2°) The second journey to Cajaneborg (1769)

Planman returned at Cajaneborg to observe the next transit of Venus on 1769 June 3. For his observation he applied the 21-feet telescope combined with a 2.9-inch eyepiece, giving a power of about 250 x. Among his other instruments were a 3-feet achromatic telescope with a power of 40 x, a 6-feet telescope and an accurate timepiece by Ernst, which ran quite regularly, even when temperatures varied. The transit of Venus would commence shortly before sunset on June 3, but because of the short summer nights at this northern latitude, egress would be visible well after sunrise, the next morning.

Cajaneborg experienced a dull summer. On the day of the transit, the sky was completely overcast from 10 a.m. to 8 p.m., preventing Planman to even catch a glimpse of the sun. Then, just in time, the low sun peeped out from behind the clouds, for first contact would be just after 9 p.m. At 9h 8m 37s Planman discerned the pitch-black outline of Venus when it had entered the sun’s disk for about one third of its diameter. Despite the heavy boiling of the limbs, Planman was able to determine the time of inner contact fairly accurate. At 9h 20m 45s the black ligament between Venus’ and the sun’s limbs vanished and a thread of light became visible between them. Then, the setting sun was blotted out again by clouds, leaving Planman in a state of suspense whether he would meet Venus on the sun again next morning, or not.

Bad luck was with Planman, for after sunrise on June 4 the sun’s disk became visible only when Venus had already been in contact with the sun’s limb for the third time. At 3h 20m 46s he could see just two third of Venus silhouette left on the sun and at 3h 32m 27s the last dent of Venus in the sun’s disk disappeared. A friend of Planman, local postmaster Uhlwyk, joined the Swedish astronomer in observing last contact. Uhlwyk, who had already some experience in astronomical observing, had the 3-feet instrument placed at his disposal, with a reddish glass fitted on to the eyepiece in order to reduce the morning sun’s glare. He thus attributed 3h 32m 24s to last contact, which agreed very well with Planman’s observation.

Yet, they had still some astronomy to do on June 4, because from about 9 to 11 a.m. the sun would be partially eclipsed! According to Planman, observing with the 3-feet telescope, the eclipse started at 9h 0m 53 s and ended at 11h 0m 0s. Uhlwyk, still joining Planman and observing with the 6-feet telescope, found these times to be 9h 1m 8s and 10h 59m 59s respectively. During the eclipse, Planman continuously measured the distances between the sun’s and moon’s limbs with a micrometer. He thus found that the magnitude of the partial solar eclipse was about 0.42. Deriving the sun’s distance





Using the observations of the transit of Venus, the sun’s distance from the earth could be accurately established. In 1716 famous English astronomer Edmond Halley showed how such calculations could be performed. Owing to the effects of parallax, the ingress and egress as seen from a point on the surface of the earth would appear a little earlier or later than when viewed from the centre of the earth. As a result, the apparent stay of Venus on the sun’s disc would vary according to an observer’s location. Therefore, if the transit of Venus was seen from two distant places, the observed durations between the interior contacts would differ from each other by a sensible amount of time. The difference between the durations could theoretically be obtained by assuming a certain known quantity for the parallax of the sun. If this difference was found to be greater or less by observation, then, according to Halley, the sun’s parallax would be greater or less in the same proportion.

After the 1761 transit of Venus, Anders Planman was engaged with the computation of the difference between the durations, based on an assumed value of the solar parallax. He applied an ingenious and original geometrical method to over thirty measurements from fourteen different locations, among which were of course his own from Cajaneborg. Using Halley’s method of durations, Planman ultimately arrived at an value of the solar parallax of 8.2 seconds of arc, corresponding to a sun’s distance of 160.4 million kilometres.

If we compare the present value of the solar parallax, 8.794 seconds of arc, to the result of Planman’s analysis, it looks like if Planman’s value is too low. However, we have to bear in mind that the accuracy of his calculations chiefly depended on uncertain observations and inaccurate astronomical tables.


Acknowledgments

I am very grateful to Eva Isaksson, Tapio Markkanen and Erkki Urpilainen for providing valuable information on Anders Planman.