protected by a Lightning- Conductor. 429 



dant thunder and lightning. We can let the line ef represent 

 he limit of resistance of the air if the field be drawn to scale ; 

 and we can thus trace the conditions that determine disruptive 

 discharge. 



If the earth-surface be not flat but have a hill or a building, 

 as H or L, upon it, then the lines of force and the equipoten- 

 tial planes will be distorted, as shown in fig. 3. If the hill 

 or building be so high as to make the distance H h or L I equal 

 to ef (fig. 2), then we shall again have disruptive discharge. 



If instead of a hill or building we erect a solid rod of metal, 

 GH, then the field will be distorted as shown in fig. 4. 

 Now it is quite evident that whatever be the relative distance 

 of the cloud and earth, or whatever be the motion of the cloud, 

 there must be a space g g' along which the lines of force must 

 be longer than a! a or H W; and hence there must be a circle 

 described around G as a centre which is less subject to disrup- 

 tive discharge than the space outside the circle; and hence this 

 area may be said to be protected by the rod G H. The same 

 reasoning applies to each equipotential plane ; and as each 

 circle diminishes in radius as we ascend, it follows that the 

 rod virtually protects a cone of space whose height is the rod, 

 and whose base is the circle described by the radius G a. It 

 is important to find out what this radius is. 



Let us assume that a thunder-cloud is approaching the rod 

 A B (fig. 5) from above, and that it has reached a point D' 

 where the distance D / B is equal to the perpendicular height 

 D' C It is evident that if the potential at D be increased until 

 the striking-distance be attained, the line of discharge will be 

 along D' C or D'B,and that the length A C is under protection. 

 Now the nearer the point D' is to D the shorter will be the 

 length AC/ under protection ; but the minimum length will 

 be A C, since the cloud would never descend lower than the 

 perpendicular distance D C. 



Supposing, however, that the cloud had actually descended 

 to D when the discharge took place. Then the latter would 

 strike to the nearest point; and any point within the circum- 

 ference of the portion of the circle B C (whose radius is D B) 

 would be at a less distance from D than either the point B or 

 the point C. 



Hence a lightning-rod protects a conic space whose height is 

 the length of the rod, whose base is a circle having its radius 

 equal to the height of the rod, and whose side is the quadrant 

 of a circle whose radius is equal to the height of the rod. 



I have carefully examined every record of accident that I 

 could examine, and I have not yet found one case where 

 damage was inflicted inside this cone when the building was 



