50 



Prof. G. F. Fitzgerald. On the 



[Jan. 27, 



second being (/i +fy -tfd™') j an d that between tlie second and third 



C/ 2 +/3 + w/ 2 ). 



If the lenses are nearly but not quite in the afocal position, greater 

 power and a wider field may be obtained, but it is at the expense of 

 the penetration, which may, however, with advantage be limited to 

 the thickness of the object. The instrument offers great advantages 

 for artistic purposes, but lenses or mirrors of specially wide angle are 

 needed for the farther development of the invention. 



The optical conditions of a system of two thin lenses at varying 

 distance apart are shown by diagrams. 



In Diagram I the u and v of the formula employed are set off as 

 abscissas and ordinates, and the curves (which are rectangular hyper- 

 bolas) drawn for several values of H. In the afocal position of the 

 lenses the curve degrades into a line which is a tangent to all the 

 hyperbolas at the point (/^/g). The locus of vertices and locus of 

 centres of these curves being straight lines, and the hyperbolas all 

 touching the point (/ 1 ,/ 2 )» ^ * s snowrL that the principal foci, principal 

 points, and equivalent focal length for any given position of the lenses 

 can be found by rule and compasses, without drawing the curve. 



In Diagram II the actual position of the lenses, their principal foci, 

 separate and combined, and the principal points, positive and negative 

 (answering to the vertices of the curves in Diagram I), are plotted 

 down as abscissae, the values of H on an enlarged scale being taken as 

 ordinates. 



Diagram III shows the same for two lenses of equal focal length. 



Comparison of these two diagrams suggests the employment of the 

 term "Pseudo-Principal Points" for those positions at which the 

 magnitude of the image is in the constant ratio / 2 //i ^° that of the 

 object for every value of H, inasmuch as the distance from these to 

 the principal points gives the measure of the " penetration " of the 

 system. 



II. " On the Thermodynamic Properties of Substances whose 

 Intrinsic Equation is a Linear Function of the Pressure 

 and Temperature." By Professor George F. Fitzgerald, 

 M.A., F.R.S. Received January 11, 1887. 



Professor Ramsay has communicated to me that he and Mr. Young 

 have found that within wide limits several substances in the liquid 

 and gaseous states have the following relation connecting their pres- 

 sure (p), temperature (T), and specific volume (y), 



p = aT + b, 



where a and b are functions of v only. 



