734 Prof. H. C. Plummer on the 



This is the first approximation to the integrand in (2) 

 when the first order in p is retained, and the result of 

 integration is 



s — s =O[tan#-fp{^ sec 3 6— sec 6 



+ tan log tan (Jit + £0)}]. . . (4) 



4. Captain Hollingworth's equation XIL, which corre- 

 sponds with (4), is a very mixed approximation. It contains 

 a further error in the deduction from X., which can be 

 amended by substituting (2 — 'dp)/^/p for the factor (1 — 3/>) 

 in the second line. Then by developing the corrected form 

 of XII. to the first power in p, or much more simply by 

 applying the same process to X. and afterwards integrating;, 

 it is found that 



5- s o = C[tan0-!-£>(^sec 3 + sec 0)], 



thp discrepancy from (4) being due to the error in X. 



5. The constant employed here is not at all the same as 

 Captain Hollingworth's constant C. In accordance with (3), 

 if W is the suspended weight and the air resistance on it b^ 

 neglected (which can never he strictly right), so that = 

 at the end of the wire, 



W = CKi- 2 (tan«r 2c032a . .... (5) 



There are two compensating errors in the deduction of 

 XI. from X. Apart from this, W/Kr 2 must be a constant 

 slightly in excess of the true one. Since the tables on 

 pp. 460-461 and the corresponding fig. 1 depend on the 

 equation X., they cannot be correct. In lig. 2 the description 

 of the full and broken curves is at variance with that given 

 in the text and is presumably inverted. The resemblance 

 between the results of calculation and observation is probably 

 due to the predominance of the common catenary, which is 

 the lowest approximation. If so, it suggests that the total 

 neglect of the weight of the wire may be justified, at least 

 in the application to practical circumstances in which the 

 condition of uniform horizontal flying will seldom be 

 accurately maintained. The effect is obtained by making 

 p = 0, a. = 45°, and the tension constant. 



6. According to (3) above, the radius of curvature and 

 the tension both become infinite when sin = cot ex.. But 

 the tension supports the attached weight and only part of 

 the weight of the wire, the latter being partly supported by 



