On the total annual heat received at each point of the Earth's surface from the Sun : and on the amount of the loss of that heat caused by radiation into space (neglecting the effect of the atmosphere) / by Samuel Haughton.

  • Haughton, Samuel.
Date:
[1878?]
Catalogue details

Licence: Public Domain Mark

Credit: On the total annual heat received at each point of the Earth's surface from the Sun : and on the amount of the loss of that heat caused by radiation into space (neglecting the effect of the atmosphere) / by Samuel Haughton. Source: Wellcome Collection.

Provider: This material has been provided by The Royal College of Surgeons of England. The original may be consulted at The Royal College of Surgeons of England.

    5/12 (page 3)
    Or, since where sin Z = sin A sin 1. A = obliquity of ecliptic, I = sun’s longitude, - sin \ sin A • sin I ■A + cos X |l—4(1 - cos 21) - - 4 cos 21 + cos it) sin®A TIT b4 (10 - 15 cos 2/ + 6 cos 4^—cos 6^) - &c. • tanX sin X 0^^ - cos2^) + - 4 cos2Z + cos4^) + (4 32 3 sin®A ~M2 >(11) (10 - 4 cos 2/ + 6 cos 4^—QOS 6^) + &c. + tan^X sin X i^^^!-^(3 — 4 cos2^ + cos4il) + ?^^-^(10-<kc.)+&c. V 1^ 12 + tan®X sin X i^^^^-^(10 — &c.) 4 &c. (2ob0^ + &c. We must now substitute for I the sun’s longitude, on each day of the year, and add the 365 terms together; this will convert all the periodic terms of (11) into the sums of sines and cosines of arcs in arithmetical progression taken all round the circumference, and with a very small common difference * The periodic terms, therefore, vanish in the summation, and we obtain. The heat received in one year = 2A sin XS sin S(//—tan R) = 2A X 365'25 cosX ii-!i sin^A 3 sin‘*A 5 sin®A 4- tan X smX 4- tan-’*X sin X 4 -64 ^ 256 (sin^A 3 siii^A 15 sin® A 4- • ( 4 ' 32 (sin^A 5 sin®A ( 64 256 4- 256 4- &C. 4- ifec. + tan®X sin X |-1^ ^ 4- &c. ( 256 + &C., &c. Substituting for A its value, 23° 28', we obtain, finally, K12) Equal to 59' 8 (the daily change in sun’s longitude), or small multiples of that arc.