rectilineal angle. It is required to describe a triangle that EXERCISE TO PROPOSITION XLII. shall be equal to the given parallelogram a D, and have one of To describe a triangle equal to a given parallelogram, and having its angles equal to the given rectilinea! angle E. an angle equal to a given rectilineal angle. Produce cp to G, making D G equal to Dc; and at the point c, in the straight line co, make the angle acf equal to the In fig. 4, let a d be the given parallelogram, and e the given given angle B (I. 23), and let the straight line of meet AB produced (if necessary) in F. Join FG. Then the triangle FCG is the triangle required. Join FD. Because cd is equal to DG, therefore the triangle TCD is equal to the triangle FDG (1. 38), and the whole triangle Fcg is double the triangle rcd. But the parallelogram AD is also double the triangle FCD (I 41); therefore the triangle F C G is equal to the parallelogram AD (Ax. 2); and it has one of its angles, F OG, equal to the given rectilineal angle e. Q. E. F.* A B F E Solved by J. H. Eastwood (Middleton); Q. PRINGLE (Glasgow); D proceeds being on the Dr, side, and the sales on the Cr. side ; LESSONS IN BOOKKEEPING.-No. XXIII. sometimes, especially where the space admits of it, the charges, etc. are placed at the bottom of the account, so that the whole (Continued from page 200.) may be coitained in one page, as exemplified in the two accounts in this book. The Account Sales Bovk is frequently ACCOUNT SALES BOOK. made up from other books, where the particulars are entered An Account Sales is an account showing the amount of the as they can be obtained from time to time. As an account sales of goods imported and sold for behoof of the merchant, sales can rarely be made up at the period when the goods are or any of his correspondents, with the different charges attend- sold, the copy in the Sulis Book must be marked with the ing the sales, and the net proceeds of the whole. The book in date where it is entered in the Day Book, or the folio where which such 'accounts are entered is called the Account Sales it is entered in the Journal; as, like the Invoice Book, the Book, or simply Sales Book. An account sales is frequently entries may be made at once in the Journal, without passing made up in the Dr. and Cr, form, the charges and the net 1 through the Day Book. ACCOUNT SALES BOOK. (1) (1) ACCOUNT SALES of 7 Hhds. of Sugar (W. S. & Co.), received per the Ballarat, Captain Jones, from Barbadoes, and sold on account of Nathan Herschell of that place. (2) ACCOUNT SALES BOOK. (2) ACCOUNT SALES of 21 Tierces of Coffee (W. 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The vessel employed is generally a small The object of Calorimetry is to measure the quantity of heat cylinder made of silver or brass, with thin and polished sides. which bodies give out or absorb when their temperature is As soon as the hot body is immersed in the liquid, the temraised or lowered by a given number of degrees, or when they temperature which it reaches, it is plain that the body is cooled perature of the latter is raised, and if a represents the highest change their state. We cannot measure the absolute quantity of heat lost or gained by a body, but only the relative quantity; down by a number of degrees denoted by (T-0), and that it that is, the ratio between this absolute quantity and that has consequently lost a quantity of heat which is measured which a body_gives out or absorbs in producing a given effect. by the expression me (T-0). The water and the vessel, on Among the French philosophers, the unit of heat, which is the contrary, are heated up by a number of degrees denoted called caloric, is assumed to be the quantity of beat necessary neat denoted by m (0 - 1) and m' ." (0 – t), because the by (0 – t), and they have absorbed respectively quantities of 10 raise the temperature of a kilogramme* of water from 00 to 1o Centigrade. Among ourselves, the unit of heat has been specific caloric of water is unity. Now, the quantity of heat assumed to be the quantity of heat necessary to raise one given out by the hot body is evidently equal to the sum of the pound of water from the boiling point to 1° Fahrenheit above quantities of the heat absorbed by the water and the vessel ; that point, that is, from 32° to 33° Fahrenheit. In what fol- therefore, we have the equation mc (T-0) = m (0 - 1) + lows, we shall adhere to the French unit, as being the most when the specific caloric d' of the vessel is known. If it be m' c' (0 – t) (A); whence, it is easy to deduce the value ofc convenient, especially in reference to the Centigrade thermometer; and as the experiments on calorimetry have been unknown, we must first find it by immersing in the water a chiefly conducted by French philosophers. body of the same material as the vessel, and thereby obtaining Specific Caloric.