Lines for the putpofe of Computation. 249 
or beam have two fixed points at the diflance cf the interval 
between 1 and 30, and a moveable point be made to range 
between thele (always to indicate the antecedent) ; thep, I 
lay, it the confcquent fixed point fall without the rule, the 
other fixed point will fhew the divition it would have fallen on, 
if the rule had been prolonged. This may be e a lily applied to 
the arrangement defcribed, N° 4. 
7. If the arrangement con fi ft only of the logarithms from 1 to 
10, and the parallel crofs lines interfeef that geometrical feries 
whofe fucceflive ratios altogether, with that of the haft to the. 
firft, make by compofition the ratio T ~, the contrivance, N J 
6, may be applied to fhew fuch. confequents as fall, laterally, 
without the rule. 
8. It is convenient that the arrangement of the lines be 
difpofed fo as to occupy a rectangular parallelogram ; or, in 
other words, that the crofs line, cutting the feries laft men- 
tioned, may be at right angles to the length of the rule. 
The conftrudtion of an inftrument on the foregoing princi- 
ples admits of various difpofitions of the graduated lines and 
apparatus for meafuring intervals upon them. Fig. 1. is a 
rule confiding of ten parallel lines, equivalent to a double line 
of numbers upwards of 20 feet in length. Fig. 2. is a beam 
compafs for meafuring intervals. The parts B, A, C, apply 
to the furface of the rule ; the middle A being moveable fide- 
ways in a groove in the piece DE, fo as always to preferve its- 
parallelifm to the external pieces B, C, which are fixed at a 
defiance equal to the length of the rule, and have their edges 
placed according to the condition in § 7. which is here at right 
angles to the length. The piece DE, in the ufe, is applied to 
the edge FG of the rule. The edges or borders H, . 1 , K, L, 
may 
