ABSENICAL CATTLE DIPS. 15 



uated by measuring successive known volumes of water into the vat 

 and marking on the rod the depth of each Imown vokime, but in many 

 cases graduation through calculation may be more practicable. 



The first step is to calculate the water-line measurements at half 

 depth and then at three-quarter depth. A little consideration will 

 show that the water-line measurements at half depth are exactly 

 half-way between the bottom measurements and the water-line meas- 

 urements of the completely filled vat ; that is, they are the average of 

 these two measurements, obtained by adding them together and divid- 

 ing by two. In the same way the water-line measurements at three- 

 quarter depth are the average of the water-line measurements at 

 half depth and at full depth. 



The second step is to calculate the capacity of the vat when filled 

 to three-quarter depth. Then, having prepared a straight, smooth 

 stick, 7 or 8 feet long and about 1^ inches square, lay off from one end 

 (marked " bottom ") the feet depth at the three-quarter level, and mark 

 the point with a pencil line, also adding the figure for gallons capac- 

 ity at that point. 



Third, subtract the capacity at three-quarter depth from the capac- 

 ity at full depth, point back to the left two decimal places in the 

 remainder, and divide it into one-fourth of the actual full depth in 

 feet. The quotient is the average number of feet increase in depth 

 per 100 gallons liquid above the three-quarter level. 



Fourth, subtract the actual capacity at the three-quarter level 

 from the next even 100 gallons above that level and set this figure 

 as the numerator of a fraction of which 100 is the denominator. By 

 this fraction multiply the figure for feet per 100 gallons, obtained in 

 the third operation. The product is the distance to be laid off on 

 the rod above the three-quarter depth point to obtain the level of 

 the next even 100 gallons above that point. By referring to Table 

 3, convert this distance to inches and lay it off on the rod with 

 proper notation. Now, having obtained this point for an even 100 

 gallons, it is only necessary to continue therefrom, marking off the 

 level of each succeeding 100 gallons by using the figTire obtained for 

 " depth per 100 gallons." The same figure can be used to obtain 

 capacities only a short distance below the three-quarter level with- 

 out serious error. But by a similar series of calculations it is pos- 

 sible to obtain the capacity at half depth, then the true average figure 

 for feet per 100 gallons between half depth and three-quarter depth, 

 and so to graduate the rod between those two levels. 



The graduations are to be made permanent by saw cuts or notches, 

 50-gallon marks being interpolated if desired, and the corresponding 

 figures are cut into the wood. 