--The specific caloric, or as it has been termed the specific caloric required. The preceding equation then takes the form the caloric capacity of a body, is the quantity of heat which it absorbs when its temperature is raised from 09 10 1° Centi- Md (T - 0) = m (0 – t) + m' ' (0 – t) (B); grade, 'as compared with that which a weight of water equal that is, the equation only contains the unknown quantity c'. 10 that of the body would absorb in the same circumstances; The specific caloric of the vessel being thus determined, the this is in fact the same thing as taking the specific caloric of equation (A) is resolved by making (8 – 1) in the second water for unity. It is easily proved that all bodies have not member a common factor, and it becomes mc(T-O)=(n + the same calorific capacity. If we mix, for instance, a kilo- | m'c') (0 – t) (C); whence, by dividing both sides by's (T-0), gramme of mercury at 100° Centigrade with a kilogramme of we have water at 0° Centigrade, we shall find that the temperature of the mixture is only about 3o Centigrade. This shows that (m + m'd') (-1) (D.) though the mercury is cooled down through 97° Centigrade, M (T – ) the quantity of heat which it has lost only heats the same weight of water up to 30 Centigrade. The water, therefore, Or, by putting m’d=, in which y denotes the weight of the which is equal in weight to the mercury, absorbs about s3 water which would absorb the ganie quantity.of heat as the times more heat than the mercury in the production of the vessel, the formula (D) may be written thus, same degree of temperature. (m + 4) (0 - 1) Three methods have been employed in the determination of (E.) the specific caloric of bodies: the method of melting ice; the M (T ) method of mixtures; and the method of the reduction of In this formula, the value of je is expressed by saying that the temperature, in the latter of which the specific caloric of a vessel reduced into water. body is calculated, according to the time which it requires to In order to give the method of mixtures that degree of precooi it down from a given number of degrees. We proceed cision which it requires, the heat absorbed by the glass and to show how the quantity of heat absorbed by a body is the mercury must be taken into account. In order to estimate determined, when its mass and specific caloric are given, and the loss of heat arising from radiation in the preceding process, its temperature is raised a certain number of degrees. a primary experiment is made with the body whose specific Let m denote the weight of a body in kilogrammes, e its caloric is sought, with the view of ascertaining approximately specific caloric, and t its temperature. The quantity of' heat the number of degrees by which the temperature of the water necessary to raise a kilogramme of water from 0° to 1o Centi- and of the vessel must be raised. Supposing, for example, that grade being assumed as unity, it will require m of these units this number was 100 Centigrade, we cool down the water and to raise a weight of m kilogramnaes of water from 0° to 1° Centi- the vessel to halt this number, below the temperature of the grade ; and to raise the latter from 0° to to Centigrade, it will surrounding air ; we then proceed to the actual experiment require t times as much, viz. mt. of heat necessary to raise m kilogrammes of water from 0° to sensibly by 10o Centigrade, it follows that the vessel whose Centigrade, its specific caloric being 1, it is evident that for temperature was at first 50 Centigrade below that of the sura body of the same weight whose specific caloric is c, it will rounding air, is at the end of the experiment 6° Centigrade require e times mt, or nec. Whence it follows, that