THE INCLINED PLANE, WEDGE, AND SCREW. 



293 



Fig. 14. 



because its action upon the wheel may be continued without limit. This ap- 

 plication of the screw is represented in fig. 14. P is the winch to which the 

 power is applied ; and its effect at the circumference of the wheel is estimated 

 in the same manner as the effect of the screw upon the nut. This effect is to 

 be considered as a power acting upon the circumference of the wheel ; and its 

 proportion to the weight or resistance is to be calculated in the same manner 

 as the proportion of the power to the weight in the wheel and axle. 



We have hitherto considered the screw as an engine used to overcome great 

 resistances. It is also eminently useful in several departments of experimental 

 science, for the measurement of very minute motions and spaces, the magni- 

 tude of which could scarcely be ascertained by any other means. The very 

 slow motion which may be imparted to the end of a screw, by a very consid- 

 erable motion in the power, renders it peculiarly well adapted for this purpose. 

 To explain the manner in which it is applied suppose a screw to be so cut 

 as to have fifty threads in an inch, each revolution of the screw will advance 

 its point through the fiftieth part of an inch. Now, suppose the head of the 

 screw to be a circle, whose diameter is an inch, the circumference of the head 

 will be something more than three inches ; this may be easily divided into a 

 hundred equal parts distinctly visible. If a fixed index be presented to this 

 graduated circumference, the hundredth part of a revolution of the screw may 

 be observed, by noting the passage of one division of the head under the index. 

 Since one entire revolution of the head moves the point through the fiftieth of 

 an inch, one division will correspond to the five thousandth of an inch. In 

 order to observe the motion of the point of the screw in this case, a fine wire 

 is attached to it, which is carried across the field of view of a powerful mi- 

 croscope, by which the motion is so magnified as to be distinctly perceptible. 



A screw used for such purposes is called a micrometer screw. Such an ap- 

 paratus is usually attached to the limbs of graduated instruments, for the pur- 

 poses of astronomical and other observation. Without the aid of this appara- 

 tus, no observation could be taken with greater accuracy than the amount of 

 the smallest division upon the limb. Thus, if an instrument for measuring 

 angles were divided into small arches of one minute, and an angle were ob- 

 served which brought the index of the instrument to some point between two 

 divisions, we could only conclude that the observed angle must consist of 

 a certain number of degrees and minutes, together with an additional number 

 of ssconds, which would be unknown, inasmuch as there would be no means 

 of aecertaining the fraction of a minute between the index and the adjacent 

 division of the instrument. But if a screw be provided, the point of which 

 moves through a space equal to one division of the instrument, with sixty revo- 

 lutions of the head, and the head itself be divided into one hundred eotial parts, 

 ! each complete revolution of the screw will correspond to the sixtieth part of 

 \ a minute, or to one second, and each division on the head of the screw will 

 i correspond to the hundredth part of a second. The index being attached to 

 ' this screw, let the head be turned until the index be moved from its observed 



