ADDITIONS AND CORRECTIOXS. 



divides the solid into parts possessing equal powers to turn 

 the axis, the other will also divide it in a similar manner, 

 and their intersections with the equatorial plane of the first 

 iixis will also be permanent axes of rotation : for the same 

 sums will express the action of the particles in both cases, the 

 distance from either plane being equally concerned in the 

 effect of each particle,and the effects of those particles which 

 are in contiguous sections of the solid either way counter- 

 acting each other, and cooperating with the effects of the 

 sections diagonally opposite. And in the same manner it 

 may be shown that the equatorial plane divides the solid in 

 such a manner with respect to both these axes as to enable 

 the body to maintain a permanent rotation round them. 



35y. C. Theorem. If a bod}', revolving 

 freely round any axis, be caused for a mo- 

 meat to revolve at the same time round an- 

 other, the joint result of both motions will 

 be a revolution round a third axis, in an in- 

 termediate position, which will continue to be 

 the axis of rotation, provided that tlic body 

 be capable of revolving permanently round it. 



If the angle formed by the axes be divided into two parts, 

 of which the sines are inversely proportional to the velocity 

 of revolution round the contiguous axes, it is obvious that 

 the line thus dividing the angle will remain at rest, in con- 

 sequence of the equ^al velocities of the two motions, the 

 angle divided being supposed to be one of those in which 

 the revolutions are in opposite directions: and the angular 

 velocity of rotation round the new axis will be to the 

 greater of the former velocities as the sine of the whole 

 angle to the sine of the greater portion thus determined, 

 as may be inferred from considering the motion of 

 the poles of either of the primitive revolutions. The 

 position of the new axis, and the motion of any other 

 point of the body, is obviously sufficient to determine the 

 velocities and directions of the motions of every other part, 

 since the form of the body is supposed to be unchangeable ; 

 so that it is unnecessary to demonstrate that the motion re- 

 sulting from the separate motions of each point is such as 

 belongs to its place with respect to the new axis of rotation ; 

 and the body, beginning once to revolve upon this axis, will 

 continue its rotation exactly in the same manner as if it bad 

 arisen from a simpler cause. 



P. .'i5. Col. 2, after art. 304, insert, 



ScHpLiu.M. In the same manner it may be shown, that 

 if B E D be any circle, or in general any curve, rolling on 

 the wheel A, and describing the line C D, and if the same 

 curve, rolling within the circle of which B is the centre, and 

 which touches A, describe the line B D, whctlicr straight 



or curved, the force will still be directed to the point of 

 contact E, and the motitn of the wheels will be uniform. 



P. 58. Col. 2. L. 2g,for "CD" read CB. 



P.34.CM.2.L. 1 5, for " 70^°" read 160-;^. 



P. 64. At the end, 



Scholium 2. It maybe demonstrated that an impulse 

 communicated to a liquid at any point of the margin of a 

 reservoir, of which the bottom is an inclined plane, termi- 

 nated by that margin, will advance every way in a cycloi- 

 dal direction j by reasoning similar to that which is employ- 

 ed for the demonstration of the property of the cycloid, as 

 the curve of swiftest descent (261). The form of the wave 

 will be that of a curve cutting an infinite number of cy- 

 cloids at right angles ; and any number of points in it may 

 be found, by drawing on any points in a parabola as centres, 

 a number of circles touching the vertical tangent of the 

 parabola, and laying off on each from the point of contact 

 an arc equal to the distance of that point from the vertex 

 of the parabola. The truth of this may easily be shown from 

 the properties of cycloidal pendulums, (25£>). 



P. 76. Col. 2. L. 5, omit " or." 



P. 79. Col. 2. L.6, for " differs . . in" read, scarcely differs 

 from this except in. 



P.80. Before art. 461, insert, Section XX. OF physical 



OPTICS. 



P. 122. Col. 1, after 1. 20, insert, Such solids of revolutioa 

 are generally called spindles, where the curve is convex out- 

 wards ; in this case, where it is concave, they might be 

 called trochi. 



P. 139. Col. 2, after 1. 14, insert. 



Pressure of Bodies in Motion. 



Hee on' the pressure of weights in machines. Ph. tr. 1 755.J. 



P. 144. Col. 1, after 1. 28, insert. 



From the British Magazine for March, 1801 



The pinacographic instrument resembles in its construc- 

 tion a musical pen, but is much broader, so as to dravr 

 parallel lines at one or two strokes over the whole surface 

 of any page. Its use is to manufacture an index. It is to 

 be accompanied by inks of nine different colours, such as 

 are the most easily distinguished from each other at first 

 sight. In order to construct an index, procure two copies of 

 the best edition of your work ; — cover each page with paral- 

 lel lines, expressive of its number, drawing them vertical 

 for units, horizontal for tens, and oblique for hundreds, de- 

 noting each figure by the ink of the bottle on which you 

 find it marked; then, with the assistance of your wife and 

 daughters, cut the pages first into lines, and tlien into words ; 

 distribute all the words into little boxes, marked with the 

 two initial letters, and then paste them on the pages of a 

 blank book in the precise order of the alphabet. The index 

 being thus complettd, — if you print it, a very little habit will 



4 