when a above it. Compensation has, therefore, taken place between body is heated from 0° to 20 Centigrade, the quantity of heat the loss and the gain of heat which arose from radiation which it absorbs may be represented by the product of these during the experiment. M. Regnault has calculated, by the its specific caloric. A similar expression may be easily formed ture, the specific caloric of a great number of bodies. The for the quantity of hest, according to Fahrenheit's scale, the following are the numbers which he obtained, uy the former pound being the unit of weight. method, for those bodies which are most frequently required Method of Mixtures. In order to calculate the specific caloric in the arts, for the temperature between 0 and 100° Centiof a solid or a liquid body by the method of mixtures, we grade, weigh it and raise it to a known temperature, which is deter- TABLE OF THE MEAN SPECIFIC CALORIC OF SUBmined, when the body is a solid, br' keeping it for a certnin time in a current of vapour at' 1062 Centigrade; we then STANCES, ACCORDING TO M. REGNAULT. immerse it in a mass of cold water of which ihe weight and Specific Caloric. the temperature are also known. From the quantity of heat Water which the body imparts to the water, we at once deduce its Oil of turpentine 0.42590 specific caloric. Thus, let x represent the weight of the body; Animal charcoal 0.26085 Charcoal (wood) A kilogramme is about 2.2 pounds Avoirdupois. Sulphur ... Substances. ... 1.00000 0.24111 0.20259 120 VOL. Y. . ... .. ... ... mi Mercury .. CALORICO SUPSTANCUS-continued. with ice as shown in the figure. The water which escapes by Seberances, Spesic Caloric. the stor.cock p, is then collected, and when its Aow is stopped, Grapl.ite its weight p is found in kilogrammes ; this weigt evidently 0 20187 Giais termemeter) shows that of the melted ice. Now, since a kilogramme oiics, 019765 Prospoorus when melting, absorbs 79 units of heat, p kilogrammes will 019949 Dianio have absorbed P times 79 units. But this quanu!y of heat is 6-14687 Many on se carburt't: a) 0.14417 necessarily equai to that which has been giver out by the Tin place 2933 body m, while it was cooling down from t'? 10 O- Cantigrade; lien 011373 that is, to mtc, as alreadv shown; for it musi be evident that Haft etech in cooling down from to to 09, a body will give out exactly 011660 Vich 0.10863 the quantity of heat which was absorbed in heating it from 6* (lubalt 010696 up to to Centigrade. Hence, we have the equation, mtos Zine 0.09556 79 r Coppor 79 P; and c = If the specific caloric be calculated by Silver 0.05701 Tin 35623 the preceding process, account must be taken of the heat given Antimony 095077 out by the vessel in whica the liquid is contained, 0173339 The nethod of the ice-calorimeter is affected with several Gold 009244 causes of error. The principal is that of a part of the water Platinum (laminated) 0.03243 proceeding from the meiting ice remaining attached to that Bismuth . 003984 which has not been meited, the weight p cannot be determined exactly, Moreaver, the exierior air which enters into the The numbers given in this table represent the mean specinc calorimeter by the stof-cocks, increases the quantity of meltcaloric of bouies, between 10 and 100° Centigrade. It appears, ing ice. These inconveniences are partly remedied by substihowever, from the labours of MM. Dulong and Petit on heat, tuting ice-welis for the calorimeter. The name ice-well is inat the spe'ific calcric increases with the temperature of the applied to a hole inade in a piece of solid ice by means of a bodies. That of metals, for example, is greater between 100hot iron, in which we immerse the body whose specific caloric and 200° Centigrade than between 0 and 100° Centigrade, is sough:, after having heated i: to a known temperature; the and greater still between 2300 and 300° Certigrade. Thus, 10 i edges of the hole are smoothed with the hot iron; and the hole raise the temperature of a body from 2000 10 250° Centigra itself is covered with a piece of ice carefully smoothed in the requires more heat than to raise it from 100° ro 1909 Centi same way, and made exactly to fit it. When the body is grade; and again, more from 1000 10 15C° Certigrade than cooled dowa to zero, it is withdrawn, as well as the water, from from Co to 50° Centigrade. the melted ice; and ihe weight of the latter being found, it is Method of Melling Ice.