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[[right corner]] (146 [[/right corner]]

the vertebral holes of the spine; whence those nerves which spring from the right side terminate in those parts which form the left side, and [[underline]] vice versa [[/underline]].

     So that the right side of the body on which the brain was wounded was not affected thereby, as expected, but the opposite side, which was supplied by the nerves whose origin was from the wounded side; while the other side, supplied by nerves proceeding from the sound side, though opposite thereto, possessed its faculties as freely as if no wound at all had happened.

     Thus we see observation and experience, are the two surest sources of certain knowledge; far beyond all uncertain hypothical reasonings a [[underline]] priori [[/underline]], however entertaining and instructing, such maybe a [[underline]] posteriori [[/underline]].

[[left margin]] Advertisement of a history of Barbados with a curious observation made by cutting down the Woods there. [[/left margin]] 

[[underline]] A Short History of Barbados, from its first Discovery and Settlement to the End of the year [[/underline]] 1767. Small 8. [[superscript]] ve [[/superscript]] 2. [[superscript]] s [[/superscript]] 6 [[superscript]] d [[/superscript]] Dodsley. 

     In which are these remarkable words, quoted by the Reviewers of the Monthly Review for July 1768. p. 16. [[underline]] viz. [[/underline]]  

     "The Destruction of the Woods in that Island, (Barbados) though it renders the Country more healthful, hath decreased the Quantity of Rain, and hath been thereby detrimental to the Planters.

[[left margin]] To find the focal lengths of Object-glasses & Diameter of the Apertures of Telescopes. [[/left margin]]

Problem

The Magnifying Power of ^ [[insertion]] a [[insertion]] Refracting Telescope, the Focal length of the Object Glass, the Diameter of its Aperture, the focal length of the Eye Glass [[strikeout]] and the Diameter of its Aperture: [[/strikeout]] any One of these being given to find all the rest. 

Put a= Magnifying power 
{B=focal length of the Object Glass in Feet. 
{D= the diameter of the Aperture of the Object Glass in Inches. 
{b = focal length of the Eye Glass in Inches. 
{[[strikeout]] d = the diameter of the Aperture of the Eye Glass [[/strikeout]]

Then per Rule on page 44, [[sqrt]] ,3B [[/sqrt]] [[in red beneath]] 9,7385606 ½ [[/red]]= D, and 1, 1 [[sqrt]] ,3B [[/sqrt]] [[in red beneath]] 9,7799533 ½ [[/red]]= b; whence 12B/b, or 12B/ [[denominator]] 1,1 [[sqrt]] ,3B [[/sqrt]] [[/denominator]] = a; which divided and reduced, [[strikeout]] E [[/strikeout]] the equation becomes 19,9126 B [[superscript]] 1/2 [[/superscript]] [[in red beneath]] 1,2991278 ½ [[/red]] = a; Whence, 

I. [[strikethrough]] [[?]] [[strikethrough]] [[insertion]] B = [[/insertion]] ^ [[square root]] ,0502195a [[/square root]] [[in red beneath]] [[bar]] 8 [[/bar]] ,7008721 ½ [[strikethrough]] =B [[/strikethrough]] or, ^ [[insertion]] B= [[/insertion]] ,002521995a [[superscript]] 2 [[/superscript]] [[in red beneath]] [[bar]] 7 [[/bar]] ,4017443 [[/red]][[strikethrough]] =B [[/strikethrough]]  = 3,33D = [[in red beneath]] 0,5228787 [[/red]] = 2,754814b. [[superscript]] 2 [[/superscript]] [[in red beneath]] 0,4400923 [[/red]]

II. a = 19,9126B [[superscript]] ½ [[/superscript]] [[in red beneath]] 1,2991278 ½ [[/red]] = 36,35526D [[in red beneath]] 1,5605672 [[/red]] = 33,05023b. [[in red beneath]]  1,5191745 [[/red]].

III. b = ,030257a [[in red beneath]] [[bar]] 8 [[/bar]] ,4808255 [[/red]] = ,602495B [[[superscript]] ½ [[/superscript]] [[in red beneath]] [[bar]] 9 [[/bar]] ,7799533 1/2 [[/red]] = 1,1D. [[in red beneath]] 0.0413927 [[/red]]

[[In red in right margin]] N.o. The Red figures are the Log. [[superscript]] ms [[/superscript]] of the Nat. N. [[superscript]] os [[/superscript]] over them.

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