765 



PLATE Vlir. 



Fig. 103. Tlie heights of the housp5, -windows, doors, 

 »nd figures are determined by lines directed to the 

 centre of the picture ; tlio true height being measured 

 on the lines A B, C D, where the objects are supposed 

 to touch the plane of prnjection. The distance EF> 

 ■and all other parts of lines perpendicular to the pic- 

 ture, are measured bj laying off the lengths of the 

 originals, as Gil, on the line AC, and drawing I EG 

 I EH, from I, the point of distance; which, inmost 

 cases, will be mbrc remote fi-om the centre of the pic- 

 ture than it is here made. The line K L, and others 

 parallel to A C, may be measured by the assistance 

 of any point M in the horizontal line, the distances, 

 NO, O P, being laid off on AC, or simply by reduc- 

 ing the scale in the proportion of M P to M L. P- 

 116. 



Fig. 104. A circle thrown into perspective, by 

 means of the ■ circuiffscribfed square, the points of con- 

 tact being found by bisecting the sides. P. 116. 



rig. 105, Two perspective delineations, and two 

 orthographical projections of a cube, in differen' 

 positions. For the orthograpliical projection, the 

 ground plan being A BCD, the image of any point 

 A,B, may be found by drawing A E, B F, perpendicu- 

 lar to the ground line, EG, FII, parallel to the line 

 assumed for the direction of the centre of the picture, 

 and AG, BlI parallel to the line of direction of the 

 point of distance; the interjections G and II will then 

 be the points corresponding to A and B. P. 116. 



Fig. IOC. A is the orthographical projection of a 

 sphere, with some ofits circles; B the stcrcographical 

 projection of the same circles. P. 117. 



Fi" 107. A balance made by Fidler for the Royal 

 Institution, nearly resembling those of Ramsden and 

 Troughton. The middle column A is raised at plea- 

 sure by the cock B, and carries the round ends of the 

 VOL. I. 



axis in the forks at its upper part, iu order to rcmOTC 

 the pressure ou thfe sharp edges of the axis within the 

 forks. The scales are occasionally supported by the 

 pillars C and D, which are elevated or depressed by 

 turning the handle E. The screw F serves for rais- 

 ing or lowering a weight within the conical beam, by 

 means of which the place of the centre of gravity is 

 rculated. The extent of the vibrations is measured 

 on the graduated arc G. P. 125. 



Fig. 108. A balance for the illustration of the dif- 

 ferent kinds of equilibrium. When the scales are hung 

 on the middle pins. A, B, which are in the same hori- 

 zontal line with the support of the beam, the equili- 

 brium is neutral, the weights acting as if the centre of 

 gravity coincided with the point of suspension. If the 

 scales be hung on the lowest pins C, D, the centre of 

 gravity will be nearly in the line C D, and its path the 

 curve E, which has its concavity upwards; but if the 

 scales are hung on the pins F, G, the path of the 

 centre of gravity will be convex upwards, and the beam 

 will overset. In reality the true paths of the centre of 

 gravity would be nearly in the curves II and I, situated 

 between the weights in the scales: but these are 

 similar to the other curves. P. 125. 



Fig. 109. When the equilibrium of abalance is totter- 

 ing, the lower weight acts with the greatest advantage: 

 thus the effect of the weight A is reduced in the pro- 

 portion of BCtoDC, by the obliquity of tlie ann 

 C A, while the weight E acts on the whole length of 

 its arm CF. P. 125. 



Fig. 110. If A BC be a semicircle, and BD repre- 

 sent a given weight, and A D its counterpoise in one 

 of the scales of an unequal balance D C will be the 

 counterpoise in the other scale. It is obvious that 

 AC is more than twice as great as BD. P. 126. 



5 C 



