VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 31 



magnified by the object-glass. In this case, if the object-glass magnify the dia- 

 meter 10 times, while the index passes over 1 division, the point k will pass over 

 the image of an object, the diameter of which is -^ 4 ; of an inch. As in 

 this mode of application the point k must fall between the object and eye-glass, 

 the screws may be contained within the fulcrum by which the microscope is 

 supported. 



The machine (fig. 2) may be applied as a jack to raise great weights a little 

 way from the ground, by substituting 2 cross hand-spikes for the handle ckl; 

 or a vertical handle may be employed in the following manner. Let a (fig. 6) be 

 a pinion turned by the handle ab, which suppose a foot in length. Let the pinion 

 a have 4 teeth, and move the wheel cd of l6 teeth. The screw ef of 4 threads 

 in an inch is fixed in this wheel, and turns round along with it. Within it 

 plays the screw fg of 5 threads in an inch, and which we suppose prevented 

 from following the motion of ef: it terminates in such a shoulder as that repre- 

 sented at g, and being continued to h ends in a foot as in the figure. The 

 whole is inclosed in a strong frame. The pinion a must be connected in such a 

 manner with the wheel cd, as to rise within the frame along with it, which may 

 easily be done by making its axis play in a piece of wood or metal, which is con- 

 nected by the end to the screw ef. Or, if this should be deemed inconvenient, 

 as the rising of the pinion must raise the handle ab, the wheel cd may be hin- 

 dered from rising, and at the same time turn the screw ef, by a contrivance 

 similar to that used with the index c (fig. 4) in the micrometer. In either case, 

 the axis of the pinion should be continued through the opposite side of the 

 frame, and armed with a heavy fly to regulate the motion. When the machine 

 is to be applied to use, the bottom of the frame resting on the ground, if the 

 body to be lifted be already as high as the top g, that top is applied below it; 

 but if it be close to the ground, we put below it the foot h; then, if the handle 

 ab be turned once round, the wheel cd and screw ef will turn \ part round 

 and the point f will rise (4- X \ =) tV of an inch. The point g or h will 

 therefore be lifted upwards ( T ' T X \ =) -jV of an inch. But the end b of the 

 handle ab has described above 6 feet; therefore the velocity of the point g is to 

 that of the point b, as 1 to (72 X 80 =) 5760. Therefore, if we suppose a 

 man to act at the handle with a force equal to 30 lbs. he may keep in equilibrio 

 a weight of 172800 lbs. But a subduction of perhaps more than \ of this must 

 be made, that he may raise the weight, as the friction of the engine will be con- 

 siderable. Suppose it to be -J-, the effect still remains equal to 57600 lbs. or 25 

 tons, 14 cwts. and 32 lbs. 



It will easily appear, that this method of applying the screw may take place in 

 many other engines, particularly where great accuracy is required; or where we 

 want a motion to be performed with great power, while at the same time it need 



