64 Proceedings of the Royal Physical Society. 



the form of either fractions or that of decimal parts, if need 

 be, to three places of decimals. 



For the latter requirement some modification of the " Line 

 of Lines," given on the sector which is usually supplied as 

 part of a set of mathematical drawing instruments, will often 

 answer the purpose. The sectoral lines on the instrument 

 referred to are, however, usually too much crowded to be of 

 practical use, and the scale, moreover, is far too small for 

 the purposes at present in view. My own plan, therefore, 

 has been to take a well-made boxwood two-foot rule, such 

 as is used by carpenters, choosing for the purpose one with 

 a really good joint. With a scraper and some glass-paper 

 first erase the figures on one face of the rule, and then rule 

 two lines on the cleared face from the centre of the joint 

 outwards to the middle of each of the opposite ends, taking 

 the lines on to the metal with which the end of each limb is 

 tipped. With a fine drill, or by other means, make small 

 holes at the end of these lines at equal distances from the 

 centre of the rule. These will serve to fit needle ends into, 

 for use when the measurement of the unit is to be made with 

 calipers, or for the points of ordinary dividers in'the cases 

 in which the measurements are to be made with these 

 instruments. Between these terminal holes and the centre 

 of the rule, divide the space into tenths, and these, in turn, 

 into hundredths, and figure the larger divisions, counting 

 from the centre outwards, in the usual way. 



To use the instrument, first open the rule so that the 

 distance between the terminal holes, or between the needle 

 ends fitted into them, exactly corresponds to the particular 

 length chosen as a unit in the case of the individual speci- 

 men under examination, and fix the rule in that position. 

 Then, with the calipers or dividers opened to the dimensions 

 whose proportional length in relation to that unit is required, 

 measure across the opening to points at equal distances 

 from the centre, and note the figures in the usual manner. 

 Direct reading gives the figures to the second decimal 

 place, while the third, if required, can easily be arrived 

 at by estimation. 



It may happen, in some cases, that the proportion under 



