409 
of Edinburgh, Session 1864-65. 
The second step is to deduce from this pair of conjugate motions 
a second pair of motions also conjugate to each other, and having 
their periodic times in simple ratios to those of the preceding pair. 
The third step is to form a progression of pairs of conjugate 
motions deduced successively one from another. In this progres- 
sion, carried in the direction inverse to that just mentioned, the 
motions approach with extreme rapidity, on the one hand to a 
uniform circular motion, on the other hand to the oscillation in an 
exceedingly minute arc. 
As a practical result of the whole, it is shown that, for all cases 
of clock motions, and for experiments to determine the length of 
the seconds pendulum, the time of oscillation may be held to be 
proportional to the square of the secant of the eighth part of the 
whole arc described ; the number of oscillations per day to be pro- 
portional to the square of the cosine of the same eighth part ; and 
the daily retardation to the square of the sine. 
6. On the Action of Hydriodic Acid on Mandelic Acid. 
By Alex. Crum Brown, M.D., D.Sc. 
The relation of mandelic acid to benzoic aldehyd is so precisely 
the same as that of lactic acid to acetic aldehyd, that whatever con- 
stitution we assume for the latter acid, a similar one must be 
ascribed to the former. 
The researches of Kolbe and Lautemann, and of Wislicenus, 
prove that lactic acid is oxypropionic acid. Mandelic acid must 
therefore be oxytoluic acid, and, indeed, it has been so formulated 
by Kolbe in his work on Organic Chemistry. 
While agreeing with Kolbe and Wislicenus, I prefer, for some 
purposes, to employ formulm slightly different from those of either 
of these chemists. 
Thus, using H as a contraction for jjq | CO, the relation of alde- 
hyd, chloride of ethyliden, ethylidenic chlorhydrine, and common 
lactic acid, may be expressed by the formulee 
o 
o 
p 
OH3}o 
{(HO), 
l(HO). 
3 II 
VOL. V. 
