457 



ject, that is, the symbol on which a certain notified operation is to 

 be performed; the second, the operation itself, represented by its 

 own symbol; and the third, the result, which may be connected with 

 the former two by the algebraic symbol of equality. The operations 

 are either monomial or po 7 ynomial simple or compound; and with 

 respect to their order, are either fixed, or free. He uses the term 

 linear operations to denote those of which the action on any subject 

 is made up by the several actions on the parts, connected by the 

 signs plus or minus, of which the subject is composed ; and these 

 linear operations likewise may be monomial or polynomial. 



A variety of theorems for the developement of functions of a very 

 general nature are then deduced from expansions of the fundamen- 

 tal expressions, derived from the principles stated in the beginning 

 of this memoir : and various laws embracing the relations subsisting 

 between analytical operations, and the fundamental formulas for their 

 transformation are investigated. 



" Observations and Experiments on the Solar Rays that occasion 

 Heat ; with the application of a remarkable property of these rays 

 to the construction of the Solar and Oxy-hydrogen Gas Micro- 

 scopes." By the Rev. J. B. Reade. Communicated by J. G. Chil- 

 dren, Esq., Sec. R.S. 



The method employed by the author for obtaining, by a com- 

 bination of lenses, the convergence to foci of the colorific solar rays, 

 together with the dispersion of the calorific rays, consists in making 

 a beam of solar light, which contains both kinds of rays, pass, after 

 it has been converged to a focus by a convex condensing lens, 

 through a second convex lens, placed at a certain distance beyond 

 that focus : that distance being so adjusted as that the calorific rays, 

 which, from their smaller refrangibility, are collected into a focus 

 more remote from the first lens than the colorific rays, and conse- 

 quently nearer to the second lens, shall, on emerging from the 

 latter, be either parallel or divergent ; while the colorific rays, which, 

 being more refrangible, had been collected into a focus nearer to the 

 first lens, and more distant from the second, will be rendered con- 

 vergent by this second lens; so that the second focus, into which 

 they are thus collected, will exhibit a brilliant light without mani- 

 festing any sensible degree of heat. The light so obtained may be 

 advantageously applied to the solar, and to the oxy-hydrogen mi- 

 croscopes, from its producing no injurious effects on objects inclosed 

 in Canada balsam, or even on living animalcules exposed to its in- 

 fluence. 



Another improvement in the construction of the microscope em- 

 ployed by the author, consists in the cell for holding objects being 

 made to move quite independently of the field glass ; so that the 

 best focus is obtained by an adjustment which does not disturb the 

 field of view. 



The Society then adjourned over the Christmas vacation, to meet 

 again on the 12th of January next. 



