Management of delicate Balances. 355 



balances, because they are less liable to fracture, or to become 

 blunted than points ', but they are difficult to make, and are 

 apt to crack and bend in hardening, and after all it is almost 

 impossible to make them quite straight, in consequence of 

 which, if the bearing points become accidentally shifted 

 lengthways upon the knife-edge, the distance of the point 

 of bearing from the centre becomes shifted, and the same 

 happens if the three knife-edge bearings are not exactly 

 parallel. 



A good point, on the contrary, is very readily and easily 

 made, so much so, that an amateur workman could finish one 

 very finely in half an hour, and in making the adjustments 

 they are very readily used, and much complication is saved 

 in making the beam ; they cause none of the inconveniences 

 and inaccuracies of knife-edges, and the sole objection is, that 

 they are more liable to injury, and are not so strong as a 

 knife-edge. The points are so easily renewed and re-adjusted 

 when injured, that this inconvenience is of little consequence. 

 Even when worked so fine, that when examined by a micros- 

 cope the extremity of the point is sharper than that of the 

 extremity of a fine needle, yet they last in daily use for a very 

 long time. 



In the bob balance, the weight of the beam and bob may be 

 considered as one force acting upon the centre of gravity of 

 the system, and the load and scale-pan as another, acting upon 

 the point of suspension. In the case of an equilibrio, we have 

 the equation 



A. a. sine (|e+inclin=B. /3. sine |e — inclin.) by expand- 

 ing the value of the sine of the double arc 



A. a. (sin |e cos inclin. + cos Je sin. inclin.) = 



=B. p. (sin. |e cos inclin. — cos |e sin. inclin.) 



Dividing by sin |e cos. inclin. 



A. a. (1 X cotang |e tang inclin.)= 



=B. /3. (1 — cotang |e tang inclin.) 



Multiplying and transposing 



