TWO SOURCES OF LIGHT 81 



to AB. Lay off on AB distances hx and hy, such that hy = 2hx. From 

 x and y erect lines perpendicular to AB, they will intersect OC at f 

 and e respectively. Bisect the line ef, and at its middle point, g, con- 

 struct a line kl perpendicular to OC. From the point of intersection of 

 kl and yy' (M), draw a line to D. From the intersection of kl and 

 xx' (iV), draw a line to D. 



The angle il/DAT is the desired angle. 

 Proof: eg = gf (construction). 

 Angle egM — angle fgN (construction). 



Angle Meg = angle Nfg (alternate int. angles of parallel lines, 

 yy' and xx' being parallel by construction). 



Therefore triangle Meg = triangle Ngf (side and two adjacent angles 

 being equal). 



Ng = gM (similar sides of equal triangles). 



gD = gD (identical). 



Therefore triangle NgD = triangle MgD (rt. triangles, altitude and 

 base equal). 



Therefore angle gDM = angle gDN and side DM = side DN. 



Now by construction hx is the projection of DN on AB and hy 

 the projection of MD on AB, and by construction hy = 2hx. 



This fulfills all the conditions of construction. 



The equal lines MD and DN represent equal bilateral sensitive areas 

 inclined to each other at such an angle, MDN, that the surface represented 

 by MD intercepts an area of light twice as great as the surface repre- 

 sented by DN, its projection on the perpendicular to the light rays being 

 twice as great (hy = 2hx). But the light falling on DN is of twice the 

 intensity of the light falling on DM, so that the total amount of light 

 received by each of the equal areas is the same. 



By this method of construction, the average angle of sensitiveness 

 was computed for four intensity differences, using as a basis the angular 

 deflection of the larvaB as determined by experiment. The magnitude 

 of the angles is almost identical in all four cases. 412 



Experiments by a somewhat different method, to be 

 discussed in the next chapter, on the positively heliotropic 

 larvae of the barnacle show that these results of Patten 

 are more general. 



We may, therefore, say that the migration of animals 

 to or from the light is of the nature of a forced movement 

 determined by the effect of light on the photosensitive 

 elements of the body. Unequal illumination of symmetri- 



6 



