a new 



addition to the Slide-Rule. 57 



3. The temperature of an adiabatic at any point can be 

 determined from either pressure or volume by using suitable 

 indices for 



i 

 v . T^ -1 = constant; 

 also 



Y 



p . Ti-y = constant. 



In determining temperatures from volumes or vice versa it 

 is only necessary to proceed as before (1). In dealing, how- 

 ever, with pressures and temperatures the index is negative 

 (where 7 is > unity), the interpretation of this being that an 

 increase of pressure is accompanied by an increase in the 

 temperature. The slide therefore does not require to be 

 reversed as in pv and vT calculations ; but with a rule of the 

 Gravet type, owing to the scales C and D being the square 

 roots of A and B, it is necessary to use a fictitious index 



obtained by dividing by the logarithmic ratio of the 



1—7 



scales, giving , — r-. It would also be quite possible to 



graduate one edge of the index slide with fictitious values to 

 compensate for the ratio of the scale-readings. 



4. In the process described in (1) we have the means of 

 plotting a series of adiabatics or isentropics, and each position 

 of the radial cursor on the rule gives in its readings on the 

 index line a corresponding isentropic, and a movement of the 

 cursor to the left corresponds to a gain in entropy and vice 

 versa, and it can be shown that equal increments of linear 

 movement of the cursor correspond to equal increments of 

 entropy. In other words, the scale of inches or centimetres 

 on the edge of the rule may be regarded as a scale of entropy 

 in arbitrary units. 



5. The following is a very good example of the use of the 

 radial cursor in practice. 



The theoretical efficiency of an Otto cycle gas-engine is 



independent of the working temperatures and is given by the 



(v V -1 

 expression 1 — (-) , where v Y is the total effective volume 



of the cylinder and compression-space, and v 2 = volume of 

 compression-space alone. 



Taking 7=1*408, 7 — 1 = '408. This is beyond the range 



of the instrument, so we will employ -jtto =2*45. 



