112 



All levels will not, of course, give such results, owing to the difference of the pro- 

 ducts of different makers, or to change of curvature after grinding, or to mode of 

 mounting, too tight packing, etc. A level which seems of good quality when being 

 tested may be found irregular after it has been mounted in its brass tube, which shows 

 that the level has been improperly mounted. We do not wish to be understood as 

 saying that a level is necessarily a bad one if its irregularities are too small to be re- 

 vealed by the telescope whose power is properly adapted to the character of the grad- 

 uations and other fine features of the instrument. 



If the Civil Engineer should wish to know the value of one division of the tele- 

 scope level bubble, in minutes or seconds of arc, it may be readily found in the field as 

 follows : Having setup and brought the level over a pair of leveling screws a reading 

 is taken on a rod held perpendicular to the line of sight, and a distance of from one to 

 two hundred feet and the position of the bubble noted. The inclination of the level 

 to the horizon is now changed by moving the leveling screws and a new reading taken 

 on the rod and the new postion of the bubble noted. 



Knowing the distance of the leveling rod from the instrument, the difference of 

 rod reading and the number of divisions and distance over which the bubble traveled, 

 we may readily write the following : Let 



x = the change in inclination of the line of sight. 

 r = the difference of rod readings. 

 d = distance of rod from instrument. 

 n = number of divisions passed over by bubble. 

 a = distance passed over by bubble. 

 R = radius of curvature of inner surface bubble tube. 

 # = number of seconds corresponding to one division of bubble. 



tan. x = -3 

 d 



_._ z_in seconds. 



Example. Bubble divided to tenths of inches. Distance from bubble to rod, 

 200 feet. 



Movement Bubble. Rod Reading. Difference in Rod Reading. 



Inches. Feet. Feet. 



0.0 4.499 02Q 



0.3 4.519 rtor 



0.4 4.544 



0.5 4.572 



0.5 4.608 



0.6 4.580 



0.5 4.542 'g* 



0.4 4.515 '4 



0.3 4.493 



Mean, .425 .028 



For a movement of bubble over one division the difference of rod reading is .0066 ft 



.0066 



200 X 000005 = 6 - 6seC nds - 

 (.000005 is the natural tangent for one second. 



Note FOR TESTING LEVELS OF THE HIGHEST GRADE AS REQUIRED FOR -ASTRONOMICAL PURPOSES 

 ONLY, PROF. C. A YOUNG suggests the following modification : To MAKE THE AROVE DESCRIBED LEVEL 

 TRIER A REPEATING INSTRUMENT. The base plate of pur Level Trier will be lengthened and, at a small 

 additional expense, an auxiliary screw of reasonable fine pitch and having a large but coarsely graduated head 

 for convenient settings, will pass through it and rest against the masonry direi t. This \\ill make the Trier a 

 repetition instrument ; after running the bubble from one end of the level to the other by the micrometer 

 screw, the bubble can be sent back by the auxiliary screw, and then the micrometer screw may be used again, 

 getting a new reading on a different part of the screw. If this is repeated until the reading of the graduated 

 disc of the micrometer screw is the same as that started with, it will eliminate an error of excentricity, if any 

 exist, of the graduated disc, but what is more important, that of the scrnv point also, which in a i: 

 always may exist after careless handling of the instrument, and then it may describe a little circle on the 

 resting surface. If this surface is perfectly plane and at right angles to the axis of the measuring screw, this 

 little excentricity of the screw point is harmless ; but since it seldom happens that the bearing surface is truly 

 at right angles to the screw point, a serious periodic error results. To make this arrangement complete, a 

 small level will also be attached to the base plate to indicate when the latter occupies its normal position. 



