LOGARITHMIC RATE SCALE 17 



rates now in force indicate that a value of x of about 0.84 

 comes nearer to representing present average rates.* 



From a purely theoretical standpoint such a rate is simple 

 and distributes the slide over the whole length of the scale with 

 the utmost uniformity. Theoretically this is very attractive. 

 From a practical standpoint bills would have to be made out 

 from a line drawn on large scale logarithmic paper, or by the 

 use of a log-log slide rule. Such methods of computation could 

 not be understood by more than a very few of the takers, and it 

 would be difficult to convince takers of the justice of rates 

 computed by methods which they could not understand. 



The logarithmic scale has probably had more influence on 

 the form of water rates now in use than would at first be supposed 

 because it is possible to select rates under the common form of 

 sliding scale that will produce results that do not differ widely 

 from logarithmic rates; and a study of water rates of many Amer- 

 ican systems and discussion of them with those who have drawn 

 them convinces the writer that the logarithmic scale idea has 

 been entertained in many places, and without being named as 

 such it has entered to a considerable extent into the preparation 

 of the rates that have been used. 



As to the Frequency with which Different Kinds of Rates 

 are Used. An examination of about 100 meter rates in repre- 

 sentative American cities where meters have been adopted to a 

 substantial extent indicates the following distribution of kinds 

 of rates. Statistics from other sources would undoubtedly 

 show somewhat different distribution. Nevertheless the figures 

 probably give a fair idea of the present American practice 

 in regard to forms of meter rates. 



In about 2 per cent of the cases, the uniform rate is used 

 without a minimum or service charge. In a further 9 per cent 

 there are no minimum or service charges, but the sliding scale 

 is used, so that the smaller takers pay more per thousand gal- 

 lons than the larger ones. In about 10 per cent of the cases 

 a service charge is used with either a uniform rate or a sliding 



* See Fig. 19, p. 65, for a graphic representation of a logarithmic rate 

 in comparison with certain average values. 



