ON THE PERIODS AND NODES OF LOCHS EARN AND TREIG. 827 
We may take the mean of these (H.T.S. § 35) as a first approximation, viz., T,= 
15°15’. A few rough trials shew that T, is very near to 14°5’. Taking this as a basis, 
and using the table of H.T.S. § 38, we get the following table :— 
ity I, Ate 
Parabolic : : ; 14°5 8°33 5-91 
Semiparabolic . : : 14°5 7:94 5°48 
Means : ie ‘ 14:5 8:13 5°69 
We therefore take T,;=14°5, T,=8'1, and T,=57 as first approximations in our 
more rigorous calculations. 
§ 6. The most logical procedure would be to calculate the value of ¢ (or c’ ) from the 
‘ ti 
ee x(c)=K(e, 1)+pK(c’, 1)=0 ; ‘ ; i ; (6) ; 
and deduce the value of T from the equation 
T = 27a/,/(egh) , . . : : . ‘ (i): 
Seeing, however, that good first approximations to T are known, it is convenient to 
assume values of T; calculate the corresponding values of c and c’ by means of the 
é 
oo e=4ra7/giT?, « =4ra%/ghT?; . : . : s . (8); 
then calculate the corresponding values of x(c); and finally find the value of T corre- 
sponding to the root c, by interpolation. 
The following tables give the principal elements of the calculation. The letters 
used have the same meanings as in H.'T.S. §§ 25 and 39. 
§ 7. UninopaL Prriop oF Harn. 
T c a 4(5 +a) 4(5 — a) 1(3 +a) (3 - a) K(c, 1) 
14:4 36284 3°9383 2°2346 2654 1°7346 — *2346 — 1°62507 
14:5 3°5785 3°9133 2°2283 CALA 1:7283 - 2283 — 154970 
146 | 35297 | 38883 D231 2779 17221 2) — 1:47850 
T e a H5+a) | 5-a') | 4(8+a’) 4(3 — 2) K(“, 1) 
14:4 7353 19853 1.7463 ‘7537 1:2463 2537 69215 
145 ‘7252 19750 17438 ‘7563 12438 2563 69685 
14°6 7153 19650 17412 TST 1:2412 "2587 ‘70105 
