374 hnfrovemenis of Giinter'i Stulf. 



mark a new antecedent, the other (by 2. and 3.) will marli a number at the fame rela- 

 tive pofition and dillaiice, which will be the confequent to tliis laft antecedent, after the 

 fame ratio. 



6. Suppofe a logarithmic line to contain no more than a finglc range of numbers from t 

 to 10, it will not be neceflary, for the purpofcs of computation, to repeat it ; for, if a Aider 

 or beam have two fixed points at the diftance of the interval between i and io,anda 

 moveable point be made to range between thcfe (always to indicate the antecedent), in 

 this cafe, if the confcqucnt fixed point fall without the rule, the other fixed point will fhcw 

 the divifion it would have fallen on if the rule had been prolonged. This may be eafily 

 applied to the arrangement defcribed, N° 4. 



7. If the arrangement confill only of the logarithms from i to 10, and the parallel crofs 

 lines interfecl that geometrical ferics whofe fucceffive ratios altogether, with that of the 

 laft to the firft, make by compofition the ratio t6» the contrivance N". 6. may be applied 

 to (hew fuch confequents as fall, laterally, without the rule. 



8. It will be convenient tliat the arrangement of the lines (hould he difpofed fo as to oc- 

 cupy a re£langular parallelogram ; or, in other words, that the crofs line, cutting the feries 

 laft mentioned, may be at right angles to the length of the rule. 



The eonftruflion of an inftrument on the principles here explained will admit of various 

 dlfpofitions of the graduated lines and apparatus for meafuring intervals upon them. In 

 the Tranfaftions I gave a figure cf a rule confifting of ten parallel lines, equivalent to a 

 double line of numbers, upwards of twenty feet in length, with a beamcompafs for meafur- 

 ing intervals. 



rig. 2. Plate XVI. reprefents a Gunter's fcale, equivalent to that of ag^. inches in 

 length, publithed by the late Mr. Robertfon. It is, however, but one eighth part of the 

 length, and contains only one-fourth of the quantity of divifion. In the Aider GH is a 

 moveable piece AB, acrofs which a fine line is drawn; and there are alfo lines CD, EF, 

 drawn acrofs the Aider, at a diftance from each other equal to the length of the rule. 

 The fketch No. i. reprefents one face or fide of the inftrument, and No. 2. reprefents the 

 oppofite face. Each contains one-fourth part of the line of numbers. "When it is ufed, 

 the Aider muft be fet fo that the line on the piece AB may be placed at the antecedent, 

 and one of the end marks CD, or EF, may be oppofite the confequent. After this ad- 

 iuftmentof the Aider, the whole may be moved at pleafurc, till the piece AB is fet at any 

 other required antecedent ; and then the fame line CD or EF, as before, will indicate the 

 confequent at the fame diftance or pofition as before. But if the confequent mark of the 

 Aider fhould fall without the rule, the other line will indicate the required confequent upon 

 the rule, though at the diftance of one line on the rule farther off in pofition than the 

 other confequent mark would elfe have ftiewn it. The operations are obvious and familiar 

 upon the rule itfelf. 



Another inftrument was defcribed in the Tranfaftions, which was equivalent to the 

 fame rule, but of a circular" figure, one inch and a-half diameter. The graduations 

 were made upon three concentric circles, and a fcdlor was applied inftead of the Aider. 

 On account of the larger figure I have here given, it becomes unnecefl'ary to dcfcribe 



this. 



1 approve 



