428 REPORT— 1869. 



must be half that required to travel over part 1 in fig. 16, and the length of 

 part 1 in fig. 17 must be half that of part 1 in fig. 16. 



But the respective collars (B B') must have their weights put into motion 

 with these velocities, so that the weight B' has to move through half of the 

 space that B has to move through, and has to do it in half the time ; but to 

 move a weight through half the space that another weight is moved through, 

 and in half the time occupied by that other weight, requires double the 

 pressure ; therefore it would take double the pressure to move B' that it 

 would to move B, even if B and B' were equal in weight ; but B' is four 

 times the weight of B, therefore it will take eight times the pressure to 

 move B' that it will take to move B, and in this case also the eight times 

 the strain has to be put on by the single spring E, which thus gets eight times 

 as much strain as the spring D. 



The fourth proposition has now to be considered, namely, that abrupt 

 change of form is a cause of weakness when vibratory action has to be 

 endured. 



A.S already stated, this cause is the one that has been most recognized by 

 those who have touched upon the question. 



The writer will not pretend to investigate what the value of this source 

 of weakness is, as no means suggest themselves to his mind for doing so ; 

 it may, however, fairly be assumed that the times of vibration in the 

 large section part of the bar will be different from those in the small, and 

 that at a point where the change of shape occurs there must be a discord in 

 the vibrations, and that thus the metal in this part must be exposed to 

 strains which would not occur were the vibrations on the two sides this point 

 synchronous. 



Propositions 2 and 3 have been dealt with as though the increased strains 

 brought upon the small sections by their neighbourhood to the large sections 

 were uniformly distiibutcd over the small sections, which have, for sim- 

 plicity sake, been assumed to be composed of single springs. 



But had these small sections been dealt with as being in themselves com- 

 posed of several smaller springs, as was done in considering the cases of 

 figs. 9 and 10, then it would have been found that the outer parts of those 

 small sections were doing more than their share of the increased work, and 

 therefore the evils arising from increased section, which have been treated 

 of in propositions 2 and 3, must be multiplied by the evils due to the abrupt 

 change of form considered in proposition 1. 



The kind of fracture shown in end view in Plate III. fig. 3 a, namely, a frac- 

 ture which begins all round about the outside and gradually penetrates, is an 

 abundant practical proof that not only are strains arising from impact in- 

 creased on part of a small section by the neighbourhood of larger sections 

 abruptly joining on to the smaller ones, but that the increase is borne in an 

 undue proportion (as was shown in the case of quiescent weights) by the 

 outer particles of the small section at the part where they abruptly join on 

 to the larger section. 



So far this paper has dealt with the e\\\ influence of sudden change of 

 form when it is to be found in a suspended rod or in other positions where 

 the influences act in the direction of the length of the object under consider- 

 ation. In practice, the bolts which hold on armour-plating are instances to 

 which the foregoing considerations are applicable, us such bolts receive in the 

 direction of their length the quiescent strain, and also that arising from the 

 impact of the recoil of the armour-plating after it has been struck by the shot. 



It may be well to al'ude to the fiict that Major Palliser has overcome 



