27 
~~ 
Islanders are stated to be worn, Mr. Ball declared he could 
not doubt the golden ornaments were worn in a similar 
manner. The Sandwich Island articles to which he alluded 
formed a part of the fine collection made in Cook’s voyages, 
and deposited in the Museum of the University. He trusted 
he would-be able to make many of the weapons and orna- 
ments therein contained useful in throwing light on Irish an- 
tiquities. He referred to several curious instances, where the 
use of hypothesis had misled antiquaries, and where observa- 
tions of existing people had set their opinions aside. He men- 
tioned that he had recently proved, that an article long exist- 
ing in the University Museum, and known as the best example 
of an old form of a trumpet, had, by the discovery of its re- 
maining parts, proved to be a chemical instrument for burning 
gas, or inflammable vapour; and he concluded by stating, 
that the article figured in the seventeenth volume of the Trans- 
actions of the Royal Irish Academy, as an astronomical 
instrument of the ancient Irish, proved to be a piece of chain 
armour. ‘These two last mistakes he gave as examples of a 
want of exactness of observation, and of the mischief of hy- 
pothesis. 
The Secretary read a paper by Professor Young of Bel- 
fast, on Diverging Infinite Series, and on certain Errors in 
Analysis connected therewith. 
The subject of diverging series is one of considerable per- 
plexity in analysis, and has given occasion to theories of ex- 
planation involving views and statements entirely opposed to 
the general principles of algebraical science. It has, for in- 
stance, been affirmed of such series—when they present them- 
selves as developments of finite expressions—that, though 
algebraically true, they may, nevertheless, be arithmetically 
false. By some they are considered to justify conclusions 
palpably erroneous and absurd, as, for example, that 
D2 
