The needle will now traverse the field of the microscope, and measure the length and breadth of the image of any object that is applied to it. But further assistance must be had, in order to measure the object itself, which is a subject of real importance; for though we have ascertained the power of the microscope, and know that it is so many thousand times, yet this will be of little assistance towards ascertaining an accurate idea of its real size; for our ideas of bulk being formed by the comparison of one object with another, we can only judge of that of any particular body, by comparing it with another whose size is known: the same thing is necessary, in order to form an estimate by the microscope; therefore, to ascertain the real measure of the object, we must make the point of the needle pass over the image of a known part of an inch placed on the stage, and write down the revolutions made by the screw, while the needle passed over the image of this known measure; by which means we ascertain the number of revolutions on the screw, which are adequate to a real and known measure on the stage. As it requires an attentive eye to watch the motion of the needle point, as it passes over the image of a known part of an inch on the stage, we ought not to trust to one single measurement of the image, but ought to repeat it at least six times; then add the six measures thus obtained together, and divide their sum by six, or the number of trials; the quotient will be the mean of all the trials. This result is to be placed in a column of a table, next to that which contains the number of the magnifiers. By the assistance of the sectoral scale, we obtain with ease a small part of an inch. This scale is shewn at Fig. 5, 6, 7. Plate II. A, in which the two lines c a c b, with the side a b, form an isosceles triangle; each of the sides is two inches long, and the base one-tenth of an inch. The longer sides may be of any given length, and the base still only of one-tenth of an inch. The longer lines may be considered as the line of lines upon a sector opened to one-tenth of an inch. Hence, whatever number of equal parts ca cb are divided into, their transverse measure will be such a part of one-tenth as is expressed by their divisions. Thus, if it be divided into ten equal parts, this will divide the inch into one-hundred equal parts; the first division next c will be equal to one-hundredth part of an inch, because it is the tenth part of one-tenth of an inch. If these lines be divided into twenty equal parts, the inch will be by those means divided into two hundred equal parts. Lastly, if a b c a be made three inches long, and divided into one-hundred equal parts, we obtain with ease the one-thousandth part. The scale is represented as solid at Fig. 6, but as perforated at Fig. 5 and 7; so that the light passes through the aperture, when the sectoral part is placed on the stage.