NINTH ORDINARY MEETING. 81 
12. Diptera. 
13. Biological Exercises, Parts I. aud II. 
14. Handbook of New Zealand. 
15. Catalogue of International Exhibition, 1879 (New Zealand Court). 
V.—FOREIGN. 
1. Correspondenz-Blatt der deutschen Gesellschaft fiir Authropologie, Eth- 
nologie and Urgeschichte, XV. Jahrgang, No. 10, October, 1884. 
2. Tesis leida en el Examen Profesional de Ingeniero Geografe, per Joaquin 
de Mendezabal Tamborrel. 
Total 66 numbers. 
Dr. Macfarlane read a paper entitled : 
NOTATION FOR PHYSICAL UNITS. 
The late Professor Clerk-Maxwell in his treatise on Heat says, 
“ Every quantity is expressed by a phrase consisting of two com 
ponents, one of these being the name of a number and the other 
the name of a thing of the same kind as the quantity to be ex- 
pressed, but of a certain magnitude agreed on among men as a 
standard or unit.” Heat, p. 75. When we apply this analysis to 
the expressions of quantities, we find that in many cases there is no 
notation for the latter component—the unit. The general expression 
for a velocity isv; what does this single letter denote? It must 
be viewed either as denoting both components, or else as denoting 
the numerical phrase and leaving the unit to be understood. When 
a particular velocity is expressed, both components are expressed, as 
for instance 123 feet per second. Now if vis the general symbol 
corresponding to 123, what is the general expression corresponding 
to feet per second? But further it is only in the simplest cases 
that we have a notation for the special unit; and the consequence 
is that in the specification of quantities, as in tables of constants, 
there is considerable trouble in ascertaining from the context what 
special unit is understood. 
If we look into text-books on arithmetic and examine the rules 
given for the application of arithmetic, such as the Rule of Three, 
or the unitary method, we find that the difficulty which is met but 
not overcome, is to express the dependence of one quantity upon one 
or more other quantities. It may be objected that the formula meets 
the dittculty. Only partly, I reply, for the formula expresses only 
the numerical component, not the unit component. It is well known 
