30 REPORT— 1872. 



increase wliile an'auging that the ice shall be evaporating into steam under the 

 temperatiire of the bath t^ ; we obtain mechanical ■work, which call d. 



Now if, in this expanding process of ice to steam, the pressure were as great as 

 Pi, which was the pressure dm-ing the compressing to water, we would get back on 

 the whole from the piston all the work we gave to it ; that is, the two portions 

 c and d of work got back would together be as much as we gave, namely a ; and we 

 woiild have made a clear gain of the work b obtained from the thermodynamic 

 engine. 



A like proof could be given in respect to the second case — that in which the 

 temperature is above the triple point. 



A slight extension of this reasoning will prove that the curves, in crossing at the 

 triple point, cannot cross tangentially. 



This can be seen obviously from the consideration that the work obtainable by 

 the thermodynamic engine is proportional to the difference of the temperatures 

 between which the heat is transmitted ; and that the difference between the work 

 given to the piston of the cavity in compressing steam to water, and that obtained 

 back again during the evaporation of the ice to steam, and then pressing the steam 

 when the evaporation is complete a little down till it attains again its origina. 

 pressure and volume, -^ivill be proportional, veiy approximately, to the difierence of 

 the pressures existing during the compression of steam to water, and the expansion 

 of ice to steam, which latter pressure let us now callp/. Also let us call the tem- 

 peratm-e of the triple point <„. 



Thus it is obvious that we must have, as long as we keep very near the triple 

 point, _ p^-p^cct^-t^. 



And this shows that the crossing of tlie curves must be angular, not tangential. 



The author farther suggested that the reasoning here adduced may be followed 

 up by a quantitative calculation founded on experimental data, most if not all of 

 which are already available, by which calculation the difference of the pressures of 

 steam with water and steam with ice for any given temperature very near the 

 triple point may be foimd with a very close approximation to the truth, 



AsTEOKOMT. 



On some new Points in the Mounting of Astronomical Telescopes. 

 By HowAED Getjbb, C.E., F.R.A.S. 



The very gi-eat inconvenience attendant upon the use of the ordinary position- 

 circle of a micrometer divided on a metallic limb, and the necessity of having small 

 lamps hung on to the micrometer for producing that very useful character of 

 illumination of the wires known as the " dark field," has induced the author to 

 introduce some modifications in this (to the observer at least) very important 

 part of an equatorial instrument. 



These modifications have already been applied with success, and for the first 

 time (as far as the author is aware) to a 7-inch refracting telescope now in course of 

 erection at the Observatorj^ of the Royal Artillery Institute, "NVoolwicli ; and the 

 author has (in consequence of this success) been ordered to adapt them to the 

 Great Equatorials now in course of construction for the Royal Observatory, Edin- 

 burgh, and the Obsei-vatory of the Lord Lindsay, Aberdeen*. 



The rack-and-pinion tube carrying the eyepiece or micrometer revolves freely 

 in the casting which forms the lower end of the telescope-tube, and carries a brass 

 plate (all cast in one piece), on which is cemented a flat ring of plate glass, muffed 

 on back and in front varnished with an opaque varnish. Through this varnish the 

 divisions are cut, so that on being illuminated from behind the divisions appear 

 bright upon a black ground. The vernier is similarly treated, and the whole of 

 this circle, being covered with a cap, -with a glazed window only sufficiently large 

 to expose the vernier and about lo° of the circle, is protected from possible injury 



* The breech-piece and position-circle of the Woolwich Equatorial was here produced. 



