200 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[June, 



intention of the patentees to carry out these experiments to a prac- 

 tical result in a locomotive engine they are about to build, and tliey 

 are also now engaged in executing orders for fixed engines, whicli will 

 afford an opportunity of fully testing their power. 



We strongly recommend the engine to the notice of engineers, and 

 advise them to avail themselves of the opportunity of forming their 

 own judgment of its merits, by examining the engine at work at the 

 premises of the patentees, who will be happy to explain its action. 



The following is the Table of experiments above alluded to. 



ON THE THEORY OF THE STEAM ENGINE. 



BY ARISTIDES MORNAY, ESQ. 



In our April number we promised to lay before our readers a new 

 formula for calculating the force of steam at different temperatures, 

 which it seemed possible might represent the true law, since it con- 

 tains but one arbitrary constant, and that a very simple one, and 

 agrees pretty well with those experiments which appear most worthy 

 of confidence, between temperatures very far distant from each other. 

 It presents likewise, as we shall show in the ensuing number, 

 facilities in calculation not to be met willi in any other formula 

 which has as yet been proijosed ; not in calculating simply the force 

 of steam at different temperatures, (TredgoUVs rule being simpler for 

 that purpose,) but in calculating the force corresponding to different 

 densities, or rather the variations of elastic force occasioned by 

 changes in the density of the steam. This is principally useful in 

 estimating the effect of expansive steam engines, for which the for- 

 mula was specially sought, and if it does not give the actual density 

 with perfect accuracy, the error, which cannot be very great in any 

 practical case, may be almost entirely eliminated in its application 

 to that object. 



Our formula is founded in part on the two physical laws discovered 

 by Gay Lussac and Mariotte; the former, that elastic Ihiids receive, 

 under a given pressure, for every additional degree (Fahr.), an acces- 

 sion to their bulk equal to one 480th of the volume they would 

 occupy, under the same pressure, at the freezing point of water ; (he 

 latter, lliat the elastic force of gases is directly proportional to their 

 density, or inversely as their vohune. If, therefore, we divide the 

 volume of a given quantity of any elastic fluid at 32 deg. into 480 

 equal parts, its volume at deg. will be equal to 448 of those parts, 

 and at any temperature /, i+448. Thus, if a given quantity of Iluiil 

 occupies at the temperature t' and luider the pressure p', the volume 

 v', it will, at any liigher temperature t, and under the same pressure 



p', occupy a space equal to*' 7, ■ ; but if confined to its original 



volume, it will support a pressure equal to f' JIZtL. If now we 



^'+448 



suppose it compressed into a still smaller space, so that its density 

 shall be increased from d' to d, its temperature being still /, its elastic 

 force p will be 



= , rf(<+448) 

 ^~^ rf'(«'-t-448) ' 



and if we take the density of steam generated under a pressure of 30 

 inches of mercury for unity, and make in the above equation />— 30, 

 f/'=l, and i— 21'i, the elastic force of steam at any temperature t will 

 be 



_.,n tf(<+448) ri(<-h448) 

 ^^-^°— 660- =— ^2-' • • - 1 



the density d to be hereafter determined. 



Having by this formula calculated a series of densities from the 

 experiments of Dulong and Ai-ago, the density seemed to increase 

 in a geometrical ratio, while the temperature increased in an arith- 

 metical ratio ; but a formula constnicted on this principle gave by 

 far too high results at high temperatiu-es, in consequence of wliich 

 we introduced the divisor <-l-448, wliich in a great measure corrected 

 that fault of the formula. It then became 



5(t— 212) 

 «+448 • • • • 

 Combining the equations I and II, we obtain finally 



log.d — ''- 



II 



log.iJ = log. («-H48)-l- 



5(<— 212) 



■1.3424227. 



Ill 



The following table has been constructed for the purpose of com- 

 paring the results of experiment with those calculated by Tredgold's 

 rule and by the above equation, affording a comprehensive view of 

 their variations and discrepancies up to an elastic force of 24 

 atmospheres : — 



Tempe- 

 ratvire. 



Elastic force by 

 Experiment, 



32-00 

 64-OU 

 9G-0U 

 132-011 

 173-00 

 212-OU 

 2'2U-0U 



230-00 



234-32 



240-00 



212 



•2.')ll-l)U 



'250-3U 



250-79 



•>r)4-GG 



2(19-87 



27U-(Xl 



271-94 



■272(1(1 



275-(IU 



2siO-(.l(.t 



2SU-91 



292-91 



293- 11) 



3(17 



307-9 1 



320-00 



.320-30 



.331-70 



33G-S7 



33G-91 



310-OU 



311 



311-83 



3r.0-78 



3r,l-32 



.3r)S-SN 

 .•ryj-Gi) 



371-()(l 



3!)H-4N 



JlH--l( 



435-.'')6 



Elasti 

 force by 

 Tred- 

 gold's 

 ride. 