-- This joethod is founded on the only neressary to apply the formula given above. principle of the latent caloric absorbed by melting ice, a Specific Caloria of Gases. The specitic caloric of gases is quantity of heat which, as we shall soon have occasion to referred to that of water pr of air; in the former case, it repre. remark, is about 73 units for i kilogramme of ice. The appa- sents the quantity of heat necessary to raise a given weight of ratas employed in this method was invented by MM. Lavoisier gas big 1o Centigrade, as compared with that which would be and Laplace, and is denominated the calorimeter of ice. The necessary to raise the same weight of water by the same exterior view of this apparatus is represented in liģ. 221, and quantity; in the second case, the quantity of heát necessary a vertical section in fig. 222. to raise a given volume of gas by 1o Centigrade, as compared with that which would be necessary to raise the same volume Fig. 221. Fig. 222. of air by the same quantity. In the latter way of considering the specific caloric of gases, we can throughout suppose them ui a constant pressure and a variable volume; or, even at a constant volume and a variable pressure. The specific caloric of bodies at a constant volume is always less for the same gas, than it is at a constant pressure The speciric calorie of gases, as compared with water, were determined in 1912, by MM. Delarnche and Berard. in doing this, iney measured the quantity of neat given out by a known weight of gas to a known weight of water, the former being made to pass through a worm placed in the liquid. They then deduced the specitic caloric of the gas by a calculation analogous to that which has been given for the method of mistures. They also determined the specilic caloric of gases, at a constant pressure, in reiation to air, by comparing the quantities of neat given out by equai volumes oi gas and air to the same we'ght of water, at ihe same temperature and atmos, pheric pressure, during the whole of the experiments. Since these experiments. MM. De la Rive and Marcet, in 1835, applied the method of the reduction of temperature to the determination of the same quantities, Lastiy, the specific caluric of gases, at a constant volume, It is formed of three cor.centric cylinders in tin plate. In the always with relation to air, has been calculated by M. Dulong central one is placed the body m, tig. B, whose specific heat is by means of the formula employed to determine the velocity required; the other two compartments are filled with pounded of the progagation or sound in different gases. The following ice. The ice of the compartment a, is intended to be melted tubie of the specific caloric of different gases is taken from by the hot body; and that of the compartment 1, is merely Peschell's Inysics :intended to prevent the radiation of the caloric from the air surrounding the apparatus. Two stop-cocks D and b, are used TABLE OF THE SPECIFIC CALORIC OF GASES. only to allow the water whicn proceeds from the meiting ice Specific Caloric, to escape. In order to finu the speciác caloric of a solid body as compared by means of this calorimeter, we tind firsi the weight of this Atmospucrie air 1.0000 body m in kilogrammes, we then raise it to a known tempera Oxygen 0.9069 0 2421 turé t by keeping it for soine time in a hot bath of water or of 14-6348 3.8793 Hydrogen oil, or in a current of steam; we then place it quickly in the Nitrogen 1.0318 0.2754 middle cylinder, instantly put on the lids, and cover them Gases. with air; with water. 0.2669 . 239 CALORIC OF GASES- continued. quantity of heat, which is denominated the coloric of elasticity, Specific Cioric, or the caloric of vaporisation. In order to determine the Gaeus. quantity of heat absorbed then by the yuit of weigh: os diferwith pic; ent liquids, we adopt as evident, the principle that a vapour Carhonic oxide 1:0267 02749 which is liquified, gires ou a quantity of caloric precisely Protoxide of nitrogen 0905 0.2145 equal to that which it hai absorbed i' vaporisation. The Carbonic acid 0.8195 method employed in his case is the same as inat resorted to Bayi (Olefiant gae) ... 