This balance is subject to the inconvenience of the divisions becoming much shorter as the weight increases. The distance between the divisions indicating one and two pounds being, in the example we have given, about seven tenths of an inch, whilst that between 20 and 21 pounds is only one tenth of an inch; consequently a very small error in the place of the divisions indicating the larger weights would occasion very inaccurate results. The Danish balance is represented at _fig. 194._ _The Bent Lever Balance._ This instrument is represented at _fig. 195._ The weight at C, is fixed at the end of the bent lever A B C, which is supported by its axis B on the pillar I H. A scale-pan E, is suspended from the other end of the lever at A. Through the centre of motion B draw the horizontal line K B G, upon which, from A and C let fall the perpendiculars A K and C D. Then if B K and B D are reciprocally proportional to the weights at A and C, they will be in equilibrio, but if not, the weight C will move upwards or downwards along the arc F G till that ratio is obtained. If the lever be so bent that when A coincides with the line G K, C coincides with the vertical B H, then as C moves from F to G, its momentum will increase while that of the weight in the scale-pan E will decrease. Hence the weight in E, corresponding to different positions of the balance, may be expressed on the graduated arc F G. _Brady’s Balance, or Weighing Apparatus._ This partakes of the properties both of the bent lever balance and of the steelyard. It is represented, at _fig. 196._ A B C is a frame of cast iron having a great part of its weight towards A. F is a fulcrum, and E a moveable suspender, having a scale and hook at its lower extremity. E K G are three distinct places, to which the suspender E may be applied, and to which belong respectively the three graduated scales of division expressing weights, _f_ C, _c d_, and _a b_. When the scale and suspender are applied at G, the apparatus is in equilibrio, with the edge A B horizontal, and the suspender cuts the zero on the scale _a b_. Now, any substance, the weight of which is to be ascertained, being put into the scale, the whole apparatus turns about F, and the part towards B descends till the equilibrium is again established, when the weight of the body is read off from the scale _a b_, which registers to ounces and extends to two pounds. If the weight of the body exceed two pounds, and be less than eleven pounds, the suspender is placed at K; and when the scale is empty, the number 2 is found to the right of the index of the suspender. If now weights exceeding two pounds be placed in the scale, the whole again turns about F, and the weight of the body is shown on the graduated arc _c d_, which extends to eleven pounds, and registers to every two ounces.