai one inch of the 

 stem weighs ten grains, the part of it innn. 

 weigh 4000 5O=S95O grains, 50 grains cnrr rending 

 to half the lenzth of the item. But the qutn'ity of water 

 displaced must weigh 4000 grains, equal t the whole 

 weight of the hydrometer ; consequently the instru- 

 ment will serve to compare together the different bulks 

 of 4OOO grains of water ; and sim-c one tenth of an 

 inch in the scale corresponds to one tenth of a grain, it 

 will obvioii.lv dioiiiDrauh the strength of a grain in 

 4000, or the 40,000th part of the whole bulk of wa- 

 ter. By altering the quantity of *het in the ballast 

 ball, this hydrometer may be fitted for comparing nny 

 other two liqtinrs that have nearly the same specific 



gravity. See Dr Desagulier* Course of Expenme*lal 

 :i 