1.7876 0:17 in the determination ci tbe verific calcric of the gases in relaSteam at 2120 31380 9 $70 tion to that o warer. The apparaius employed in this kind of research is exhihisei ir fiz. 223. Application of Specific Calorio.--The knowledge of the specific crioric of bodies affords the means of measuring approximately Fig. 223. the most elevated temperatures, Thus, if we place in a medium whose temperature is required, a mass of difficultly fusible metel, as a cylinder of platir um. and allow it to remain so long as to acquire the temperature of the medium; then, it we immesse it in water whose weight and temperature are known, and observe the highest temperature & which the quid reaches, we can thence deduce from formula (C) the emperature ? to which the mass of platinum has bee? raised, Yet the temperature thus obtained will be only approximate; for we have seen that the specific caloric increases with the temperature, and as we do not know that of the platinum a the elevated temperature to which it has been brought in the supposed experiment, we can only substitute for c in the formula an approximate valuo. Latent Caloric of Fusion.--We have seen that when bedies (T-2); and in another, at the moment of solidification, oni at the temperature to Cent. ; while at the end of it, ir disengages a quan:ity of heat represented as Mr. We comes out at ° Cent. ; whence it follows, that Juring the gave, therefore, the equation mc (1 -- 8) +- Mind - "); whole experiment it comes out at a m.can temporale berween thiese, that is, at the temperarure of it -- es. l'he weigh v m (8 - t) -- MT -- 01 of the vapouc has, therefore, given out a qilation of beat I denoted by a 7-11&to; tut at the moment of its Caloris or Melting Ice. — The knowledge of the caloric of the liquefactior, il sisengaged a quantiiv o beut represented by meting of ice.is interesting on account of iss useful applica- *: puoreover, the hoac aosu, bed or the cold water, e tions. It is also determined by the method of mixtures. Thus, worin, and the versel, is it (f -- i), ire nare therefore, tre warm water uit te cenilierade su ti ciente med nad nhe rice equation mx+x{r – }(4.01} = :n (0 – 2,; wheace the Let the ice be thrown into the water, and as soon as it is all vaiuz of w may be found. H. Dinspreie has ascertained by melted, let the finai temperature of the mixture be noted. I this means, for the calorie of eiastici:p in the vapour of water. Prepresents this temperature, the water being cooled down at 100oCent., that is, s'een, the number á !0; in other words, trom do Centigrade tu 0. has given nut a quantity of heat repre- a gramme of water ui 190° Conf. xbsordz in its vaporisation Benced by m( – 6); and if x represents the caloric of the melt- the quantity of hea :) ce arv 10 raian 540 grammes of water ing of ice, it has a hsorbed, in crder to melt , a quantity of heat from 0° to i? Ceute; or, which is the same thing, the quanti. enoted by Ma; but it is heated throughout, alter the meltins, of heat necessary to ruse ! gramme fr«-un ou to 540o Cens. and its teraperature rises from 0° to Cenizrade ; it has there" As 100° Cent are eque: to 180° Fah:., we heve this proportie: ore absorbed a quartity of heat denoted ne. We have, there to express the seme quantity in drziees of Fabrenhei:'s ther. educe the value of x. By this process, and at the same time expresse? what is alled the la'ent...cat of stenin, according to praiding with the greatest care all sources of error. MM. La M. Despretz. The latent neat visueann is generalig rockorc... Propostaye and Desains found that the calcrico. the welting in rounc numhers al 1000Fahr. of ice is 79; that is, a kilogramme of melted ice absorbs, in the State of latent calori, the quantity of hea: necessary to raise SOURCES OF HEAT. The different sources or neat are the following:- 1s?, the thing, : ilogram me cf water trorú 0° ro 19° Centi- mechanical souries. riz triviin percussion, and presel; 2na, the mysiocł sources, viz. Sulat caduction, te iesirin hep Latent Caloric of Vaporisation.--We have seen thai liquids, molecular action, change , of slave, ale tiec mr.y ; Bru, ie when converted into vapour, make latent a very considerable chemical sources, Viz. comdination 'anit combustion; line hence, : the same grade. |