Prof. Young on Vanishing Fractions. 295 
tended to; and it may be proper to notice what effect the 
gloom has upon animals and plants, &c.* 
I remain, Gentlemen, yours, &c. 
Epping, March 15, 1836. Tuomas SoQuire. 
P.S. During the annular observation the light and heat 
will be about zy of that of the full sun. 
LXI. Observations upon Mr. Woolhouse’s Theory of Vanish- 
ing Fractions. By J.R.Youne, Esq., Professor of Mathe- 
matics in Belfast College.+ 
T was a remark of D’Alembert, that in all subjects except 
in the mathematical sciences, there was room for difference 
of sentiment. This exception, however, in favour of mathe- 
matics was unadvisedly made by D’Alembert, as his own dis- 
putes with Euler, on the subject of imaginary logarithms, 
fully prove. Nor is this, the only mathematical topic upon 
which very considerable difference of sentiment has prevailed. 
The doctrine of vanishing fractions, a subject of far higher 
interest and importance, has been the source of much more 
keen and frequent controversy among mathematicians, and 
respecting which doctrine there is by no means harmony of 
opinion even at the present day; and this is a circumstance 
doubtless to be regretted, because of the frequent and un- 
avoidable occurrence of these fractions in various departments 
of analytical research. To the aspiring student such con- 
flicting theories in a part of the “ exact sciences” must be a 
source of much perplexity. It must be embarrassing to feel 
that if he assent to the reasoning of the profound Waring, he 
must oppose himself to that of the cautious Maseres; and that 
if he adopt the views of Professor Woodhouse, he must dis- 
card the arguments of Dr. Hutton. It cannot, however, be 
denied that the opinions of Waring and Hutton are those 
which most accord with the ordinary views of modern analysts, 
in reference to this subject; and it was scarcely to have been 
expected that any mathematical theory should now be pro- 
mulgated condemnatory of conclusions which, in the works 
of our ablest modern analysts, wear all the aspect of mathema- 
tical certainty. An essay has, however, been recently pub- 
lished, by a very ingenious and able mathematician, embody- 
[* Particular directions for observing an Annular Solar Eclipse, adapted 
to every class of observers, and to the use of instruments of every degree 
of perfection and power, will be found in Mr. Baily’s Memoir on the An- 
nular Eclipse of Sept. 7, 1820,—Phil. Mag., First Series, vol. lv, p..85.— 
Epit. | 
+ Communicated by the Author, 
