Manchester Memoirs, Vol. lix. (191 5), No. 12. 25 



tion of the fundamental mechanics, in his essay on the 

 Measure of Moving Force." 



Up to 1686 the force of a body in motion was 

 measured by the product of the mass of the body into 

 its velocity. Leibnitz thought that this was erroneous, 

 and maintained that it should be the product of the mass 

 into the square of the velocity. This he termed the vis 

 viva, which is equal to twice the kinetic energy. The 

 great controversy was not ended until the resistance to be 

 overcome was taken into account. This may sometimes 

 be conveniently measured by a space integral ( \m V' 2 ), 

 and in other cases by a time integral (m V). 10 



Heat. 

 Sheet 22. 



Shows Fahrenheit, Centigrade and Reaumur ther- 

 mometers, each with a length of 14 inches. They are 

 marked in steps of 10 degrees between the freezing and 

 boiling points. The spherical bulbs in each case are 

 represented as full of mercury up to the freezing point. 

 The Fahrenheit has two scales, one being the ordinary 

 scale marked from - 20 to 21 2°, and the other Dalton's 

 new scale. 



The new scale is described in Part I., section 1 of 

 Dalton's "New System of Chemical Philosophy." It is 

 based on Dalton's assumption that all pure homogeneous 

 liquids expand from their point of congelation or greatest 

 density by an amount proportional to the square of 

 the rise of temperature from that point. 



Dalton arranged that his new scale should agree 

 with the Fahrenheit scale at 32° and 212°, and -40°F. was 

 taken as the freezing point of mercury. Hence it can 



10 See Routh's "Rigid Dynamics," Chapter VII.. where references will 

 be found relating to the history of the controversy. 



