■Zai 



ERICSSON'S ENGlXt:. 



risss 



originall}- filled the supply cylintler at 15 lbs. pressure, will oc^ 

 cupy one-half the space at 30 lbs. pressuvo. Now, while the 

 communication between the receiver and the working cylinder 

 continues open, that is during the | stroke, if we disregard the 

 leakage, &e., the same quantity of air, at the same pressure of 

 30 lbs. will flow from the former to the latter. It is capable of 

 filling a space equal to one-half of the supply cylinder, or what 

 amounts to the same, one-third of the working cylinder, at the 

 same temperature, without any change of pressure; therefore in 

 expanding to fill two-thirds of the working cylinder, its expansi\-e 

 force will be reduced to 15 lbs. To compensate for this it is 

 only necessary that its temperatu;-e, as fast as it flows in, should 

 be elevated 480 ° , when its expansixe force will be retained at 

 30 lbs. 



A similar explanation may bo given for any other supposed 

 pressure and temperature, and the question of the leakage may 

 be considered from this point of view. 



It has been stated that the cut oflj whatever may be the rela- 

 tive sizeof the two working cylinders, should be so "adjusted that 

 the portion of the working cylinder into which the air is admit- 

 ted while the valves remain open, will be equal in volume to the 

 whole supply cylinder. To show this, we will at first leave the 

 leakage out of view, and denote the fractional part of the stroke 

 answering to the cut off' supposed, (in the present engines |) by 

 a, and a larger fraction of the stroke, answering to a different cut 

 off", by b. Let b be n times greater than a. Now, if we conceive 

 the fractional cut-off stroke to less than a, the actual workino- 

 pressure remaining the same, the mean effective pressure for the 

 whole stroke, will be less than when a is used. If, on the other 

 hand, it be made greater, (as b=na,) the body of the air which 

 originally filled, the supply cylinder at 15 lbs. pressure and 32 ° 

 emperature, on entering the working cylinder will expand ?i times, 



15 

 and its working force will be — X2 (supposing working temper- 

 re 

 ature to be 480 ° +32 ° ;) whereas, for to cut off a tire force will 

 be 15X2, and in the subsequent expansion from a to b, the mean 

 force throughout the fractional stoke b will be greater than 

 15X2 

 , since this will be the actual force after the expansion to b. 



n 



The same will be trae if we take the leakage into account ; 

 for suppose the leakage to reduce the pressure of the air that fills 



15 

 a, before it is heated, to — , then when heated 480 ° the pressure 



becomes — X2, which we will put equal to I: Now, if we sup- 



m 

 pcse, as before, the cut off to be increased from a to b, the force 



k 

 k will be reduced to — ; but the mean effocti\-e pressure for the 



n 

 same fractional stroke b, when the cut oft' « is used, will be greater 



k 

 than this, and the actual pressure after the expansion to b, will h-— 



H 



So that the constant pressure for the b cut off is equal to the 

 pressure for the a cut off reduced by the expansion to b. 



It may be well to inquire, in this connection, into the proper 

 relative size to be given to the supply and working cylinders to 

 obtain the greatest amount of moti\'e power from the engine. 

 Let A^^area of supply piston, and .r=ratio of working to sup- 

 ply piston; then, by what we have soon, the jiortion of the stroke 

 during which the air is flowing into the workimv cvlimler, and 



acting with i.s full constant pressure is equal to-. Calling 



«^ 

 this pressure per square inch, P, the foUowmg proportion gives ns 

 the me.in effective pressure (p) on working piston for the whole 



P Ivg. x+P 

 stroke, viz., x : hyp. log. .t-M : : P : ;;= . . The mean 



X 



eft'ective upward pressure upon the whole piston will therefore be 



P log. aH-P 

 expressed by x A.r, or P.A log. .r-fP. A. The down 



X 



wai-d pressure on the working piston=15ft)s.xAa:, and hence 

 the resulting effective pressure=P. A log. a+P.A— 1 5 A.t. With 

 the aid of the differential calculus, wo find this expression to Le 



^ / P \ 



a maximum whenj= — | more accurately- |; from which 



15 \ ■ 14.7/ 



it appears that the engines will have the greatest possible ]-ower, 

 at any given working pressure, when the 'cut off, taken invei-sely, 

 and the ratio of the volumes of the two cylindei-s, are each equal 

 to the working piessnre per square inch, divided by the atmos- 

 pheric pressuie (15 lbs). Accordingly the ratio of "the 1 ulks of 

 the cylinders ought to vary with the working piessuie used. 

 When this pressure is 8 lbs. above the pressure of the atmosphere 

 the cubical content of the supply cylinder ought to be yVinr of 

 that of the working cylinder, and the portion of the stroke fiom 

 the commencement at which the air is cut off; the same. The 

 actual ratio of the cubical contents of the cylinders of the engines 

 of the Ericsson is /irni-, (tfit "early), and the fi'acti^.n of the 

 stroke at which the air is cut off is said to be about -{^\. 



If a pressure of 1 2 lbs. instead of 8 lbs. were used, the same 

 ratio ought to be j\\. This would make the radius of the work- 

 ing piston 1 5-4 feet. It was Eiicsson's original design that it 

 si'ould be 16 feet. 



let us see now how the power nf the engines of the caloric 

 shi[i is to be determined. The actual pressures upon the two 

 l)istons a:-e the same, or nearly the same, while the communic.i- 

 lions ai'e 0])en ; the pressure on the top of the supply jiiston begins 

 at 15 lbs., becomes 8 lbs. -f 15 lbs. at the f stroke fiom the enil 

 (more accurately j-6%), and continues the same to the end of the 

 sti oke. The air is shut oft' f oin the working cylinder at the ?amo 

 fractional part of the stroke, and acts expansively to the end of the 

 stroke. The mean eft'ective pressure per square inch, for the 

 whole stroke, is thou the s:une upon both pistons. It may be 

 f >und in the usual manner, by the use of hyperbolic logarithms. 

 Multiply this, diminished by 1 5 lbs., into the dift'erence between 

 (he areas of the two pistons, expressed in squareinches, and again 

 into the velocity of the piston per minute, and divide the product 

 by 33,000, and the result will Lo the hcrse-power of one of the 

 engines. 



But it is to be observed that the result thus obtained will be 

 somewhat too large, for the following reasons. 1. The actual 

 pressure in the supply cylinder is greater than the pressure in the 

 receiv er (8 lbs. J, and the actual pressure in the working cylinder 

 is less than this. 2. During the ^ stroke from the commence- 

 ment, the outlet valves at the top of the supply cylinder lemain 

 closed, and consequently the expansive forces of the air in the re 

 cei\er must be somewhat reduced by the flow of air from it into 

 the working cylinder. 3. After the cut oft' valve is closed, the 

 eliu^tic pressure of the air in the working cylinder during the I'e- 

 maining ^ stroke, must be diminished somewdiat by leakage. 

 Tlie effect of this lerdcago has not hilhcrto been taken into 

 account. 



To be Coufi'iinol 



