212 MEASURING THE MAGNITUDE OF MICROSCOPIC OBJECTS. 



extremity of the object, as shown hy aO b, fig. 6. The index, 

 which is attached to the eje-piece, is by this movement brought 

 into the position O F, and the distance E F, when read by 

 means of the rule with the diagonal scale, gives the dimen- 

 sions of the microscopic object to three places of figures. Let 

 the distance E F, for example, when measured by the scale, 

 be 3*45 half-inches; t!iis gives at once as the length of the 

 microscopic object •00345 inch. 



When a higher power was applied to the microscope, the 

 radius of the dotted circle was measured exactly by * 004 inch 

 on the stage micrometer ; but if the radius is accurately known 

 in thousandths of an inch, there is no difficulty in adapting 

 the method above suggested to this or anv other radius. 

 Suppose, for instance, that an object, much smaller than the 

 former, from its being more highly magnified, still appears of 

 the same size as M N, fig. 6, and that the reading given by 

 the scale is as before 3*45 half-inches, then the length of the 

 object will be, not • 00345 inch, but a quantity bearing the 

 same proportion to it that 4 does to 10 : nothing more, 

 therefore, is requisite than to add a cipher to the left and 

 multiply the result by 4 : thus • 000345 inch x 4 = • 000138 

 inch, which is the length of the object. 



For those who prefer greater accuracy and more expen- 

 sively-divided instruments, the plan of measuring by the 

 tangent is more easy in manipulation, and the trigonometrical 

 calculation is more simple, than when the chord is employed. 

 The equation, 



log. M N = log. O M + log. tan. M O N, 



gives all that is necessary at once ; and if the radius O M be 

 unity, it is sufficient to find the number corresponding to the 

 log. tan. of the degrees and minutes, &c. of any observed angle. 

 In the case chosen above, the angle M O N was taken to 

 be 19°, of which the log. tan. = 9 '536972, and the number 

 corresponding with this gives, for the length of M N, 



with the lower power, * 034432 

 and with the higher, '00137728. 



The error, therefore, by the plan now proposed, is less than 

 one ten-thousandth part of an inch in the one case, and less 

 than one hundredth-thousandth in the other. The triangle 

 can be made of wood, brass, zinc, card-board, or any other 

 suitable material, and is recommended on the score of cheap- 

 ness, portability, facility in use, and accuracy of result. 



