THE ART OF WEIGHING AND MEASURING 609 



In 1742 Gralmiii iiseil beam compasses, wliicli lie considered trust- 

 worthy to 0.00002 of an inch, in comparing standards of length ; but at 

 that time the French Academicians made their comparisons of toises 

 oidy to one twentieth or one thirtieth of a line, say 0.()0300 of an inch, 

 and it was not until 1758 that La Condamine declared they should be 

 compared to 0.01 of a line, or 0.00089 of an English inch " if our senses 

 aided by the most perfect instruments can attain to that."* Half a 

 century later, ten times that accuracy was attained by the lever com- 

 parator of Lenoir, which was regarded as trustworthy to 0.000077 of an 

 iiich.t 



The heads of micrometer microscopes are usually divided into one 

 hundred equal parts, and if we regard one of tliese parts as the least 

 reading of a microscope, then in 1707, Sir George Shuckburgh's micro- 

 scopes read to one ten thousandth of an inch ; and the least reading 

 of microscopes made since that date has varied from one twenty thou- 

 sandth to one thirtj^-five thousandth of an inch. A few investigators, 

 among whom may be mentioned Prof. W. A. Rogers, of Colby Uni- 

 versity, have made the least reading of their mi<;roscopes as small as 

 one ninety thousandth of an inch, but it is doubtful if there is any ad- 

 vantage in so doing. At the present day the errors committed in com- 

 paring standards arise, not from lack of power in the microscopes, but 

 from the difficulty of determining sufficiently exactly the temperature 

 of the standard bars, and the effect of flexure upon the position of their 

 graduations. In order to ascertain the length of a three-foot standard 

 with an error not exceeding 0.000020 of an inch, its temperature must 

 be known to 0.06° Fahr. if it is of brass, or to 0.09^ Fah. if it is of irou. 

 To get thermometers that will indicate their own temperature to that 

 degree of accuracy is by no means easy, but to deteruiine the tempera- 

 ture of a bar from their readings is far more difficult. Again, we im- 

 agine the length of our standards to follow their temperature rigorously, 

 but what proof is there that such is the case? If we determine the 

 freezing point of an old thermometer, then raise it to the temperature 

 of boiling water, and immediately thereafter again determine its freez- 

 ing point, we invariably find that the freezing point has fallen a little; 

 and we explain this by saying that the glass has taken a set, from which it 

 requires time to recover. Is it not probable that an effect similar in 

 kind, although less in degree, occurs in all solids when their tempera- 

 ture is varying ? When we look at the highly polished terminals of 

 an end standard we are apt to regard them as mathematical surfaces, 

 separated bj^ an interval which is perfectly definite, and which could 

 be measured with infinite precision if we only had the necessary instru- 

 mental appliances ; but is that a correct view? The atomic theory 

 answers emphatically. No. According to it, all matter consists of 

 atoms, or molecules, of a perfectly definite size, and with definite inter- 



* 17, p. 483. t Base du Syst^me Mdtriqne. T. 3, pp. 447-462. 



H. Mis. 142 39 



