78 



THE POPULAR EDUCATOR 



5. A wheel revolves 1,000 times in travelling a mile ; what is 

 its diameter ? 



6. Supposing the earth is always 91 millions of miles from 

 the sun, and that it makes a complete revolution in its orbit in 

 365J days ; how many miles per minute does it move ? 



HYDROSTATICS. V. 



SPECIFIC GRAVITY. 



THE principle we examined in our last lesson is of great use in 

 the determination of the density, or " specific gravity," as ii 

 is termed, of different bodies. 



It is a well-known fact that different substances contain 

 different quantities of matter in the same bulk. If we take a 

 number of 1-inch cubes of various bodies, as, for example, cork 

 oak, iron, stone, etc., and carefully weigh them, we shall fine 

 that they differ very greatly in their weight. The cork wil 

 weigh about 60 grains, the oak about 190, while the iron wil 

 weigh nearly 4 ounces. But though there is this difference 

 between different substances, we shall find that a cubic inch o: 

 any one substance always weighs nearly the same. If, then, we 

 could procure equal blocks of all substances, and note their 

 weights, we could form a table of densities. The advantages 

 of this would be very great. Sometimes we have a large 

 block of known size, and we wish to know the weight, or we 

 may want to know how much space a given weight of any 

 substance would occupy, and all such questions could be solved 

 from this table. It is, however, impossible to procure such 

 blocks of many substances on account of their shape or physical 

 properties, and many other bodies are too small or too valuable. 

 We cannot, then, compare their densities in this way, but we 

 may take some substance as a standard, and compare the 

 weights of all others with this. 



Now any substance might be chosen for this purpose, the 

 main requisites being that it shall be easily procurable in 

 state of purity, and easy of manipulation. Water has been 

 chosen as this standard, and is found to answer well. When, 

 therefore, we speak of the specific gravity of any body, we 

 mean this the proportion which exists between its weight 

 and that of an equal bulk of distilled water at a temperature 

 of 60. 



The reason why we thus fix on a certain temperature is that 

 water expands by heat, and therefore a cubic inch of hot water 

 weighs less than an equal bulk of cold. The temperature of 

 is chosen merely as a matter of convenience, that being 

 about the average, and therefore involving less trouble. When, 

 then, we say the specific gravity of mercury is 13'6, wo mean 

 that any amount of mercury weighs 13'6 times as much as an 

 equal bulk of distilled water at 60. Now, as' we have seen, 

 the weight of a cubic inch of distilled water is 252'5 grains ; a 

 cubic inch of mercury therefore weighs 252'5 grains X 13'6, 

 or 3,434 grains, which is nearly 8 oz. We can in this way, if 

 we know the specific gravity of a body, tell the weight of any 

 bulk of it. Questions like the following frequently occur, and 

 can thus be solved : What is the weight of a block of coai 

 3 feet X 5 X 4, the specific gravity of coal being 1'270 ? 



Since the specific gravity of the coal is T270, the weight of 

 a cubic foot is T270 times that of an equal bulk of water. But a 

 cubic foot of water weighs about 1,000 oz. ; a cubic foot of coal 

 must then weigh 1,270 ounces. Now the total bulk of the coal 

 is 3 X 5 X 4 = 60 cubic feet. Its weight, therefore, is 

 60 X 1,270 ounces = 76,200 ounces, or 42 cwt. 2 qr. 2 Ib. Again, 

 strong oil of vitriol has a specific gravity of T850 ; how much 

 will 6 Ib. measure? A fluid ounce of water, it must be re- 

 membered, weighs one ounce avoirdupois ; 6 Ib. of water, 

 then, would measure 96 oz. : but since oil of vitriol is heavier 

 than it, in the proportion of 1,850 to 1,000, it will measure pro- 

 portionately less. Hence the following proportion will give us 

 the bulk : 



As 1,850 : 1,000 : : 96 : the required volume. 



On working this out, we shall find that the vitriol will measure 

 51 '89 oz., or nearly 3j ordinary pints. 



