380 
Proceedings of the Royal Society 
4. Latent Heat of Mercury Vapour. 
By James Dewar, Esq. 
5. Notes by James Dewar, Esq. (1.) Problems of Dissoci- 
ation ; (2.) Formation of Allotropie Sulphur; (3.) Heat 
of Fermentation. 
6. Further Note on Continuants. By Thomas Muir, M.A., 
F.R.S.E., Assistant to the Professor of Mathematics in 
Glasgow University. 
In my paper on Continuants, recently communicated to the Royal 
Society, it was shown that the order of a continuant may he de- 
pressed if the first element of the main diagonal be unity, viz., 
thus 
/ b, b 2 b 3 \ / 
Kll aj a 2 a. A . . . j = K l a x + b x 
and from the definition it is evident that 
K 
( mb l b 3 \ / 
ma x a. 2 a A . . . ) = m K ( a x < 
b y b 2 
a , a .. 
Hence we have 
( + »,)&, (b 2 + a 2 )b 3 \ 
K \1 a x a % a 3 J 
f + {b 2 + a 2)b 3 \ 
'= K \b x + a, a 2 « 3 J 
( t> 3 (b 2 + a 2 )b 3 \ 
7 (Pi + «i)K\l a z .... ) 
= (b l 4- a A ) (Z> 2 + « 2 ) (& a + a 8 ) 
) 
From this it is clear that, in virtue of the relation which has 
given rise to the name “ continuant,” continued fractions of a 
certain class may he transformed into simple fractions, with con- 
tinued products for numerator and denominator. 
