144 Remarks on Dr. Enfield's Institutes 



properly referred to the subject of apparent velocity, than 

 of apparent magnitude. As referred to the head of appa- 

 rent velocity, the proposition might have been thrown into 

 the following simple and not inelegant form : " When a body 

 moves uniformly in a right line, its apparent velocity will 

 be inversely as the square of the distance from the eye." 



In demonstrating the 83d and 85th propositions, it is 

 stated as the reason why the image produced by a convex 

 or concave lens is erect, that the axis of the pencils which 

 proceed from the extremities of the object " only cross one 

 another at the lens." It should be, " becau'^e they only 

 cross one another at the eye." The pencils which pass 

 from the extreme points through a lens, do notj in fact, meet 

 each other till they reach the eye. Figs. 8 and 9 convey 

 no idea of the manner in which the pencils come to the 

 eye, except in the single case in which the eye is in contact 

 with the lens; nor is there any other diagram in the Optics 

 which gives the student any information on this important 

 point. — The remark scarcely need be added, that almost all 

 the propositions in this chapter which state the effect of 

 lenses on apparent magnitude, have unsatisfactory demon- 

 strations. It is taken for granted that at whatever distance 

 from the lens the eye is placed, the pencil which enters ii. 

 from the same point of the object diverges as if from the 

 same point in space. But the fact is, that as the eye re- 

 cedes from the lens, the rays which enter the pupil from 

 the same point of the object, gradually change : the axis of 

 the pencil, instead of coinciding with the centre of the lens, 

 passes above or below it, according as the point of the ob- 

 ject is above or below. Hence it is improper to assume 

 that the pencil from A (figs. 8 and 9) diverges as if from the 

 same point D for all distances of the eye from the lens. 

 The assumption is erroneous, except when the object is 

 extremely small, and it ought not to be made even in this 

 case without proof.* 



Prop. 89. If this proposition were one of the least val- 

 ue, it would be desirable that it should have a more satis- 

 factory demonstration than its present one, which on several 

 accounts is wholly inconclusive. 



* The remarks made in Ibis parngraph are equally applicable to the pro- 

 positions in Iho succeeding chapter, which relate to vision as affected hy 

 mirrors. 



