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tenus partibus convocatis audias causam et appellatione remota 
debito fine decidas faciens quod decreveris per censuram eccle- 
siasticam firmiter observari. ‘Testes autem qui fuerint nomi- 
nati, si se gratia odio vel timore subtraxerint censura simili 
appellatione cessante compellas veritati testimonium perhibere. 
Dat. Viterbii non. Octobr. Pontificatus nostri anno secundo.” 
A vote of thanks was passed to the Rev. Mr. Thomson 
and Mr. Brophy for their interesting donations, and to the 
Rev. Mr. Abbott for his kindness in allowing the Papal Bull 
to be exhibited to the. Academy. 
The Rev. Dr. Graves read a paper on a generalization of 
_ the Symbolic Statement of Taylor’s Theorem. 
Lagrange was the first to show that Taylor’s theorem ad- 
mits of the symbolic statement, 
d 
p(w +h) = el g(2). 
The object of the present paper is to discuss the problem 
of determining that more general symbol which shall have the 
effect of changing z into any proposed function of x, such as 
y (x), throughout the whole of a given function @ (x), which 
is made the subject of the operation. 
The following synthetic course leads readily to the desired 
end. As the effect of the symbol 
sa 
e i 
is to change x into x + 1, it appears that 
d 1 od 
e F@) or ef @) dx (2) 
will change f(x) into f(«)+ 1; and consequently will have 
the effect of changing z into y (x) where 
b (2) =f UF (@) + 1} (2) 
— 
&! 
er 
2 
|e 
