NINTH ORDINARY MEETING. 81 



12. Diptera. 



13. Biological Exercises, Parts I. aud II. • 



14. Handbook of New Zealand. 



J5. Catalogue of International Exhibition, 1879 (New Zealand Court). 



v.— FOEEIGN. 



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 

 poneiits, 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 is v ; 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 com})onents are expressed, as 

 for instance 123 feet per second. Now if v is the geneial symbol 

 corresponding to 123, what is the genei-al 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 tlie 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 Pule of Three, 

 or the \initary method, we find that the diiificulty 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 Jbrmuia meets 

 the difficulty. Only partly, I reply, for the formula expresses only 

 the numerical component, not the unit component. It is well known 



