NINTH ORDINARY MEETING. 83 
inversely upon another unit, the relation of the two independent 
units is expressed by per ; for instance, the unit of velocity is ex- 
pressed by L per T. The words by and per correspond to the signs 
x and +, or rather now used by scientific men instead of the cum- 
brous +. 
Sometimes, as in the unit for conductivity, a bracket is required 
after per (just as in the case of a numerical 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 expressed 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 (@ per L), 
or, k Ef per T per S. == @ per I. 
A velocity .has only one reciprocal, namely 
1/v T per L; 
but a conductivity has several, as 
1/k 8 per L = H per T per S, 
and 1/k H per T per 0 = 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 hour in terms of kilometres per second : 
ekslometren pean cite a s.3 + ec = 1,000 metres. 
MINetre es yrs otis sees -s EE Rsons aie = 39.37 inches. 
DONG Ny es oe amasenes ORES = Sole == yard. 
MOOV ALAS ystas ta. ote ms Peeks. '< Merete sce, ove === TLE 
GOemileswes yee eee ee). MMM = hour. 
eh CUrsys eects |. eens...) ==. 3000 Seconds: 
_ 36x 176 x6 
” " 3937.x 360 
i.e. ‘0268 kilometres per second. 
kilometres = sec, 
