11 
TV. If we take a law of force. 
P- 
- 2 yu tan. 
y 
the equations ©f motion can be solved. 
And = tan.~ ^ i. 
We get = _^ 
( 0 a 
6 ^^-l-2^0 + /.^log.(l+r) 
And for the plane curve K = -^e 
l-‘ - e^^^-l-2^9 + ;unog.(l + t^) 
And therefore 
K 
From which, for any given value of 6, we may obtain the actual 
value of 
When d is small, so that where we may neglect high powers 
without error = ;:«• 
K 2 
Which result is in exact accordance with those previously 
obtained, for, it must be noticed, that with this law P is 
nearly constant. Hence we arrive at the following con- 
clusions : — 
(1) That when the pressure of the powder is constant. 
Work spent in friction with parabolic grooves 3 
Work spent in friction with plane grooves “2 
(2) That when the pressure diminishes rapidly the above 
ratio = 2. 
(3) That this ratio may have any values between these 
two, but that it cannot go beyond these limits. 
Mr. Baxendell read the following extract from a letter 
he had received from the Pkesident : — 
You will see that I have put a little drying apparatus to 
the short limb of my syphon barometer. I believe that a 
long open tube attached to the short end by a bit of india- 
