356 Dr. Everett on a new Proportion-Table, 



longer be needed, as all cases of proportion could be easily worked 

 in natural numbers. 



It would not be difficult to construct, on the parallel-column 

 principle, logarithmic scales of sines and tangents to be used 

 with the Proportion-Table, in the same manner as Gunter's 

 " lines of sines and tangents " are used with his " line of lines." 

 But, on the ground of greater simplicity and intelligibility, it is 

 considered better to dispense with these auxiliaries, and in their 

 stead to use small Tables of natural sines and tangents. 



While alluding to Gunter's scale, we cannot forbear quoting 

 from Mackay's ' Description and Use of the Sliding Gunter in 

 Navigation' (2nd edit., 1812) . He says in the preface, " Although 

 a scale 2 feet long may be sufficient for performing any day's 

 work with all the accuracy that may be desired, yet its divisions 

 are too small for obtaining with exactness the apparent time from 

 the altitude of a celestial object, the latitude from double alti- 

 tudes aud the elapsed time, or for reducing the apparent to the 

 true distance ; and therefore it is to be wished that its length 

 was increased to at least double its present size." What would 

 he have said to the present " Table," which instead of being only 

 double is seven* times the size of the old " Gunter." 



We may add, by way of appendix, that we are at present try- 

 ing the experiment of putting the Proportion -Table round a cy- 

 linder, the arrangement being so contrived that those divisions 

 which work together will be in the same plane, and that the outer 

 piece can be either rotated about the inner or moved longitudi- 

 nally without rubbing the divisions. This plan promises some 

 advantages, among others the abolition of the parallel lines 

 which are now necessary for accurate adjustment; but we 

 scarcely expect it will be found to admit of such rapid working 

 as the present arrangement. 



In concluding this paper, the author desires to express his 

 obligations to Messrs. Pulton Brothers, engravers to calico- 

 printers, Glasgow, for the valuable assistance which they afforded 

 him in the mechanical execution of the Table, and for gra- 

 tuitously allowing him the use, during a period of several weeks, 

 of the very convenient and accurate dividing- engine with which 

 the divisions were engraved. 



* The real length of the so-called two-foot Gunter's scale is only 1 foot 

 I0f inches, after deducting margins, 



