224 Royal Society :— 
It is probable that wherever any observations are taken, 
meteorological observations are also taken and published ; so that 
it would not be adding materially to the work of observers of the 
scintillation to ask them to add those observations to their own. 
There are many more details which I pass over, because they 
depend on the peculiarity of the sight of different observers, and 
on the circumstances under which they may be placed, and 
which of course vary in every individual case: I have contented 
myself with indicating the principal points, to which I call the 
attention of observers, and the importance of which I know by 
experience. 
In concluding, let me be permitted to express a wish, addressed 
to all who may be disposed to observe the scintillation of the 
stars in countries whose climates are different to that of Morges ; 
and that is, that they would kindly communicate to me a brief 
summary of their work—for it is needless for me to say that any 
result that they may arrive at will be of the highest interest to 
me; and reciprocally, if they desire it, I shall have great pleasure 
in giving any further details or directions to any persons who 
will interest themselves in this research. 
Morges, December 1859. 
XXX. Proceedings of Learned Societies. 
ROYAL SOCIETY. 
[Continued from p. 158.] 
May 26, 1859.—Sir Benjamin C. Brodie, Bart., Pres., in the Chair. 
ee following communication was read :-— 
“On the Laws of Operation, and the Systematization of Ma- 
thematics.” By Alexander J. Ellis, Esq., B.A., F.C.P.S. 
The object of the following investigation is to give a firmer basis 
to the calculus of operations, to assign the strict limits and con- 
nexion of the mathematical sciences, and to found them upon purely 
inductive considerations, without any metaphysical or @ priori 
reasoning. 
Starting with the indemonstrable but verifiable hypothesis, that 
objects exist external to the subject, we recognize equality as exist- 
ing between objects with common and peculiar properties, in respect 
of their common properties. Operations, which, when performed on 
equal objects, produce equal objects as their result, are recognized as 
equal, in respect to the common properties considered in the equali- 
ties of the objects. When one operation is performed on an object, 
and another on the resultant object, the single operation by which the 
first object is transformable into the last is regarded as the product 
of the other two, the order of succession being important. When 
the resultant object is the same as the original operand, the product 
of the operations is termed unity. When two operations performed 
