THE ART OF WEIGHING AND MEASURING. 599 



ininien.se, tlie pro<;i'ess in a week or a month is nsnally almost nil. 

 Optimism has its uses in many departments of human affairs, but 

 science should be cool and dispassionate, havini>- regard only lor the 

 truth. To make a trustworthy estimate of the actual state of the whole 

 vast realm of science would be a task beyond the powers of any one 

 man; but perhaps it will not be amiss to spend the time at our disposal 

 this evening in briefly reviewing the recent progress and present con- 

 dition of the fundamental processes upon which the exact sciences 

 rest;— I allude to the methods of w^'ighing and measuring. 



Physical science deals with many quantities, but they are all so re- 

 lated to each other that almost every one of them can be expressed in 

 terms of three fundamental units. As several systems of such units 

 are possible, it is imi)ortaut to select the most convenient, and the con- 

 siderations which guide us in that respect are the following: 



(1) The quantities selected should admit of very accurate comparison 

 with other quantities of the same kind. 



(2) Such comparisons should be possible at all times and in all places. 



(3) The processes necessary for making such comparisons should be 

 easy and direct. 



(4) The fundamental units should be such as to admit of easy defi- 

 nitions and simple dimensions for the various derived units. 



Scientific men have long agreed that these requirements are best 

 fulfilled by adopting as the fundamental units, a definite length, a 

 definite mass, ami a definite interval of time. Length is an element 

 which can be very accurately measured and copied, but it must be 

 defined by reference to some concrete material standard, as for ex- 

 ample, a bar of metal, and as all substances expand and contract with 

 changes of temperature, it is necessary to state the temperature at 

 which the standard is correct. A standard of mass, consisting of a 

 piece of platinum, quartz, or other material not easily affected by 

 atmospheric influences, probably fulfills the conditions set forth above 

 better than any other kind of magnitude. Its comparison with 

 other bodies of ap[)roximately equal mass is effected by weighing, 

 and as that is among the most exact of all laboratory operations, very 

 accurate copies of the standard can be made, and they can be carried 

 from place to i)lace with little risk of injury. Time is also an 

 element which can be measured with extreme precision. The imme- 

 diate instruments of measurement are clocks and chronometers, but 

 their running is checked by astronomical observations and the ulti- 

 mate standard is the rotation of the earth itself. 



It is important to note that the use of three fundamental units is 

 simply a matter of convenience and not a theoretical necessity, for the 

 unit of mass might be defined as that which at unit distance would 

 generate in a material point unit velocity in unit time; and thus we 

 should have a perfectly general system of measurement based upon only 

 two fundamental units, namely, those of space and time. Such a sys- 

 tem is quite practicable in astronomy, but can not yet be applied with 



