142 LECTURES TO SCIENCE TEACHERS. 



hyperbolic expansion curve of steam, taken on the assumption 

 that the volumes are inversely as the pressures. Supposing 

 we once more begin with the pressure of 120 Ibs. above 

 zero and let the steam in through a space of one, viz., A to a, 

 then shut it off and expand it through an equal space (a to a'), 

 we shall obtain a pressure of 60 Ibs. above zero as the final 

 pressure, and obviously we should have got in addition to 

 the work represented on the upper part of the diagram by the 

 parallelogram (A X a x) of the steam let in, the work repre- 

 sented by the part next below it, this figure (a x a! #'), the 

 area of which is all but -j^-ths of the area of the top figure. 

 Now if one expands that steam which is at this time of the 

 capacity of 2 into the capacity of 4 (a" x" line), it is quite 

 clear that the area contained between the line a x and the 

 a" x" (the steam being now 301bs., above zero pressure 

 finally), is exactly the same as that of the previous figure, 

 because while every one of the horizontal lines, b' c f , &c., is 

 half the length of the horizontal lines, b c corresponding to it 

 in the figure above, every one of the vertical lines is double 

 the length of the similar vertical line above, and therefore the 

 area is the same, and thus by this further expansion we have 

 got nearly a further -j^-ths of the original pressure. Again, 

 if we pursue that and double the volume we get a further 

 i^ths and it would appear on the face of it, as if one might 

 go on ad infinitum and get infinitely great power. That of 

 course cannot be true. It would be at once seen it was not 

 so if, instead of taking a curve varying inversely with the 

 pressures, we had made our lines after allowance for the 

 difference of temperature; then the true expansion curve 

 thus obtained would have been found to be one that could 

 not be infinitely pursued. But even without taking that into 

 consideration it would not pay to carry the expansion curve 

 down to a very great extent, because the size of the machinery 

 would become so enormous ; and therefore, one is compelled 

 for commercial considerations to keep the expansion within 

 certain reasonable limits. 



Diagram 4 shows, in a tabular form, the value of expansion 

 when non-condensing. Supposing in lieu of using a cylinder 

 full of steam at 120 Ibs. the steam is cut off at half stroke, it 

 is quite clear that we have only used half the steam, and the 

 work which we shall get in that part before cutting off will be 

 of the value of 60, but in the part after the cut off we shall get 



