It was not long before it became an established custom that a candidate, who was dissatisfied with the class in which he had been placed as the result of his disputations, might challenge it before the examination began. This power seems to have been used but rarely; it was, however, a recognition of the fact that a place in the tripos list was to be determined by the senate-house examination alone, and the examiners soon acquired the habit of settling the preliminary classes without exclusive reference to the previous disputations. The earliest extant paper actually set in the senate-house, to which we can with certainty refer, is a problem paper set in 1785 or 1786 by W. Hodson, of Trinity, then a proctor. The autograph copy from which he gave out the questions was luckily preserved, and is in the library[50] of Trinity College. It must be almost the last problem paper which was dictated, instead of being printed and given as a whole to the candidates. The paper is as follows: 1. To determine the velocity with which a Body must be thrown, in a direction parallel to the Horizon, so as to become a secondary planet to the Earth; as also to describe a parabola, and never return. 2. To demonstrate, supposing the force to vary as _1/D²_ how far a body must fall both within and without the Circle to acquire the Velocity with which a body revolves in a Circle. 3. Suppose a body to be turned (_sic_) upwards with the Velocity with which it revolves in an Ellipse, how high will it ascend? The same is asked supposing it to move in a parabola. 4. Suppose a force varying first as _1/D³_, secondly in a greater ratio than _1/D²_ but less than _1/D³_, and thirdly in a less ratio than _1/D²_, in each of these Cases to determine whether at all, and where the body parting from the higher Apsid will come to the lower. 5. To determine in what situation of the moon's Apsid they go most forwards, and in what situation of her Nodes the Nodes go most backwards, and why? 6. In the cubic equation _x³ + qx + r = 0_ which wants the second term; supposing _x = a + b_ and _3ab = -q_, to determine the value of _x_. (_sic._) 7. To find the fluxion of _x^r × (y^n + z^m)^{1/q}_. 8. To find the fluent of _aẋ / (a + x)_. 9. To find the fluxion of the _m_^th power of the Logarithm of _x_. 10. Of right-angled Triangles containing a given Area to find that whereof the sum of the two legs _AB + BC_ shall be the least possible. [This and the two following questions are illustrated by diagrams. The angle at _B_ is the right angle.] 11. To find the Surface of the Cone _ABC_. [The cone is a right one on a circular base.] 12. To rectify the arc _DB_ of the semicircle _DBV_.