1891.] Diffraction at Caustic Surfaces: 137 



approximate theory like the above to be applied with much 

 certainty. For them, as Prof. Stokes has remarked, a perfectly 

 satisfactory procedure is to simply consider the difference of path 

 of the two pencils of light which reach a given band by different 

 ways ; these may be considered as two separate interfering rays, 

 exactly in the manner of Thomas Young's first apergu of the super- 

 numerary rainbow. Now the difference of paths of the two rays 

 up to the point P is clearly the excess of the two tangents from 

 P to the geometrical caustic over the arc between their points of 

 contact. Thus we obtain the following simple and elegant graphical 

 construction, which applies to all the system of bands except the 

 first two or three ; imagine the caustic curve constructed as a 

 disc, and let an endless thread be placed round it, the bands will 

 be traced by a pencil strained by this thread in the same manner 

 as in the ordinary construction of an ellipse by a thread passing 

 round its foci ; and successive bands will correspond to equal 

 increments in the length of the thread. 



(3) The effect of Temperature on the Conductivity of Solutions 

 of Sulphuric Acid. (Plates IV. and V.) By Miss H. G. Klaassen, 

 Newnham College (communicated by Prof. J. J. Thomson). 



Graham has shown that the viscosity of sulphuric acid increases 

 upon addition of water until a maximum is reached at the com- 

 position of nearly one molecule of water to one of acid. Upon 

 further dilution the viscosity continually decreases. 



If a curve, in which the ordinates represent the electrical 

 resistance and the abscissae the percentage composition of solutions 

 of sulphuric acid in water, be drawn from Kohlrausch's observa- 

 tions, it will be seen that a point of maximum resistance exactly 

 corresponds to this degree of concentration. The fact, that these 

 maxima should both occur when the composition of the solution 

 is almost exactly one molecule of water to one of acid, points to the 

 existence of the hydrate H 2 S0 4 . H 2 0. 



If the increase of viscosity and of resistance, supposing it due 

 to this hydrate, were found to diminish with a rise of temperature, 

 this fact would furnish strong evidence in favour of the theory 

 that the hydrate H 2 S0 4 . H 2 dissociates into H 2 S0 4 and H 2 at 

 higher temperatures. 



That the increased viscosity does diminish with the rise of 

 temperature has been proved by some recent determinations of 

 the viscosity of sulphuric acid solutions at temperatures between 

 15° C. and 100° C. 1 



1 Phil. Mag., Oct. 1N89. 



