104 Prof. A. W. Riicker on the Suppressed 



of experiment. I should not like to press this point, but the 

 method, if carried out with suitable care and precautions, 

 might be usefully applied to test FresnePs values of a and 6, 

 especially the former. For instance, by using first a pile of 

 five plates and then a pile of eight, two independent equations 

 in a, b would be obtained for each angle of incidence. The 

 plates should be thin and the Nicol large. 

 Davos Platz, Jan. 4tli. 



XIII. On the Suppressed Dimensions of Physical Quantities. 

 By A. W. RiJCKEE, M.A., F.R.S."^ 



IN the calculation of the dimensions of Physical quantities 

 we not unfrequently arrive at indeterminate equations in 

 which two or more unknowns are involved. In such cases 

 an assumption has to be made, and in general that selected 

 is that one of the quantities is an abstract number. In 

 other words the dimensions of that quantity are supjwessed. 



The dimensions of dependent units which are alterwards 

 deduced from this assumption are evidently artificial, in the 

 sense that they do not necessarily indicate their true relations 

 to length, mass, and time. They may serve to test whether the 

 two sides of an equation are correct, but they do not indicate 

 the mechanical nature of the derived units to which they are 

 assigned. On this account they are often unintelligible. 



Another difficulty is caused by the fact that the units 

 which we find it convenient to use are sometimes themselves 

 of an artificial character, and not such as would have been 

 chosen had those who originally defined them possessed a 

 clear conception of the nature of the phenomena with which 

 they were dealing. 



The obstacles which the study of the subject presents to 

 students w^ould, I think, be' greatly reduced if in develop- 

 ing it symbols were retained in the formulse to represent the 

 quantities the dimensions of which are suppressed, and if the 

 artificial appearance of the dimensions of many quantities were 

 more clearly traced to the artificial character either of the 

 quantities themselves or of the assumptions on which these 

 dimensions are calculated. 



It is probable that, as the mechanical explanation of phy- 

 sical phenomena proceeds, the use of units based on simple 

 mechanical conceptions will be extended, that some quantities 

 now employed will be dispensed with or regarded from a 

 different point of view. 



* Communicated by the Physical Society : read November 24, 1888. 



