LIV PHILOSOPHICAL SOCIETY OF WASHINGTON. 
meters, which were also end standards, the French Metric Commis- 
sion used a lever comparator by Lenoir. 
In 1742 Graham used beam compasses, which he considered trust- 
worthy to 0°00062 of an inch, in comparing standards of length ; 
but at that time the French Academicians made their comparisons 
of toises only to one twentieth, or one thirtieth of a line, say 0:00300 
of an inch, and it was not until 1758 that La Condamine declared 
they should be compared to 0°01 of a line, or 000089 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 comparator of Lenoir, which was regarded as trust- 
worthy to 0°000077 of an inch.” 
The heads of micrometer microscopes are usually divided into 
one hundred equal parts, and if we regard one of these parts as the 
least reading of a microscope, then in 1797, Sir George Shuckburgh’s 
microscopes read to one ten thousandth of an inch; and the least 
reading of microscopes made since that date has varied from one 
twenty thousandth to one thirty-five thousandth of an inch. <A few 
investigators, among whom may be mentioned Professor W. A. 
Rogers, of Colby University, have made the least reading of their 
microscopes as small as one 90,000 of an inch, but it is doubtful if 
there is any advantage in so doing. At the present day the errors 
committed in comparing 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° F. if it is of brass, 
or to 0°09° F. if it is of iron. To get thermometers that will indicate 
their own temperature to that degree of accuracy is by no means 
easy, but to determine the temperature of a bar from their readings 
is far more difficult. Again, we imagine 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 ther- 
mometer, then raise it to the temperature of boiling water, and im- 
mediately thereafter again determine its freezing point, we in- 
variably find that the freezing point has fallen a little; and we ex- 
plain this by saying that the glass has taken a set, from which it 
114, p. 483. 2Base du Systéme Métrique. T. 3, pp. 447-462. 
