ABOUT MEASURES OF LENGTH. 653 



work, as well as the most elaborate and costly apparatus. Allowance 

 must be made for errors that are so small as to be almost inappreci- 

 able, but which can not be eliminated until they have been subjected 

 to future investigations of a very delicate nature. Every careful ob- 

 server will obtain results which are almost marvelously accordant inter 

 se ; but the results obtained by two observers, with different instru- 

 ments, will probably not agree. The "personal equation "has not 

 yet been eliminated from work of this kind. 



In the comparison of weights and measures, science demands the 

 utmost accuracy, and it would not be possible, even if it were 

 desirable, in an article like this, to more than allude to a few of 

 the steps which have resulted in the final adoption of national and 

 international standards. Professor W. A. Rogers, of Harvard Ob- 

 servatory, has devoted himself to a critical study, of measures of 

 length, and to him we are indebted for many observations on the sub- 

 ject, of great scientific importance, and for some very ingenious de- 

 vices for making accurate comparisons of spaces. He has recently 

 published a valuable contribution to the literature of the subject,* in 

 which the present state of the question of standards of length is dis- 

 cussed with considerable detail. 



As the comparisons of measures of length are made with micro- 

 scopes, the results are affected by the magnification and by the method of 

 illumination employed. The measurements are made so carefully that 

 the standard metal bar upon which the graduations are made must 

 be carefully supported on rollers, mutually connected by a system of 

 levers, so that no flexure can take place, or else a bedplate must be so 

 carefully adjusted in an horizontal plane that no effect of flexure can 

 be detected. Professor Rogers has adopted the latter plan, and he 

 believes that no part of the bedplate of his comparator is more than 

 00002 of an inch from the true level. 



In constructing a standard, the shape of the bar and the material 

 of which it is composed require careful consideration. In a few cases, 

 standard bars seem to have undergone some molecular change by 

 which their length has been altered. As an example, we may cite this 

 instance : A Russian standard, which was used at one time in geodetic 

 surveys, after it had been transported for a distance of about eight 

 thousand miles, was found to have shortened in length by about one 

 six-thousandth of an inch. This bar was of iron, about seven feet 

 lono;. 



The influence of temperature upon the length of a metal bar is 

 very noticeable, when careful measurements are made. Xot long ago, 

 before our knowledge of this subject was as complete as it is now, it 

 was assumed that, if two bars were allowed to remain in a liquid 

 maintained at a certain temperature, they would soon acquire their 



* " Proceedings of the American Academy of Arts and Sciences," vol. vii, New Series, 

 p. 273. 



