1888-89.] A. B. Griffiths on “Liver” of Carcinus mcenus. 181 
similar salivary glands to those found in the Yertebrata ?* And 
is not the so-called “ liver ” of the Invertehrata a true pancreas, 
capable of producing the same chemical and physiological reactions 
as the pancreas of higher forms ? 
On the Air’s Resistance to an Oscillating Body (its 
Influence on Time-Keepers). By Edward Sang, LL.D. 
(Bead April 15. 1889.) 
The influence of the air on the going of time-keepers has naturally 
been the subject of much discussion, particularly in reference to 
time-keepers used by astronomers. On pendulums the air acts in 
two ways : — by its buoyancy it lessens the downward tendency of 
the parts, and so lengthens the time of the oscillation ; and it opposes 
resistance to the motion. On the chronometer balance, the latter 
action alone is felt ; to this action we shall confine our remarks. 
The incitement to motion is thus composed of two parts : the one 
due to the inclination of the curve or to the flexure of the balance 
spring, proportional to the distance from the point of rest; the 
other proportional to the square of the velocity ; so that, if x repre- 
sent the distance from the point of rest and v the velocity, the 
civ 
differential coefficient of that velocity, — or lt v } is represented by 
an expression of the general form 
lt v = ~Px + Qv 2 , 
or, in Leibnitz’s notation, 
The resolution of this equation, which expresses a relation among 
the function, its first and its second derivative, belongs to what I 
have called the Third co-ordinate branch of the Higher Calculus, 
or the Calculus of Primaries. Here we seek the relation of the 
primary variable t , to some one Of the three functions. 
The only useful application of this inquiry is to the doctrine of 
* See the author’s papers in the Proc. Boy. Soc. JEdin., and the Proc. Boy. 
Soc. Bond., ] 885-88. 
