384 



Mr. H. C. Sorby on some Optical [June 21, 



with facility — simply because the large space covered by related notes 

 cannot be, in the general case, brought within reach of the hand. But 

 any system can be demonstrated in this manner. 



Keyboard of the Second Order. 



The keyboard of the second order furnishes results of some interest. 

 It can be easily arranged according to the foregoing rules. The pecu- 

 liarity in the result is, that performance on a complete system of the 

 second order and first class, by means of it, is nearly as easy as perform- 

 ance on systems of the first order by means of the keyboard formerly 

 constructed. The problem of representation and performance is thus 

 solved both for the Hindoo system of 22 and for the system of 34, the 

 interest of which has been already indicated. 



Diagram II. (p. 382) represents a portion of the keyboard of the second 

 order. 



c—\e—g is a major triad ; whence the major thirds are better situated 

 for the finger than on the first-order keyboard with positive systems ; but 

 the presence of continuous rows of keys in all twelve divisions is some- 

 what less advantageous than in that arrangement. 



c — /t\)—g is the minor triad. 



In the general transformation of the rth order, transformation with 

 regard to colour (white or black) is not generally practicable. For 

 the most general purposes it would be necessary to have a sufficient 

 supply of keys of both colours for every pattern ; for any particular case 

 the requirements are more limited. 



June 21, 1877 (continued). 



IX. <( On some hitherto Undescribed Optical Properties of Doubly 

 Refracting Crystals." — Preliminary Notice. By H. C. 

 Sorby, F.R.S., President of the Royal Microscopical and of 

 the Mineralogical Societies. Received June 20, 1877. 



In the Proceedings of the Royal Society (vol. xxiv. p. 393) Dr. 

 Royston-Pigott described a new refractometer to determine the index 

 of refraction of liquids and other substances by means of the displace- 

 ment of the focal point of an object seen through them with a low 

 magnifying-power. Another paper on the subject was communicated 

 by him to the Royal Microscopical Society, and subsequently published 



