NINTH ORDINARY MEETING. 83 



inversely upon another unit, the relation of the two independent 

 units is expi-essed by per ; for instance, the unit of velocity is ex- 

 pressed by L per T. The words hy and per correspond to the signs 

 X and -=- , or rather now used by scientific men instead of the cum- 

 brous -f . 



Hometimes, as in the unit for conductivity, a bracket is required 

 after per (just as in the case of a numei'ical expression a bracket is 

 sometimes required after — ), to show that the sign attaches to the 

 whole of the unit included within the bracket. And as - followed 

 by - is equivalent to + , so per followed by per is equivalent to by. 



A rate of exchange may be expi-essed either by means of \per, or 

 by means of =. For example, 4"85 dollars per pound, and 4-85 

 dollars = pound. Here the sign = is read 'for every.' In the 

 same way a velocity may be written v L per T, or v L ^ T. Again 

 a conductivity can be expressed as 



k H per T per S per [0 per L), 

 or, k H per T per S ==6' per L. 



A velocity has only one reciprocal, namely 

 1/v T per L ; 

 but a conductivity has several, as 



1/k per L = H per T per S, 

 and 1/k H per T per 6* ^ S per L. 



Kquations of the kind which occur in exchange have not, so far as 

 I know, been adequately treated. They are more properly termed 

 equivalences. In ordinary equations the units of the two sides are 

 identical ; in equivalences they are either different in nature or dif- 

 ferent in description. The equations of exchange are combined by 

 what is called the Chain Rule ; and in the work referred to I show 

 that a development of that rule is the method corresponding to the 

 analytical expression of a quantity. For example, to express a 

 speed of 60 miles per hoar in terms of kilometres per second : 



1 kilometre = 1,000 metres. 



1 metre ^ 39.37 inches. 



36 inches == yard. 



1,760 yards = mile. 



60 miles = hour. 



1 hour = 3,600 seconds. 



36x176x6,., 

 •■•3937x360 kilometres = sec. 



i.e. "0268 kilometres per second. 



