242 MEMORANDA. " 



of an individual one, and will probably be much less. The 

 advantage, then, of taking a large space of the stage micro- 

 meter as a basis for estimating the value of that in the eye- 

 piece is quite evident ; for, not only is the absolute amount of 

 error likely to be less, but that amount will be proportionally 

 diminished in measuring all smaller objects, whereas it would 

 be increased in measuring larger ones. 



In the micrometer recommended by Dr. Robertson, the 

 object is made to occupy the chord of an arc, and the extent 

 that can be measured by it is the diameter of the dotted circle 

 described by the revolution of the point of intersection of the 

 lines a h and cd, fig. 2, p. 155. 



To find the value of this quantity, make the line c d parallel 

 and coincident with one of the divisions of the stage micro- 

 meter, then turn the eye-piece half round, and when the same 

 line is again parallel to a division, read off the number of 

 divisions passed over, which will be equal to the chord of 

 180°, or twice the size of 90°. The chord, then, of any ob- 

 served angle will bear the same proportion to the chord of 

 180°, that the sine of half the angle does to the sine of 90° ; 

 and as the latter quantity is taken as unity in the tables of 

 sines, the calculation becomes quite easy, either by logarithms, 

 whole numbers, or the sliding-scale. Whether this instru- 

 ment is capable of the accuracy assigned to it by Dr. Robert- 

 son, must depend on the relative position of the eye-piece and 

 the object on the stage remaining invariable during the opera- 

 tion ; and this can only be insured by sound workmanship 

 in the maker, and delicate manipulation in the observei'. 



The latter, however, will, I think, find some difficulty in 

 placing the line to be measured (which may be either in the 

 length or breadth of an object) in the exact direction of the 

 chord of the imaginary circle (for there is no trace of it in the 

 microscope) ; and the calculations, though simple, will become 

 wearisome when often repeated. When Dr. Pereira was 

 engaged on the last edition of his ' Materia Medica,' I made 

 the measurements of the different starch-globules for him ; 

 and as I generally measured eight or ten in each specimen, I 

 am sure that it would have taken me a much longer time than 

 I spent over it to accomplish the task with the above instru- 

 ment. The eye-piece micrometer that I used was a glass one, 

 furnished with the fine-movement screw, described in the 

 transactions of the Microscopical Society, and in Mr Quekett's 

 treatise. It was divided into 250ths of an inch, and, by means 

 of a draw-tube, was made to read 10,000ths with the quarter 

 inch object-glass employed. The measurements may therefore 

 be relied on to the 30,000th of an inch ; for the third, or even 

 fourth of a division can be easily estimated. 



