16 Frederick Guthrie on certain 



line, the nodes by single ones, and the lath itself by a straight 

 line. 



§ 2. Fig. 1, Plate II. , shows the results of the first series 

 of experiments with A. 



In the next series the same lath was used, but its other 

 end was clamped. This comparison tests the uniformity of 

 the lath in density, elasticity, thickness, and width, the latter 

 condition being only negligible when the edges are parallel. 

 The results were : — 



A x 218-5, 61-5. 



A 2 140-5, 102, 37-5. 



A 3 99, 80-5, 74, 26-5. 



A 4 77, 62, 63, 57-5, 20-5. 



A. 62, 51, 51-5, 52, 47, 16-5. 



Similar experiments with B gave, when one end was 

 clamped : — 



B x 218, 62. 



B 2 140-5, 102-5, 37. 



B 3 99, 81, 73, 27. 



B 4 77, 62-5, 63, 57, 20-5. 



B 5 62-3, 51-7, 51-3, 51-7, 46-5, 16-5. 



And when the other end was clamped : — 



B x 218, 62. 



B 2 140-5, 102-5, 37. 



B 3 99, 80-5, 74, 26-5. 



B 4 77, 62-5, 63, 57, 20-5. 



B 5 62-3, 51-2, 51-5 51-5, 46-5, 17. 



Taking the mean of these closely concordant results with B, 

 we have : — 



B x 218-00, 62-00. 



B 2 140-50, 102-50, 37-00. 



B 3 99-00, 80-75, 73-50, 26-75. 



B 4 77-00, 62-50, 63-00, 57-00, 20-50. 



B 5 62-30, 51-45, 51-40, 51-60, 46-50, 16*75. 



Two generalizations are at once manifest : — i. All the seg- 

 ments are equal except the first, second, and last. So that if 

 there are four segments, they are all unequal ; if there are 

 five, the third and fourth are equal ; if there are n segments, 

 the third, fourth, &c. up ton — 1 are equal, ii. It is seen that 

 the first and second segments are together equal to the last. 

 From the latter generalization it of course follows that when 



