Dr. Everett on a new Proportion- Table. 353 



fully, on account of the difficulty of setting it with sufficient ex- 

 actness, and of reading off correctly when the answer falls be- 

 tween two divisions. Such persons may content themselves with 

 reading off from the Proportion-Table to the nearest division 

 only, as the error thus involved averages considerably less than 

 1 part in a thousand. To produce so great an error as 1 per 

 cent., there must be an error in setting or in reading off to the 

 amount of fully J of an inch. In fact if all the divisions were 

 erased and only the figures left, the instrument would still work 

 as correctly as the ordinary slide-rule. 



These considerations have not, however, operated as induce- 

 ments to carelessness in the execution of the divisions. On the 

 contrary, every effort has been made to carry accuracy to the 

 utmost attainable degree. To this end the plates were first ruled 

 with equidistant lines by means of a dividing-engine, the dis- 

 tance between the lines on plate B being equivalent to 1 in the 

 third place of logarithms, and the distance between those on A 

 one-tenth greater. Then, after proofs of these lines had been 

 printed, and the principal divisions filled in with a pen to serve 

 as a check against mistakes, the divisions were executed on the 

 plates by means of the dividing-engine, the regulating wheel 

 having fifty teeth, and each tooth corresponding to two in the 

 fifth place of logarithms. The lines which had previously been 

 ruled on the plates furnished a test of the equality of different 

 parts of the screw ; and the small inequalities, which were thus 

 with the aid of a magnifying-glass detected, amounting in their 

 greatest combined effects to three teeth of the regulating wheel, 

 were in part corrected by advancing or retarding the wheel, the 

 correction thus applied being generally less than the observed 

 error, and never exceeding it ; for it is obvious that the true cor- 

 rection would be in general about half the observed error. 



It is considered certain that the distance of a division from its 

 true place in no instance amounts to so much as 2 J teeth of 

 the wheel, or 5 in the fifth place of logarithms, with the excep- 

 tion of the last two inches of the first column of B, where the 

 divisions seem to be placed too high by something more than 

 this amount, owing in part to an accident which occurred in this 

 portion of the work, and in part to the fact that this column was 

 the first executed, and that the corrections above mentioned 

 were not applied until its completion. When great accuracy is 

 required in the use of the Proportion-Table, this first column can 

 always be dispensed with and the duplicate column (the eleventh) 

 used in its stead, as plate B contains one column more than ne- 

 cessity requires. 



A more serious source of error to be guarded against is un- 

 equal stretching or shrinking of the material on which the Table 



Phil. Mag. S. 4. Vol. 32. No. 217. Nov. 1866. 2 A 



