294 TECHNICAL MICROSCOPY. 



three figures. If it be preferred to express the actual values in 

 millimetres, a decimal fraction is the most convenient in practice, 

 for example, '0048 mm. ( = 4*8 mic.), since everyone knows that 

 the units of the micromillimetres are to be found in the third place 

 of decimals. Vulgar fractions, such as y^ T or ^^ mm., give, in 

 our opinion, just as vague an idea of the actual size of an object 

 as the expression ^ or z ^ of a year does of the corresponding 

 time. They are also unquestionably less convenient than integers 

 or decimal fractions in calculations. Vulgar fractions, whatever 

 may be the numerator, such as T |^, f 7 , &c., are wholly objec- 

 tionable, since the relation of the numerator to the denominator 

 has first to be determined by division before we can form an 

 approximate .idea of the measured dimensions. 



For the comparison of the different units of measurement 

 which are usually employed for statements of the dimensions 

 of microscopic objects, in addition to millimetres and micro- 

 millimetres, the following table of reductions will be of service : 



Paris line ... ... = 2*2558 millimetres 



inch = 27-07 



English duodecimal-line = 21166 



inch = 25-3997 



Rhenish line = 21802 



inch = 261622 



Vienna line = 21952 



inch = 26-3419 



For the opposite ratio we thus get : 



One millimetre = '4433 of the Paris line 



= *0369 inch 



= -4724 English line 



= '0394 inch 



= -4587 Pihenish line 



= '0384 inch 



= -4555 Vienna line 



= '0379 inch 



The determination of angular magnitudes is best effected with 

 the goniometer, of which a very convenient arrangement is that of 

 0. Schmidt (Fig. 164). It consists of a graduated circular disc 



