11 
IV. If we take a law of force. 
P = 
11 tan. 
the equations of motion can be solved. 
And if ^ ^ -p, 0 rr tan." ^ i. 
We get Kj = « ^ i -l-2fi8 4 ;u*Iog.(l 4 r) I 
2^h ^ j 
And for the plane curve K== — e 
And therefore |? = ^ ^ ~ 2^.8 + ^nog. (1 4»-^) 
From which, for any given value of 6, we may obtain the actual 
value of 
IV 
When 0 is small, so that where we may neglect high powers 
without error ^ 
IV 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 Peesident : — 
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- 
