Mr. C. J. Hargreave on the Calculus of Operations. 351 



around the edge, and expose the little apparatus to the air so 

 that the balsam may become dry ; it is then fit to mount in the 

 brasswork of the microscope in the same manner as a tourmaline. 



I have found it best to employ an sethereal solution of Canada 

 balsam in this process, made by dissolving the hard old balsam 

 in washed pure sulphuric aether, afterwards adding a little iodine 

 to it as before. This dries more rapidly, hardens quicker and 

 more perfectly than the usual fluid Canada, and it does not 

 attack the crystals — a very great advantage. 



These directions may appear very prolix, tedious, and excess- 

 ively troublesome ; but, however, when set in practice, the whole 

 operation resolves itself into the utmost simplicity, habit soon 

 reconciling oneself to the routine, and the different precautions 

 appear to offer themselves unconsciously to us as we proceed. I 

 have frequently prepared a dozen good tourmalines in an hour, 

 as far as the catching and drying part of the operation ; the 

 others of course require longer time, but for these we must wait, 

 and occupy ourselves with some other stages of the same process. 



There is not the least doubt that before long these splendid 

 and useful crystals will be offered for sale by opticians at as many 

 shillings as tourmalines now cost pounds, and certainly of equal 

 value and practical utility — in my own opinion, of even greater, 

 for less light is lost by these than by any of our polarizing appa- 

 ratus at present in use. 



I have invariably used in this description the original terms 

 employed by me,namely, "artificial tourmalines" and "crystals of 

 sulphate of iodo-quinine." Professor Haidinger's term of " Hera- 

 pathite M is certainly a highly complimentary one to myself ; but 

 as it does not give either an idea as to the optical properties or 

 chemical characters of the substance in question, it does not 

 appear to me so suitable as those I originally attached to them. 



32 Old Market Street, Bristol, 

 October 1853. 



LIV. Applications of the Calculus of Operations to Algebraical 

 Expansions and Theorems. By Charles James Hargreave, 

 Esq., LL.D., F.R.S.* 



IN a paper " On the Solution of Linear Differential Equa- 

 tions," written by me in the year 1847, and published in 

 the Philosophical Transactions for 1848, the following formula 

 was enunciated as a leading theorem in the Calculus of Operations : 



* Communicated by the Author. 



