NOTES. NOTE A. p. 39. THE term solidity is used here in the customary sense, to express the magnitude of any geometrical quantity of three dimensions, length, breadth, and thickness; whether it be a solid body, or a fluid, or even a portion of empty space. This use of the word, however, is not altogether free from objection. The same term is applied to one of the general properties of matter; and also to that peculiar quality by which certain substances are distinguished from fluids. There seems to be an impropriety in speaking of the solidity of a body of water, or of a vessel which is empty. Some writers have therefore substituted the word volume for solidity. But the latter term, if it be properly defined, may be retained without danger of leading to mistake. NOTE B. p. 76. The following simple rule for the solidity of round timber, or of any cylinder, is nearly exact : Multiply the length into twice the square of of the circum It is common to measure hewn timber, by multiplying the length into the square of the quarter-girt. This gives ex actly the solidity of a parallelopiped, if the ends are squares. But if the ends are parallelograms, the area of each is less than the square of the quarter-girt. (Euc. 27. 6.) Timber which is tapering may be exactly measured by the rule for the frustum of a pyramid or cone (Art. 50, 68.); or, if the ends are not similar figures, by the rule for a prisBut for common purposes, it will be suf moid. (Art. 55.) ficient to multiply the length by the area of a section in the middle between the two ends. N. B. In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to 0's, points or dots are introduced instead of the O's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. 150 176091 6381 151 8977 9264 152 181844 2129 153 4691 4975 154 155 .156 7521 | 7803 7803 190332 | 0612 3125 3403 157 5899 158 8657 159 6670 | 6959 6959 7248 | 7536 7825 9552 9839 9552 9839.126.413 | .699 2415 | 2700 2985 3270 3555 5259 | 5542 5825 6108 6391 8084 8366 8647 8928 9209 9490 | 9771 ..51 281 0892 1171 1451 1730 2010 2289 2567❘ 2846 279 3681 3681 | 3959 | 4237 | 4514 4792 5069 5346 5623 278 6176| 6453| 6729 7005 7281 7556 7832 8107 8382 276 8932 9206 9481 9755..29 .303 .577 .850 1124 274 201397 1670 1943 2216 2488 2761 9086 9380 9674 9968 295 293 1558 287 4407 285 3033 3305 3577 3848 272 N. 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | D. 171 2996 3250 172 3504 3757 173 174 240549 175 3038 3286 176 177 178 250420 179 2853 4011 4264 4517 4770 5023 5276 253 7544 7795 252 |