1 



0-25 



0-75 



1-95 



rrU7 



13-ls 



3U-0U 



34-20 



34-95 



41-51 



4.'i-00 



.OU-OO 



.')2-r)(i 

 rj9-i2 



GO-UO 

 60-UO 

 C4-20 

 82-50 

 82-5(1 

 «G-12 



90-0(1 

 97-75 

 100-21 

 120-UU 

 1 20-00 

 15(l-(.10 

 150-00 

 179-40 

 1SO-0(I 

 180-00; 

 210-OU; 

 2'25-00' 

 225-011' 

 •231 -OU 

 2 10-11(1 

 210-0(1 

 270-00 

 270-00 

 300-0o! 

 300-0(l! 

 3G0-00 



iso-oo 



GOO-00 

 7'20-00 



D. 



T. 



C. 



T. 



C. 



'1'. 



8. 



C. 

 U.A 



C. 



T. 

 U.A 



D. 



C. 



T. 

 D.A 



0. 



8. 

 U.A 



C. 



T. 



C. 

 U.A 



C. 



U. 

 U.A. 



C. 

 U.A. 



C. 

 U.A. 



O. 

 U.A 



Differ- 

 ences. 



o-i 



0-G3 

 1-S4 

 .5-07 

 13-4G 

 30-00 

 34-9'i 



42-00 



45-41 



50-21 



52 



59-79 



GO-00 



GO-GO 



G4-72 



83-2G 



s3-ir 



><f;-|(l 



.x(;-20 



90-41 

 97-92 

 99-38 

 119-Gi 

 1 20-50 

 1 49-0(1 

 M9-8S 

 178-50 



179-43 

 210-50 

 •22G-09 

 22G-,30 

 23G-00 

 241-77 

 241-93 

 272-8G 

 '274-83 

 3(.I3-G4 

 306-51 

 .368-83 

 498-91 

 631-61 

 767-38 



0-08 — 

 0-12 — 

 0-11 — 

 0-00 

 0-28 -f 

 0-00 

 0-72 -k- 

 0-03 

 0-49 -i- 

 0-11 + 

 0-21 -j- 

 0-25 + 

 0-G7 + 

 0-00 

 0-GO -f 

 0-52 + 

 (J-7G-4- 

 0-95 + 

 0-02 

 '2-70 

 0-41 + 

 0-17 + 

 0-83 — 

 0-35 

 0-50 + 

 1-00 — 

 (1-12 

 0-90 

 1-50 

 0-57 — 

 0-50 + 

 1-09 + 

 l-.3(l + 

 5-00 + 

 1-77 + 

 1-93 + 

 •2-86 + 

 4-83 -f 

 .3-64 + 

 6 51 + 

 8-83 + 

 18-94 + 

 31-61 + 

 47.38 + 



Mean 

 Differences. 



Elastic 

 force by 

 Formu- 

 la III. 



0-.330 

 0-075 + 

 0-5G0 - 



0-990- 



1-195 + 



1-850 + 

 3-845 + 

 5-075 + 



0-29 



0-83 



'2-12 



5-39 



13-69 



30-00 



34-85 



41-84 



45-'20 



49 96 



.52-45 



59-38 



59-69 



60-19 



G4-'21 



82-65 



8'2-72 



85-3 1 



8i5-42 



89-62 



9G-99 



98-43 



118-41 



I19-'29 



1 17-29 



118-13 



176.'22 



177-13 



207-54 

 ■2-2'2-77 

 222-99 

 •232-43 



238-08 

 238-21 

 '268-.36 

 270-27 

 '298-23 

 301-00 

 3G1-30 

 486-08 

 611-9( 

 739-48 



Differ- 

 ences. 



0-04 + 

 0-08 + 

 0-17 + 

 0-32 + 

 0-51 + 

 0-00 

 0-65 + 

 0-10 — 

 0-33 + 

 0-20-1- 

 0-04 

 0-05 

 0-'26 + 

 0.3) 

 0-19 + 

 0-05 -f 

 0-15 + 

 0-'22 + 

 0-78 

 3-48 

 0-.38 

 0-76 — 

 1-78 

 1-59 

 0-71 

 '2-71 — 

 1-87 — 

 .3-18 — 

 3-78 — 

 •2-87 — 

 2-4G — 

 •2-23 — 

 2-01 — 

 1-43 + 

 1-92 — 

 1-76- 

 1-64 — 

 0-27 + 

 1-77 — 

 1-00 + 

 1-30 + 

 6-08 -h 

 11-9G + 

 19-48 + 



Mean 

 Difl'erences. 



0-275 + 



V 0-2G5 + 

 \ 0-045 



0-047 + 



0137- 



\ 1-270- 



[ 1-150 — 



I 2-290 — 



i 3-277 



I 2120 — 



I 1-840- 



I 0-665- 



I 0-385 — 