We see thus the importance of knowing the specific gravity 

 of any substance, and there are several modes of ascertaining 



it, one or other of which is more applicable according to the 

 circumstances of the case. If, however, we bear in mind 

 exactly what it is we wish to know, we shall find little difficulty 

 in remembering which way to proceed. 



We will consider, first, how to proceed in the case of a liquid. 

 Procure a thin glass flask (Fig. 13, A) provided with an accurately 

 fitting stopper. Instead, however, of this being solid, let it be 

 drawn out, as shown at B, into a long tubular neck, so that when 

 it is put in its place any excess of liquid may escape through it. 

 The flask is best made of such a size as to hold 1,000 grains up 

 to the mark o in the neck. Now procure a small piece of metal, 

 and file or grind it till it exactly balances the flask and stopper 

 when empty. If the flask, filled with distilled water to the 

 level o, be put in one pan of a balance and the counterpoise or 

 weight in the other, we must add just 1,000 grains to balance 

 the water. Empty this out, and fill it with the liquid whose 

 specific gravity we want to know say, for instance, the strongest 

 alcohol and weigh again; we shall now find that only 792 

 grains are required to balance it. The weight, then, of any 

 volume of alcohol is to that of an equal bulk of water in the 

 proportion of 792 to 1,000; or, in other words, the specific 

 gravity of the alcohol is '792. The reason why we chose a flask 

 containing 1,000 grains is now clear, for all trouble in calcula- 

 tion is thus avoided. We have only to take the weight of the 

 liquid in grains, and point off three figures as decimals, and we 

 have the specific gravity. 



Thus, if we fill the bottle with sea water, wo shall find it 

 will weigh 1,028 grains; the specific gravity is therefore T028. 



Sometimes, however, it is difficult or costly to procure a 

 sufficient quantity of the liquid to fill such a large flask. We 

 then use a much smaller one, usually made out of a glass tubes 



and, as before, we first find the weight of water required to fill 



it to a certain mark, and then the weight of the liquid wo are 



operating upon. 



The details of an actual experiment will make this clearer. 



A sample of nitric acid was taken, of which it was desired to 



ascertain the specific gravity. The 



small bottle was first put in the 



scales and found to weigh 80 grains. 



On being filled with the acid it 



weighed 159 grains. The acid was 



next emptied out, the bottle rinsed, 



and filled to the same height with 



water, the weight being then 136 



grains. 



Now, since the bottle weighed 



30 grains, we subtract this amount 



from its weight when filled with 



the different liquids, and thus see 



that the water in the bottle weighed 



56 grains, while the weight of the same bulk of acid was 79 

 grains. We have, then, the following equation by which we 

 an determine the specific gravity of the liquid : 

 As 56 : 79 : : 1 : 1'41. 



This, then, is the specific gravity of the acid, and from this we 

 can form an idea of its strength. In our next lesson we shall 

 see how to proceed in the case of solids. 



EXAMPLES. 



1. A cubic foot of glass weighs 166 pounds; what is its specific 

 fravity ? 



2. A flask holds 8 ounces of water and 10J of another liquid; what 

 s the specific gravity of the latter ? 



3. A small flask weighs when empty 150 grains, when full of au oil 

 290 grains, and when full of water 315 grains; what is the specific 

 gravity of the oil P 



4. A rectangular block of timber measures 14 in. x 14 x 10. Its 

 specific gravity is '850. If it floats with its largest surface horizontal, 

 " LOW deep will it be immersed ? Also, how deep if it be vertical ? 



5. A block of chalk 3 feet 3' 0" * g Q" x 2' 6" is suspended in water. 

 Taking its specific gravity as 2 '660, what is the strain on the rope 



lupporting it ? 



ANSWERS TO EXAMPLES IN LESSON IV. (page 54). 



1. Since the areas of the pistons are to one another in the propor- 



ion of the squares of their diameters, the larger has 144 times the 



area of the smaller. There is also a gain of 6 by the lever. Thus the 



dvantage gained is 144 x 6 or 864. If we divide 20 tons by this, we 



ind the required pressure is 51'85 pounds. 



Fig. 13. 



