Sept. 12, 1884.] 



♦ KNOWLEDGE • 



225 



illustrations of the fourth factor in the case, and its influence. As 

 the upright posts show only as points ou the ground-plan, so does 

 the upri<;ht plane of the picture show only as a mere line. I will, 

 in the first place, show it at P P ; o, h, c, d, c, and / being the posts, 

 and A the observer, agreeably to your correspondent's intention. 

 Under these circumstances former correspondents have already 

 threshed out the subject. I may refer especially to letter 13il, 

 from J. Bacon (K.nowledge Xo. 142). But other positions Q Q, 

 R R for the jjlane of the pictviro will cciually answer the condition 

 of intercepting the rays of light a to A, and / to A. 



Let me examine the result of assuming Q Q to be the position of 

 the plane of the picture, with the help of tho accompanying vertical 

 section. Uere A being the observer, the several posts coincide 

 with another in place on the section ; or stated otherwise, the last 

 post, /, hides aU tho others. The several rays of light, Aa, Afc, Ac, 

 &c., on the plan, are shown in section leading from foot and top of 



■:y- 



post to A. Set off the distance a z from the plan horizontally on 

 the section from the post a. This shows the part of the plane of 

 the pictai-e Q Q whereon the post a should be d^a^vn. It is at 

 ZZ on the section, being bounded by the rays of light a A. Also 

 set oS the distance to y from the row of posts as obtained from the 

 ground-plan upon the section. This gives us at i/ y the length upon 

 the plane of the picture which will be occupied by the image of 

 the post /. Thus, with the assumption of a plane of the picture 

 P P in parallel perspective (as in letter 13-11) the posts should be 

 drawn of equal height ; 2ndly, with the assumption of Q Q as the 

 place of the plane of the pictm-e, the post /should be drawn as at 

 y y, much longer than the image j ; of the nearer post ; and, 3rdly, 

 it would be equally easy to show that with the assumption of R R 

 as the place of the plane of the picture, the image of the further 

 post /, at n; in R R, would be shorter than the image of the 

 nearer post a, at c in R R. The results of this third assumption 

 alone agree with the three impressions of your latest corre- 

 spondent. I cannot dispute the impressions on his inner conscious- 

 ness ; I am only showing the geometry of a drawing to be placed 

 outside the physical eye. An Old Dkaughtsman. 



LIFE. 



[1393]— Reading in the Times of Sept. 2 the Rev. W. H. 

 Dallinger's lecture on Life, I am tempted to ask him why, like 

 Tyndall, he is unwilling to go beyond no life without antecedent 

 life, and therefore close the door to further inquiryl? The object of 

 science is to discover (if possible) the origin) of all things our 

 senses can take cognizance of, the elements out of which all 

 matter is built up, and, in my opinion, something that at present 

 the human senses are unable to take cognizance of, inasmuch as 

 hey are only to be found in what we call space, immediately they 



are subjected to any influences. They love their elemental con- 

 dition, and form combinations out of which all things are built up. 

 I once before ventured to suggest the origin of the vital spark, 

 and I should like to ask the Rev. W. H. D. if any violence is done 

 to the principle of evolution by asserting that there is a moment 

 of time when the substance of conception springs into animation, 

 I therefore take it that there is no necessity to ask for matter, 

 other than that we already know of, but have only to investigate 

 the special condition of matter out of which life springs. 



A NON-Y. Z. 



THE CURVES ON A BICYCLE WHEEL. 



[1394] — An interesting optical effect may be observed by anyone 

 with ordinarily good sight who watches a bicycle passing rapidly 

 by him. Looking carefully at the driving-wheel as it approaches, 

 he will see a number of shadowy curves above and below the asle. 

 These change their figvires slowly until the instant of passing, when 

 they shift position suddenly, and again gradually alter as the 

 machines recedes. The rationale of these curves seems to be that 

 they are the optical effect of the apparent intersections of the 

 spokes, the appearance being rendered continuous by the rapid 

 rotation of the wheel. The spokes of a bicycle, it will be remem- 

 bered, are not, like those of an ordinary carriage wheel, carried out 

 to the circumference from a central point, but spring alternately 

 from drums at opposite sides of its plane, thus forming a cage of 

 two cones base to base. 



When the eye is situated anywhere except in the plane of the 

 wheel, or the line of the axle, the two sets of spokes appear to 

 intersect, each spoke from the nearer drum crossing (in general) a 

 number of the spokes which spring from the remoter drum.* If 

 the spokes are numbered consecutively round the circumference of 

 the wheel, all the odd numbers belong to one drum and all the even 

 numbers to the other. The intersections nearest to the circum- 

 ference are those of consecutive spokes, and it will be found, on 

 plotting down their points of intersection, that they all lie on two 

 loops, one above, the other below, the axle, and both springing 

 sharply from the two drums. In like manner, the intersec- 

 tions of each spoke with the third in order from it (1 and 

 4, 3 and 6, 5 and 8, &c.) determine two loops which lie 

 entirely within those first mentioned. The intersections of spokes 

 separated by fotir (1 and 6, 3 and 8, &c.), give rise to the third 

 pair of curves, and so on, until when the intersecting spokes are 

 widely separated the number of intersections in either semicircle 



win be too small to define the form of the cm-ve. Xow the manner 

 in which the rotation of the wheel helps to make these curves 

 optically continuous seems to be as follows : — When the wheel 



* It will be easily seen that, although two sets of n lines intersect 

 in n- points, when the lines proceed from fixed points, and are not 

 produced beyond those points, the number of actual intersections 



cannot exceed — , however large may be the wheel. 



